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[[Image:Splash-fdtd.jpg|right|800px720px]]<strong><font color="#961717" size="4">Fast Multi-Core And Multicore & GPU-Accelerated FDTD Solvers For Tackling The for Simulating the Most Complex Electromagnetic Modeling Problems</font></strong><table><tr><td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]]</td><tr></table>[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Tempo_Documentation | EM.Tempo Tutorial Gateway]]''' [[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''
==Product Overview==
=== EM.Tempo in a Nutshell ===
EM.Tempo is a powerful time-domain electromagnetic simulator for full-wave modeling of 3D radiation, scattering and propagation problems. It features a highly efficient Finite Difference Time Domain (FDTD) simulation engine that has been optimized for speed and memory usage. EM.Tempo brings to your desktop the ultimate in computational power. Its FDTD solver has been parallelized to take full advantage of multi-core processor architectures. With a large variety of geometrical, material and excitation features including open-boundary and periodic structures, you can use EM.Tempo as a general purpose 3D field simulator for most of your electromagnetic modeling needs. EM.Tempo's new advanced simulation capabilities are your the key to the a thorough understanding of wave the interaction in of electromagnetic waves with complex media such as anisotropic composites, metamaterials or biological environmentsor with passive and active devices and nonlinear circuits.
EM.Tempo is the outcome of evolution of our older FDTD simulation tool, EM.Lounge, first introduced has undergone several evolutionary development cycles since its inception in 2004. The original simulation code engine utilized an FDTD formulation based on the uniaxial perfectly matched layer (UPML) boundary termination. Through subsequent expansionsSubsequently, a far superior more advanced boundary termination based on the convolutional perfectly matched layer (CPML) was implemented, which performs impeccably with a far superior performance for all oblique wave incidences in different types of media. EM.Tempo now has the ability to model laterally infinite layered structures as well as using CPML walls that touch material media. A novel formulation of periodic boundary conditions with oblique plane wave incidenceswas implemented based on the constant transverse wavenumber method (or direct spectral FDTD). In 2013 we introduced an Open-MP optimized multi-core version of the FDTD engine as well as a hardware-accelerated versions solver that runs on CUDA-enabled graphical processing unit (GPU) platforms. Both of these fast solvers are now a standard part of the EM.Tempo Pro package.
[[Image:Info_icon.png|40px30px]] Click here to access for an overview of the '''[[EMBasic Principles of The Finite Difference Time Domain Method | Basic FDTD Theory]]'''.Cube#EM <table><tr><td>[[Image:ART GOLF Fig title.Tempo_Tutorial_Lessons png| thumb|left|400px| The 3D far-field radiation pattern of a vehicle-mounted antenna structure simulated by EM.Tempo Tutorial Gateway.]]'''.</td></tr></table>
=== EM.Tempo as the FDTD Module of EM.Cube ===
[[Image:Info_icon.png|40px30px]] Click here to learn more about '''[[Getting_Started_with_EM.CUBE Cube | EM.Cube Modeling Environment]]'''.
=== The Advantages & Limitations of EM.Tempo's FDTD Simulator === A time domain simulation like FDTD offers several advantages over frequency domain simulations. In certain applications, the time domain signature or behavior of a system, e.g. the transient response of a circuit or an antenna, is sought. In other applications, you may need to determine the wideband frequency response of a system. In such cases, using a frequency domain technique, you have to run the simulation engine many times to adequately sample the specified frequency range. In contrast, using the FDTD method requires a single-run simulation. The temporal field data are transformed into the Fourier domain to obtain the wideband frequency response of the simulated system. Among other advantages of the FDTD method are its versatility in handling complex material compositions as well as its superb numerical stability. It is worth noting that unlike most frequency domain methods, the FDTD technique does not involve numerical solution of large ill-conditioned matrix equations that are often very sensitive to the mesh quality. Like every numerical technique, the FDTD method has disadvantages, too. Adding the fourth dimension, time, to the computations increases the size of the numerical problem significantly. Unfortunately, this translates to both larger memory usage and longer computation times. Note that the field data are generated in both the 3D space and time. EM.Tempo uses a staircase "Yee" mesh to discretize the physical structure. This works perfectly fine for rectangular objects that are oriented along the three principal axes. In the case of highly curved structures or slanted surfaces and lines, however, this may compromise the geometrical fidelity of your structure. EM.Tempo provides a default adaptive FDTD mesher that can capture the fine details of geometric contours, slanted thin layers, surfaces, etc. to arbitrary precision. However, with smaller mesh cells, the stability criterion leads to smaller time steps; hence, longer computation times. Another disadvantage of the FDTD technique compared to naturally open-boundary methods like the method of moments (MoM) is its finite-extent computational domain. This means that to model open boundary problems like radiation or scattering, absorbing boundary conditions are needed to dissipate the incident waves at the walls of the computational domain and prevent them from reflecting back into the domain. The accuracy of the FDTD simulation results depends on the quality of these absorbers and their distance from the actual physical structure. EM.Tempo provides high quality perfectly matched layer (PML) terminations at the boundaries, which can be placed fairly close to your physical structure to reduce the total size of the computational domain. <table><tr><td>[[Image:Info_iconAirplane Mesh.png|40px]] Click here to learn more about the basic functionality thumb|left|480px|The Yee mesh of '''[[CubeCADan imported aircraft CAD model.]]'''.</td></tr></table>
== EM.Tempo Features at a Glance ==
=== Sources, Loads & Ports Physical Structure Definition ===
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Uniaxial and fully anisotropic materials with four complete constitutive tensors</li> <li> Dispersive materials of Debye, Drude and Lorentz types with arbitrary number of poles</li> <li> Generalized uniaxial and doubly negative refractive index metamaterials with arbitrary numbers of both electric and magnetic poles</li> <li> Two types of gyrotropic materials: ferrites and magnetoplasmas</li> <li> PEC, PMC and convolutional perfectly match layer (CPML) boundary conditions</li> <li> Doubly periodic structures</li></ul> === Sources, Ports & Devices === <ul> <li> Lumped voltage sources with internal resistance placed on a PEC line or thin wire object with an arbitrary orientation</li> <li> Distributed sources with uniform, sinusoidal and edge-singular profiles</li> <li> Microstrip, coplanar Waveguide (CPW) and coaxial ports</li> <li> Waveguide sources with the dominant TE<sub>10</sub> modal profile in hollow rectangular boxes</li>
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Multi-port and coupled port definitions</li>
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Two types of filamentary current sources: Hertzian short dipole radiators with arbitrary orientation and long wire current sources aligned along one of the principal axes with a uniform, triangular or sinusoidal current distribution profile</li>
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Plane wave excitation with linear and circular polarizations</li>
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Multi-ray excitation capability (ray data imported from [[Propagation ModuleEM.Terrano]] or external files)</li>
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Gaussian beam excitation</li>
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Source arrays with weight distribution & phase progression</li>
Standard excitation waveforms (Gaussian pulse, modulated Gaussian and sinusoidal) for optimal frequency domain computations </li>
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Arbitrary user-defined temporal excitation waveforms using mathematical expressionsand Python functions</li> <li> Passive lumped devices: R, L, C, series RL and parallel RC and nonlinear diode device</li> <li> Active lumped one-port and two-port devices placed on PEC lines aligned along one of the principal axes with arbitrary Netlist definitions</li> <li> Active distributed one-port and two-port devices placed under microstrip lines with arbitrary Netlist definitions</li>
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=== Mesh Generation ===
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Geometry-aware and material-aware adaptive mesh generator with gradual grid transitions</li>
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Fixed-cell uniform mesh generator with three unequal cell dimensions</li> <li> Mesh view with mesh three principal grid profilerprofilers</li>
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Manual control of mesh parameters and fixed grid points</li>
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OpenMP-parallelized multi-core and multi-thread FDTD simulation engine</li>
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GPU-accelerated FDTD simulation engine based on NVIDIA CUDA platforms</li>
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Total-field-scattered-field analysis of plane wave and Gaussian beam excitation</li>
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Infinite material half-space Green's functions for calculation of far fields in presence of a lossy ground</li>
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Accelerated computation of S-parameters of resonant structures based on Prony's method of exponential interpolation</li>
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Parametric sweeps of variable object properties or source parameters including frequency and angular sweeps</li>
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Multi-variable and multi-goal optimization of structurestructures</li>
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Near -field intensity (colorgrid), contour and surface plots (vectorial - amplitude & phase)</li>
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Near -field probes for monitoring fields field components in both time & frequency domains</li>
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Far -field radiation patterns: 3-D 3D pattern visualization and 2-D 2D polar and Cartesian graphs</li>
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Far -field characteristics such as directivity, beam width, axial ratio, side lobe levels and null parameters, etc.</li>
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Radiation pattern of arbitrary array configurations of the FDTD structure or periodic unit cell</li>
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Bistatic and monostatic radar cross section</li>
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Huygens surface data generation for use in other [[EM.Cube]] modules</li> <li> Periodic reflection/transmission coefficients and k-ßbeta; diagrams</li>
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Port characteristics: S/Y/Z parameters, VSWR and Smith chart</li>
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Animation of temporal evolution of fields</li>
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Custom output parameters defined as mathematical expressions or Python functions of standard outputs</li>
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==An FDTD Simulation Primer Building the Physical Structure in EM.Tempo ==
=== An Overview of FDTD Modeling Material Variety in EM.Tempo ===
{| class="wikitable"|-! scope="col"| Icon! scope="col"| Material Type! scope="col"| Applications! scope="col"| Geometric Object Types Allowed|-| style="width:30px;" | [[ImageFile:Info_iconpec_group_icon.png]]|40pxstyle="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Perfect Electric Conductor (PEC) |Perfect Electric Conductor (PEC)]] Click here for an overview | style="width:300px;" | Modeling perfect metals| style="width:250px;" | Solid, surface and curve objects|-| style="width:30px;" | [[File:thin_group_icon.png]]| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Thin Wire |Thin Wire]]| style="width:300px;" | Modeling wire radiators| style="width:250px;" | Lines parallel to one of '''the three principal axes|-| style="width:30px;" | [[Basic_FDTD_Theory File:pmc_group_icon.png]]| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Perfect Magnetic Conductor (PMC) | Basic FDTD TheoryPerfect Magnetic Conductor (PMC)]]'''| style="width:300px;" | Modeling perfect magnetic sheets | style="width:250px;" | Rectangle strips parallel to one of the three principal planes|-| style="width:30px;" | [[File:diel_group_icon.png]]| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Dielectric Material |Dielectric Material]]| style="width:300px;" | Modeling any homogeneous material| style="width:250px;" | Solid objects|-| style="width:30px;" | [[File:aniso_group_icon.png]]| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Anisotropic Material |Anisotropic Material]]| style="width:300px;" | Modeling unaxial or generalized anisotriopic materials| style="width:250px;" | Solid objects|-| style="width:30px;" | [[File:disp_group_icon.png]]| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Dispersive Material |Dispersive Material]]| style="width:300px;" | Modeling Debye, Drude and Lorentz materials and generalized metamaterials | style="width:250px;" | Solid objects|-| style="width:30px;" | [[File:voxel_group_icon.png]]| style="width:150px;" | [[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Gyrotropic_Material |Gyrotropic Material]]| style="width:300px;" | Modeling ferrites and magnetoplasmas| style="width:250px;" | Solid objects|-| style="width:30px;" | [[File:Virt_group_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]| style="width:300px;" | Used for representing non-physical items | style="width:250px;" | All types of objects|}
==Building the Physical Structure= Material Hierarchy in EM.Tempo ===
[[Image:FDTD1.png|thumb|250px|[[FDTD Module]]'s Navigation Tree.]]In EM.Tempo, a physical structure consists of sets of objects that are grouped together and identified by their material types. All the objects belonging to the same material group share the same color and same material properties. Materials are divided into seven categories that are listed under the '''Physical Structure''' node at the top of the navigation tree (click on each type to learn more about it): * '''[[Defining_Materials_in_EM.Cube#Perfect_Electric_Conductors_.26_Metal_Traces |Perfect Electric Conductor (PEC) Objects]]'''* '''[[Defining_Materials_in_EM.Cube#Perfect_Magnetic_Conductors_.26_Slot_Traces |Perfect Magnetic Conductor (PMC) Planes]]'''* '''[[Defining_Materials_in_EM.Cube#Defining_Dielectric_Materials |Dielectric Materials]]'''* '''[[Defining_Materials_in_EM.Cube#Anisotropic_Materials |Anisotropic Materials]]'''* '''[[Defining_Materials_in_EM.Cube#Dispersive_Materials |Dispersive Materials]]'''* '''[[Defining_Materials_in_EM.Cube#Inhomogeneous_Materials |Inhomogeneous Materials]]'''* '''[[Defining_Materials_in_EM.Cube#Thin_Wires |Thin Wires]]''' Under each material node, you can create new material groups of the same type/category but with different properties (color, texture, or electric and magnetic constitutive [[parameters]]). These material groups are used to organize the CAD objects you draw in the project workspace or import from external model files. [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Defining_Materials_in_EM.Cube#Defining_a_New_Material_Group | Defining a New Material Group]]'''. Once a new material node has been created on the navigation tree, it becomes the "Active" material group of the project workspace, which is always listed in bold letters. When you draw a new CAD object such as a Box or a Sphere, it is inserted under the currently active material type. There is only one material group that is active at any time. Any material can be made active by right clicking on its name in the Navigation Tree and selecting the '''Activate''' item of the contextual menu. It is recommended that you first create material groups, and then draw new objects under the active material group. However, if you start a new EM.Tempo project from scratch, and start drawing a new object without having previously defined any material groups, a new default PEC group is created and added to the navigation tree to hold your new CAD object. [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Defining_Materials_in_EM.Cube#Moving_Objects_among_Material_Groups | Moving Objects among Material Groups]]'''. {{Note|You can import external objects only to '''[[CubeCAD]]'''. You can then move the imported objects form [[CubeCAD]] to EM.Tempo.}} [[Image:Info_icon.png|40px]] Click here for a general discussion of '''[[Defining Materials in EM.Cube]]'''. ===Geometrical Rules & Material Hierarchy=== [[Image:fdtd14_tn.png|thumb|320px|Geometric construction of a dielectric-coated metallic cylinder.]]The following rules apply to the definition of materials and objects in EM.Tempo: * Under the PEC category, you can define all types of solid, and surface and curve CAD objects.* Under the PMC category, you can define only define rectangle strip objects parallel to the principal planes. * Under the Dielectric, Anisotropic and Dispersive material categories, you can define only solid CAD objects.* Under the Inhomogeneous Material category, you can only import a Cartesian ".CAR" data file.* Under the Thin Wire category, you can only define line objects parallel to the principal axes. EM.Tempo allows overlapping objects, although it is generally recommended that object overlaps be avoided in favor of clearly defined geometries and object boundaries. If two or more objects of the same material type and group overlap, they are merged using the Boolean union operation during the mesh generation process. If two overlapping objects belong to two different material categories, then the material properties of the FDTD cells in the overlap region will follow the [[EM.Tempo]]'s material hierarchy rule. In that case, the overlap area cells will always be regarded as having the material type of the higher priority. According to this rule, the material types are ordered from the highest priority to the lowest in the following manner:
# PEC
# PMC
# Dispersive
# Gyrotropic
# General Anisotropic
# Uniaxial Anisotropic
# Dielectric
If planned carefully, taking advantage of [[EM.Tempo]]'s material hierarchy rule would make the construction of complex objects easier. For example, a dielectric coated metallic cylinder can be modeled by two concentric cylinders: an inner PEC of smaller radius and an outer dielectric of larger radius as shown in the illustration below. The portion of the dielectric cylinder that overlaps the inner PEC cylinder is ignored by the FDTD engine because the PEC cylinder takes precedence over the dielectric in the material hierarchy. Alternatively, you can model the same structure by an inner solid PEC cylinder enclosed by an outer hollow pipe-shaped dielectric cylinder. <table><tr><td> [[Image:FDTD_MAN2.png|thumb|left|360px|The geometric construction of a dielectric-coated metallic cylinder with a conformal foil.]]</td></tr></table> === Moving Objects Among Different Material Groups or EM.Cube Modules === You can move any geometric object or a selection of objects from one material group to another. You can also transfer objects among [[EM.Cube]]'s different modules. For example, you often need to move imported CAD models from CubeCAD to [[EM.Tempo]]. To transfer objects, first select them in the project workspace or select their names in the navigation tree. Then right-click on them and select <b>Move To → Module Name → Object Group</b> from the contextual menu. For example, if you want to move a selected object to a material group called "Dielectric_1" in [[EM.Tempo]], then you have to select the menu item '''Move To → [[EM.Tempo]] → Dielectric_1''' as shown in the figure below. Note that you can transfer several objects altogether using the keyboards's {{key|Ctrl}} or {{key|Shift}} keys to make multiple selections. <table><tr><td>[[Image:Tempo_L11_Fig2.png|thumb|left|720px|Moving an imported object from CubeCAD to EM.Tempo.]]</td></tr></table>
==Setting EM.Tempo's Computational Domain & Boundary Conditions==
===The FDTD Solution Domain===
The FDTD method requires a finite-extent solution domain. This is rather straightforward for shielded structures, where a typical PEC enclosure box defines the computational domain. For open-boundary structures like antennas and scatterers, the computational domain must be truncated using appropriate termination boundary conditions. The objective of termination boundary conditions is to eliminate the reflections from the walls of the domain box back to the computational domain.
In [[EM.Tempo]], you can define two types of domain box. A "'''Default'''" -type domain is a box that is placed at a specified offset distance from the largest extents of your physical structure (global bounding box). The offset is specified in free-space wavelengths. A "'''Custom'''" -type domain, on the other hand, is defined as a fixed-size and fixed-location box in the World Coordinate System (WCS). In this case, you have to specify the coordinates of the lower left front corner (Corner 1) and upper right back corner (Corner 2) of the domain box.
When you start a new project in [[EM.Tempo]], a default-type domain is automatically created with a default offset value set equal to a quarter free-space wavelength (0.25λ<sub>0</sub>). As soon as you draw your first object, a blue domain box shows up in the project workspace and encloses your object. As you add more objects and increase the overall size of your structure, the domain box grows accordingly to encompass your entire physical structure. When you delete objects from the project workspace, the domain box also shrinks accordingly.
===Changing the Domain Settings===
To set the solution domain of your FDTD project, follow these steps:
* Click the '''Domain''' [[Image:domain_icon.png]] button of the '''Simulate ''' Toolbar or select the menu item '''Menu > Simulate > → Computational Domain > → Domain Settings...''' or right click on the '''FDTD Domain''' item of the Navigation Tree and select '''Domain Settings...''' from the contextual menu, or use the keyboard shortcut '''Ctrl+A'''. The Domain Settings Dialog opens up, showing the current domain type selection.
* Select one of the two options for '''Domain Type'''<nowiki>: </nowiki>'''Default''' or '''Custom'''.
* If you select the "Default" domain type, the domain box is defined in terms of the offsets along the X, Y and Z directions from the largest extents of your physical structure. Select one of the two options for '''Offset Units: Grid''' and '''Wavelength'''. In the section titled '''"Domain Size"''', enter the amount of domain extension beyond the largest extents of the structure along the ±X, ±Y and ±Z directions. Note that in the case of a default-type domain box, the offset values based on your current project settings (frequency and units).
By default, the domain box is shown as a wireframe box with blue lines. You can change the color of the domain box or hide it.
[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Domain_Settings | Domain Settings]]'''.
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[[Image:FDTD14.png|thumb|left|480px|EM.Tempo's domain settings dialog.]]
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===Settings the Domain Boundary Conditions===
[[Image:FDTD13EM.png|thumb|300px|[[FDTD ModuleTempo]]'s Boundary Conditions dialog]]EM.Tempo supports four types of domain boundary conditions: PEC, PMC, Convolutional Perfectly Matched Layers (CPML) and Periodic Boundary Conditions (PBC). By default, all the six sides of the computational domain box are set to CPML, representing a completely open-boundary structure. Different boundary conditions can be assigned to each of the six walls of the domain box. The periodic boundary conditions are special ones that are assigned through [[EM.Tempo]]'s Periodicity Dialog and will be discussed later under modeling of periodic structures. The current release of [[EM.Cube]] allows periodic boundary conditions only on the side walls of the computational domain, and not on the top or bottom walls.
To define the boundary conditions of the solution domain, follow these steps:
* Select the menu item '''Menu > Simulate > → Computational Domain > → Boundary Conditions''' or right click on the '''Boundary Conditions''' item in the '''Computational Domain''' section of the Navigation Tree and select '''Boundary Conditions...''' from the contextual menu. The Boundary Conditions Dialog opens.
* You need to assign the type of boundary condition on each of the six domain boundaries: ±X, ±Y and ±Z. For each face, choose one of the three options available: '''PEC''', '''PMC '''or '''PML'''.
The PEC and PMC boundary conditions are the most straightforward to set up and use. Assigning the PEC boundary to one of the bounding walls of the solution domain simply forces the tangential component of the electric field to vanish at all points along that wall. Similarly, assigning the PMC boundary to one of the bounding walls of the solution domain forces the tangential component of the magnetic field to vanish at all points along that wall. For planar structures with a conductor-backed substrate, you can use the PEC boundary condition to designate the bottom of the substrate (the -Z Domain Wall) as a PEC ground. For shielded waveguide structures, you can designate all the lateral walls as PEC. Similarly to model shielded cavity resonators, you designate all the six walls as PEC.
{{Note|[[EM.Tempo]]'s default quarter wavelength offset for the domain box and its 8-layer CPML walls are very conservative choices and can be relaxed in many cases. An offset equal to eight free-space grid cells beyond the largest bounding box usually gives a more compact, but still valid, domain box.}} [[Image:Info_icon.png|40px30px]] Click here to learn more about the theory of '''[[Basic_FDTD_TheoryBasic_Principles_of_The_Finite_Difference_Time_Domain_Method#Why_Does_FDTD_Need_Domain_TerminationCPML_vs.3F _PML | Perfectly Matched Layer Termination]]'''.
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<td> [[Image:fdtd_manual-11FDTD MAN10.png|thumb|400pxleft|360px|The boundary ABC CPML cells placed outside the visible domain box.]] </td><td> [[Image:FDTD15.png|thumb|left|400px|CPML Settings dialog.]] </td>
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You can use EM.Tempo to model planar structures of infinite extents. A planar substrate usually consists of one or more dielectric layers, possibly with a PEC ground plane at its bottom. To model a laterally infinite dielectric substrate, you must assign a PML boundary condition to the four lateral sides of the domain box and set the lateral domain offset values along the ±X and ±Y directions all equal to zero. If the planar structure ends in an infinite dielectric half-space from the bottom, you must assign a PML boundary condition to the bottom side of the domain box and set the -Z offset equal to zero. This leaves only the +Z offset with a nonzero value.
When a domain boundary wall is designated as CPML and its has a zero domain offset, meaning it touches a material block, the CPML cells outside the domain wall are reflected back inside the computational domain. In other words, the effective number of CPML layers will be twice the one specified in the CPML Settings dialog. This will effectively extend the material block infinitely beyond the boundary wall and will create an open boundary effect in the specified direction. It goes without saying that only "substrate" objects are supposed to touch the boundary walls in such a scenario. Because of the rolled-back CPML cells inside the domain, it is very important to make sure that other finite-sized parts and objects stay clear from the domain walls as well as from the invisible "interior" CPML cells. {{Note|The current release of [[EM.Tempo]] does not support full-anisotropic or dispersive or gyrotropic layers of laterally infinite extents. In other words, your anisotropic or dispersive or gyrotropic material objects must not touch the CPML domain boundaries.}}
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<td> [[Image:FDTD24AFDTD MAN8.png|thumb|left|360px|The domain box of a patch antenna with a finite-sized substrateand ground.]] </td><td> [[Image:FDTD24FDTD MAN9.png|thumb|left|360px|The domain box of a laterally infinite patch antenna with a PEC ground and zero ±X and , ±Y and -Z domain offsets. Note that the bottom PEC plate can be replaced with a PEC boundary condition at the -Z domain wall.]] </td>
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== Generating the FDTD Mesh EM.Tempo's Excitation Sources ==
A lumped source is the most commonly used way of exciting a structure in EM.Tempo also offers . A lumped source is a uniformvoltage source with a series internal resistor that must be placed on a PEC or thin wire line object that is parallel to one of the three principal axes. A lumped source is displayed as a small red arrow on the host line. Lumped sources are typically used to define ports and compute the port characteristics like S/Y/Z parameters. Using simple lumped sources, frequency-independentyou can simulate a variety of transmission line structures including filters, fixed-cell FDTD mesh generatorcouplers or antenna feeds. The fixed-cell mesh consists This approach may become less accurate at higher frequencies when the details of three uniform grids along the XY, YZ feed structure become important and ZX principal planescan no longer be modeled with highly localized lumped ports. In that casesuch cases, the fixed-cell mesh generator tries to fit your physical structure it is recommended to use “Distributed Sources”, which utilize accurate modal field distributions at the mesh grid rather than adapting ports for calculation of the mesh incident and reflected waves. Waveguide source is used to your physical structureexcite the dominant TE<sub>10</sub> mode of a hollow rectangular waveguide. Other special types of distributed sources are microstrip port, CPW port and coaxial ports that can be used effectively to excite their respective transmission line structures.
A plane wave source is a popular excitation method that is used for calculation of the radar cross section of targets or reflection and transmission characteristics of periodic surfaces. A Gaussian beam source is another source type that is highly localized as opposed to the uniform plane wave. For both plane wave and Gaussian beam sources,[EM.Tempo requires a finite incidence surface to calculate the excitation. When you create either of these sources, a plane wave box or a Gaussian beam box is created as part of their definition. A trident symbol on the box shows the propagation vector as well as the E-field and H-field polarization vectors. The time domain plane wave or Gaussian beam excitation is calculated on the surface of this box and injected into the computational domain. The plane wave box is displayed in the project workspace as a purple wireframe box enclosing the structure, while the Gaussian beam box appears as a green wireframe box. Both boxes have an initial default size with an offset of 0.2λ<sub>0</sub> from the largest bounding box enclosing your entire physical structure. In both source dialogs, the radio button '''Size: Default''' is selected by default. The radio button '''Size: Custom''' allows you to set the excitation box manually. The values for the coordinates of '''Corner 1''' and '''Corner 2''' can now be changed. Corner 1 is the front lower left corner and Corner 2 is the rear upper right corner of the box. The corner coordinates are defined in the world coordinate system (WCS).
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<td> [[Image:FDTD34FDTD MAN11.png|thumb|360px|A human head model and plane wave box enclosing a cellular phone handset on its sidePEC cylinder at oblique incidence: θ = 105° and φ = 315°.]] </td><td> [[Image:FDTD33FDTD MAN12.png|thumb|360px|A Gaussian beam box enclosing a PEC cylinder at oblique incidence: θ = 105° and φ = 315°. The FDTD mesh of concentric circles represent the human head model beam's focus point and the cellular phone handsetradius.]] </td>
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==Setting Up an Excitation Source= Simulating a Multiport Structure in EM.Tempo ===
{{Note|In order to define a waveguide sourceobtain correct results, you the port impedance must have at least one hollow box object with no caps or only one end cap or a hollow box array in your projectequal the characteristic impedance of the transmission line on which the port is established. This is not automatically taken care of by EM.Tempo.}}
[[Image:Info_icon.png|40px30px]] Click here to learn more about '''[[Common_Excitation_Source_Types_in_EM.CubePreparing_Physical_Structures_for_Electromagnetic_Simulation#Gaussian_Beam_Sources Modeling_Coupled_Sources_.26_Ports | Gaussian Beam Modeling Coupled Sources& Ports]]'''.
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<td> [[Image:FDTD_FF5FDTD MAN15.png|thumb|360pxleft|640px|A plane wave box enveloping a PEC plate at normal incidence: θ = φ = 0°two-port CWP transmission line segment.]] </td></tr><tr><td> [[Image:FDTD_FF5AFDTD MAN16.png|thumb|360pxleft|A Gaussian beam source illuming a PEC plate at oblique incidence: θ = 135°, φ = 225°480px|EM.Tempo's port definition dialog.]] </td>
</tr>
</table>
=== Excitation Waveform & Frequency Domain Computations ===
When an FDTD simulation starts, your project's source starts pumping energy into the computational domain at t > 0. [[Maxwell's Equations|Maxwell's equations]] are solved in all cells at every time step until the solution converges, or the maximum number of time steps is reached. A physical source has a zero value at t = 0, but it rises from zero at t > 0 according to a specified waveform. [[EM.Tempo]] currently offers four types of temporal waveform:
# Sinusoidal
# Arbitrary User-Defined Function
A sinusoidal waveform is single-tone and periodic. Its spectrum is concentrated around a single frequency, which is equal to your project's center frequency. A Gaussian pulse decays exponentially as t → ∞, but it has a lowpass frequency spectrum which is concentrated around f = 0. A modulated Gaussian pulse decays exponentially as t → ∞, and it has a bandpass frequency spectrum concentrated around your project's center frequency. For most practical problems, a modulated Gaussian pulse waveform with EM.Tempo's default [[parameters]] provides an adequate performance.
The accuracy of the FDTD simulation results depends on the right choice of temporal waveform. EM.Tempo's default waveform choice is a modulated Gaussian pulse. At the end of an FDTD simulation, the time domain field data are transformed into the frequency domain at your specified frequency or bandwidth to produce the desired observables.
{{Note|All of EM.Tempo's excitation sources have a default modulated Gaussian pulse waveform unless you change them.}}
[[Image:Info_icon.png|40px30px]] Click here to learn more about EM.Tempo's '''[[Waveforms and Discrete Fourier Transforms Basic_Principles_of_The_Finite_Difference_Time_Domain_Method#The_Relationship_Between_Excitation_Waveform_and_Frequency-Domain_Characteristics | Standard & Custom Waveforms and Discrete Fourier Transforms]]'''.
===Defining Ports & Modeling Feeds Custom Waveforms in Practical ApplicationsEM.Tempo ===
Select the third option of waveform definition and then choose the '''Custom''' option from the '''Waveform Type''' dropdown list. Enter a mathematical expression for your custom waveform a function of the time variable "T" or "t" in the box labeled '''Expression'''. You can use arithmetic operations, standard and library functions as well as user-defined Python functions. [[Image:Info_icon.png|40px30px]] Click here to learn more about '''[[Common_Excitation_Source_Types_in_EM.CubeUsing Python to Create Functions, Models & Scripts#Exciting_Multiport_Structures_Using_Linear_Superposition Creating Custom Python Functions | Exciting Multiport Structures Using Linear SuperpositionCreating Custom Python Functions]]'''.
<table><tr><td> [[Image:Info_iconFDTD MAN13.png|40px]] Click here to learn more about thumb|left|720px|EM.Tempo'''[[Common_Excitation_Source_Types_in_EMs excitation waveform dialog showing the default standard modulated Gaussian pulse temporal waveform.Cube#Modeling_Coupled_Ports | Modeling Coupled Ports]]'''.</td></tr></table>
In [[EM.Tempo]], you can define eigth types of lumped devices: # '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Resistor | Resistor]]''' # '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Inductor | Inductor]]'''# '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Capacitor | Capacitor]]''' # '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Series_RL_Device | Series RL Device]]''' # '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Parallel_RC_Device | Parallel RC Device]]''' # '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Diode | Nonlinear Diode]]''' # '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Active_Lumped_One-Port_Device | Active Lumped One-Port Device]]''' # '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Active_Lumped_Two-Port_Device | Active Lumped Two-Port Device]]''' Lumped devices are connected between two adjacent FDTD mesh nodes. Although lumped devices are not sources and the passive types do not excite a structure, their properties are similar to lumped sources. That is why they are listed under the '''Sources''' section of the navigation tree. A lumped device has to be associated with a PEC line object that is parallel to one of the three principal axes. Similar to lumped sources, lumped devices have an '''Offset''' parameter that is equal to the distance between their location on the host line and its start point. A lumped device is characterized by a v-i equation of the form: :<math>i(t) = L \{ v(t) \} </math> where V(t) is the voltage across the device, i(t) is the current flowing through it and ''L'' is an operator function, which may involve differential or integral operators. Lumped devices are incorporated into the FDTD grid across two adjacent nodes in a similar manner to lumped sources. At the location of a lumped device, the FDTD solver enforces the device's governing equation by relating the device voltage and current to the electric and magnetic field components and updating the fields accordingly at every time step. [[Image:Info_icon.png|40px30px]] Click here for a general discussion of '''[[Modeling_Lumped_Elements,_Circuits_%26_Devices_in_EMPreparing_Physical_Structures_for_Electromagnetic_Simulation#A_Review_of_Linear_.Cube26_Nonlinear_Passive_.26_Active_Devices | Linear Passive & Nonlinear Passive & Active Devices]]'''.
{{Note|Small values of inductance may result in the divergence of the FDTD numerical scheme. To avoid this problem, you need to increase the mesh resolution and adopt a higher mesh density. This, of course, may lead to a much longer computation time.}}
=== EM.Tempo's Simulation Modes Defining Active Distributed Multiport Networks ===
The FDTD method is one circuit behavior of the most versatile numerical techniques for solving electromagnetic modeling problemsthese devices is defined by a Netlist file. Choosing the right settings and optimal values for certain numerical [[parameters]] will have Their property dialog provides a significant impact on both accuracy and computational efficiency text editor for simply writing the Netlist description of an FDTD simulationthe device. Below are You can also import an existing external Netlist file with a number of steps that you should typically follow by order when planning your FDTD simulation:".CIR" or ".TXT" file extension using the button labeled {{key|Load Netlist}}..
=== The FDTD Simulation Engine Settings A Note on Using Active Devices ===
{{Note|Keep in mind that for highly resonant structures, If you may have want to increase use a B-type nonlinear dependent source in the maximum number Netlist definition of time steps to very large values above 20an active one-port or two-port,000it must be contained in a subcircuit definition rather than in the main circuit.}}
The "'''Acceleration'''" section of figure below shows the FDTD Simulation Engine Settings dialog give three options for geometry of a two-port amplifier device with microstrip input and output transmission lines. The Netlist of the FDTD kerneltwo-port device is given below:
<table>
<tr>
<td> [[Image:Amp ex.png|thumb|left|550px|The geometry of a microstrip-based amplifier with an active two-port device.]] </td></tr></table> == EM.Tempo's Observables & Simulation Data Types== === Understanding the FDTD Observable Types === EM.Tempo's FDTD simulation engine calculates all the six electric and magnetic field components (E<sub>x</sub>, E<sub>y</sub>, E<sub>z</sub>, H<sub>x</sub>, H<sub>y</sub> and H<sub>z</sub>) at every mesh grid node at all time steps from t = 0 until the end of the time marching loop. However, in order to save memory usage, the engine discards the temporal field data from each time step to the next. Storage, manipulation and visualization of 3D data can become overwhelming for complex structures and larger computational domains. Furthermore, calculation of some field characteristics such as radiation patterns or radar cross section (RCS) can be sizable, time-consuming, post-processing tasks. That is why EM.Tempo asks you to define project observables to instruct what types of output data you want in each simulation process. EM.Tempo offers the following types of output simulation data: {| class="wikitable"|-! scope="col"| Icon! scope="col"| Simulation Data Type! scope="col"| Associated Observable Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:fieldprobe_icon.png]]| style="width:150px;" | Temporal Waveforms| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Temporal_Field_Probe_Observable |Temporal Field Probe]]| style="width:300px;" | Computing electric and magnetic field components at a fixed location in the time domain| style="width:250px;" | None|-| style="width:30px;" | [[File:fieldprobe_icon.png]]| style="width:150px;" | Point Fields| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Temporal_Field_Probe_Observable |Temporal Field Probe]]| style="width:300px;" | Computing the amplitude and phase of electric and magnetic field components at a fixed location in the frequency domain| style="width:250px;" | None|-| style="width:30px;" | [[File:fieldsensor_icon.png]]| style="width:150px;" | Near-Field Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]] | style="width:300px;" | Computing the amplitude and phase of electric and magnetic field components on a planar cross section of the computational domain in the frequency domain| style="width:250px;" | None|-| style="width:30px;" | [[File:fieldsensor_icon.png]]| style="width:150px;" | Time-Domain Near-Field Animation| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]] | style="width:300px;" | Computing either total electric or total magnetic field distribution on a planar cross section of the computational domain in the time domain| style="width:250px;" | The field maps are generated at certain specified time intervals|-| style="width:30px;" | [[File:farfield_icon.png]]| style="width:150px;" | Far-Field Radiation Patterns| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field_Radiation_Pattern_Observable |Far-Field Radiation Pattern]]| style="width:300px;" | Computing the 3D radiation pattern in spherical coordinates | style="width:250px;" | Requires one of these source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port|-| style="width:30px;" | [[File:farfield_icon.png]]| style="width:150px;" | Far-Field Radiation Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field_Radiation_Pattern_Observable |Far-Field Radiation Pattern]]| style="width:300px;" | Computing additional radiation characteristics such as directivity, axial ratio, side lobe levels, etc. | style="width:250px;" | Requires one of these source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port|-| style="width:30px;" | [[File:farfield_icon.png]]| style="width:150px;" | Far-Field Scattering Patterns| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field_Radiation_Pattern_Observable |Far-Field Radiation Pattern]]| style="width:300px;" | Computing the 3D scattering pattern in spherical coordinates | style="width:250px;" | Requires a plane wave or Gaussian beam source|-| style="width:30px;" | [[File:rcs_icon.png]]| style="width:150px;" | Radar Cross Section| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar_Cross_Section_(RCS)_Observable | RCS]] | style="width:300px;" | Computing the bistatic and monostatic RCS of a target| style="width:250px;" | Requires a plane wave source|-| style="width:30px;" | [[File:rcs_icon.png]]| style="width:150px;" | Polarimetric Scattering Matrix Data| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar_Cross_Section_(RCS)_Observable | RCS]] | style="width:300px;" | Computing the scattering matrix of a target for various plane wave source incident angles| style="width:250px;" | Requires a plane wave source|-| style="width:30px;" | [[File:port_icon.png]]| style="width:150px;" | Port Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Port_Definition_Observable |Port Definition]] | style="width:300px;" | Computing the S/Y/Z parameters and voltage standing wave ratio (VSWR)| style="width:250px;" | Requires one of these source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port|-| style="width:30px;" | [[File:port_icon.png]]| style="width:150px;" | Port Voltages, Currents & Powers| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Port_Definition_Observable |Port Definition]] | style="width:300px;" | Computing the port voltages, port currents and total port powers in both time and frequency domains| style="width:250px;" | Requires one of these source types: lumped, distributed, microstrip, CPW, coaxial or waveguide port|-| style="width:30px;" | [[File:period_icon.png]]| style="width:150px;" | Periodic Reflection & Transmission Coefficients| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Periodic Characteristics |Periodic Characteristics]] (No observable definition required) | style="width:300px;" | Computing the reflection and transmission coefficients of a periodic surface| style="width:250px;" | Requires a plane wave source and periodic boundary conditions |-| style="width:30px;" | [[File:energy_icon.png]]| style="width:150px;" | Electric and Magnetic Energy| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Energy-Power_Observable | Energy-Power]]| style="width:300px;" | Computing the electric, magnetic and total energy inside the entire computational domain in the time domain| style="width:250px;" | None|-| style="width:30px;" | [[File:energy_icon.png]]| style="width:150px;" | Dissipated Power| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Energy-Power_Observable | Energy-Power]]| style="width:300px;" | Computing the total dissipated power inside the entire computational domain in the time domain| style="width:250px;" | None|-| style="width:30px;" | [[File:energy_icon.png]]| style="width:150px;" | Electric and Magnetic Energy Density| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Energy-Power_Observable | Energy-Power]]| style="width:300px;" | Computing the electric, magnetic and total energy density on a field sensor plane in the frequency domain| style="width:250px;" | Requires at least one field sensor observable|-| style="width:30px;" | [[File:energy_icon.png]]| style="width:150px;" | Dissipated Power (Ohmic Loss) Density and Specific Absorption Rate (SAR) Density| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Energy-Power_Observable | Energy-Power]]| style="width:300px;" | Computing the dissipated power density and SAR density on a field sensor plane in the frequency domain| style="width:250px;" | Requires at least one field sensor observable|-| style="width:30px;" | [[File:energy_icon.png]]| style="width:150px;" | Poynting Vector| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Energy-Power_Observable | Energy-Power]]| style="width:300px;" | Computing the complex Poynting vector on a field sensor plane in the frequency domain| style="width:250px;" | Requires at least one field sensor observable|-| style="width:30px;" | [[File:huyg_surf_icon.png]]| style="width:150px;" | Equivalent Electric and Magnetic Surface Currents| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens_Surface_Observable |Huygens Surface]]| style="width:300px;" | Collecting tangential field data on a box to be used later as a Huygens source in other [[EM.Cube]] modules| style="width:250px;" | None|-| style="width:30px;" | [[File:CartData_icon.png]]| style="width:150px;" | Generic 3D Cartesian Spatial Data| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#3D_Cartesian_Data_Observable | 3D Cartesian Data]]| style="width:300px;" | Visualizing the contents of generic 3D Cartesian spatial data files overlaid on the project workspace | style="width:250px;" | Requires import of an existing ".CAR" data file|} Click on each category to learn more details about it in the [[Glossary of EM.Cube's Simulation Observables & Graph Types]]. Of EM.Tempo's frequency domain observables, the near fields, far fields and all of their associated parameters like directivity, RCS, etc., are calculated at a certain single frequency that is specified as part of the definition of the observable. To compute those frequency domain data at several frequencies, you need to define multiple observables, one for each frequency. On the other hand, port characteristics like S/Y/Z parameters and VSWR are calculated over the entire specified bandwidth of your project. Of EM.Tempo's source types, lumped sources, waveguide sources and distributed sources let you define one or more ports for your physical structure and compute its port characteristics. One of EM.Tempo's real advantages over frequency-domain solvers is its ability of generate wideband S/Z/Y parameter data in a single simulation run. === Examining the Near Fields in Time and Frequency Domains === EM.Tempo's FDTD time marching loop computes all the six electric and magnetic field components at every Yee cell of your structure's mesh at every time step. This amounts to a formidable amount of data that is computationally very inefficient to store. Instead, you can instruct EM.Tempo to save a small potion of these data for visualization and plotting purposes. Using a '''Field Probe''' at a specified point, you can record the a time-domain field component over the entire FDTD loop. The time-domain results are also transformed to the frequency domain within the specified bandwidth using a discrete Fourier transform (DFT). <table><tr><td> [[Image:FDTD77.png|thumb|left|480px|Time-domain evolution of the electric field at a given point.]]</td></tr></table> In EM.Tempo, you can visualize the near fields at a specific frequency in a specific plane of the computational domain. To do so, you need to define a '''Field Sensor''' observable. EM.Tempo's field sensor defines a plane across the entire computational domain parallel to one of the three principal planes. The magnitude and phase of all the six components of the electric and magnetic fields on the mesh grid points on the sensor plane are computed and displayed. <table><tr><td> [[Image:FDTD_FS2.png|thumb|360pxleft|420px|EM.Tempo's Field Sensor dialog.]] </td></tr><tr><td> [[Image:FDTD_FS1FDTD_FS1_new.png|thumb|360pxleft|480px|Three field sensor planes defined around a PEC ellipsoid illuminated by a plane wave source.]] </td>
</tr>
</table>
<table>
<tr>
<td> [[Image:FDTD_FS3FDTD_FS3_new.png|thumb|left|360px|Electric field distribution above the PEC plate.]] </td><td> [[Image:FDTD_FS4FDTD_FS4_new.png|thumb|left|360px|Magnetic field distribution above the PEC plate.]] </td>
</tr>
</table>
Far fields are typically computed in the spherical coordinate system as functions of the elevation and azimuth observation angles θ and φ. Only far-zone electric fields are normally considered. When your physical structure is excited using a lumped source, a waveguide source, a distributed source, a short dipole source, or an array of such sources, the far fields represent the radiation pattern of your source(s) in the far zone. In that case, you need to define a '''Radiation Pattern - Far Field Observable''' for your project. When your physical structure is illuminated by a plane wave source or a Gaussian beam source, the far fields represent the scattered fields. In the case of a plane source, you can compute the radar cross section (RCS) of your target structure. In that case, you need to define an '''RCS - Far Field Observable''' for your project.
In the FDTD method, the far fields are calculated using a near-field-to-far-field transformation of the field quantities on a given closed surface. EM.Tempo uses rectangular boxes to define these closed surfaces. You can use EM.Tempo's default radiation box or define your own custom box. Normally, the radiation box must enclose the entire FDTD structure. In this case, the calculated radiation pattern corresponds to the entire radiating structure. Alternatively, you can define a custom radiation box that may contain only parts of a structure, which results in a partial radiation pattern.
<table>
<tr>
<td> [[Image:FDTD_FF1.png|thumb|360pxleft|720px|EM.Tempo's Radiation Pattern dialog.]] </td></tr><tr><td> [[Image:FDTD_FF3.png|thumb|360pxleft|600px|EM.Tempo's Radar Cross Section dialog.]] </td>
</tr>
</table>
The default radiation box is placed at an offset of 0.1λ<sub>0</sub> from the largest bounding box of your physical structure. You can change the offset value from the "Far Field Acceleration" dialog, which can be accessed by clicking the {{key|Acceleration...}} button of EM.Tempo's Radiation Pattern dialog. Calculation of far-field characteristics at high angular resolutions can be a very time consuming computational task. You can accelerate this process by setting a lower '''Max. Far Field Sampling Rate''' from the same dialog. The default sampling rate is 30 samples per wavelength. A low sampling rate will under-sample the mesh grid points on the radiation box.
=== Radiation Pattern Above a Half-Space Medium ===
# Free space background terminated in an infinite PMC ground plane at the bottom
# Free space background terminated in an infinite dielectric half-space medium
<table>
<tr>
<td> [[Image:FDTD133.png|thumb|left|480px|EM.Tempo's far field background medium dialog.]] </td>
</tr>
</table>
In other words, EM.Tempo lets you calculate the far field radiation pattern of a structure in the presence of any of the above four background structure types. You can set these choices in EM.Tempo's "Far Field Background Medium" dialog. To access this dialog, open the Radiation Pattern dialog and click the button labeled {{key|Background...}}. From this dialog, you can also set the Z-coordinate of the top of the terminating half-space medium. If you set the -Z boundary condition of your computational domain to PEC or PMC types, the cases of infinite PEC or PMC ground planes from the above list are automatically selected, respectively, and the Z-coordinates of the ground plane and the bottom face of the computational domain will be identical.
<table>
<tr>
<td> [[Image:fdtd_out36_tn.png|thumb|300pxleft|360px|Radiation pattern of a vertical dipole above PEC ground.]] </td><td> [[Image:fdtd_out37_tn.png|thumb|300pxleft|360px|Radiation pattern of a vertical dipole above PMC ground.]] </td>
</tr>
<tr>
<td> [[Image:fdtd_out38_tn.png|thumb|300pxleft|360px|Radiation pattern of a horizontal dipole above PEC ground.]] </td><td> [[Image:fdtd_out39_tn.png|thumb|300pxleft|360px|Radiation pattern of a horizontal dipole above PMC ground.]] </td>
</tr>
</table>
=== Generating and Working with Multi-Frequency Simulation Data === One of the primary advantages of the FDTD method is its ability to run wideband EM simulations. The frequency domain data are computed by transforming the time-domain data to the Fourier domain. This is done automatically when EM.Tempo computes the port characteristics such as S/Z/Y parameters. The following frequency-domain observables are defined at a single frequency: * Near-Field Sensor* Far-field Radiation Pattern* RCS* Huygens Surface The default computation frequency of the above observables is the project's center frequency (fc). You can change the observable frequency from the observable's property dialog and enter any frequency in Hz. The reason these types of simulation data are computed at a single frequency is their typically very large size. However, you can define as many instances of these observables and set different frequency values for each one. In the case of radiation pattern and RCS, there are two dialogs that can be accessed from the navigation tree. Right-click on the "Fer-Field Radiation Patterns" or "Radar Cross Sections" items of the navigation tree and select '''Insert Multi-Frequency Radiation Pattern...''' or '''Insert Multi-Frequency RCS...''' from the contextual menu. <ptable><tr><td> [[Image:RadPattern multi.png|thumb|left|360px|EM.Tempo's Multi-frequency Radiation Pattern dialog.]] </td><td> [[Image:RCS multi.png|thumb|left|360px|EM.Tempo's Multi-frequency Radar Cross Section dialog.]] </td></tr></table> Using the multi-frequency dialogs, you can set the value of Start Frequency, Stop Frequency and Step Frequency in Hz. You can also set the values of Theta Angle Increment and Phi Angle Increment in degrees. The default values of both quantities are 5 deg;. In the case of RCS, you have choose one of the two options: '''Bistatic RCS''' or '''Monostatic RCS'''. To facilitate the process of all the defining multi-frequency observables in EM.Tempo, you can also use the following Python functions at the command line: ---- emag_field_sensor_multi_freq(f1,f2,df,dir_coordinate,x0,y0,z0) emag_farfield_multi_freq(f1,f2,df,theta_incr,phi_incr) emag_rcs_bistatic_multi_freq(f1,f2,df,theta_incr,phi_incr) emag_rcs_monostatic_multi_freq(f1,f2,df,theta_incr,phi_incr) emag_huygens_surface_multi_freq(f1,f2,df,x1,y1,z1,x2,y2,z2) ---- In the above Python functions, f1 and f2 are the start and stop frequencies, respectively, and df is the frequency increment, all expressed in Hz. Note that the above commands simply create and insert the specified observables in the navigation tree. They do not run perform a simulation. The created observables have the same "base name" with ordered numeric indices. For example, far-field radiation patterns are names as Multi_FF_1, Multi_FF_2, ... EM.Tempo also provides some additional Python functions for the far-field radiation patterns and RCS observables. ---- emag_farfield_consolidate(x1,x2,dx,base_name) emag_rcs_consolidate(x1,x2,dx,base_name) emag_farfield_explode(base_name) emag_rcs_explode(base_name) emag_farfield_average(n,base_name) emag_rcs_average(n,base_name) ---- The two "consolidate" Python functions take the results of multi-frequency simulation observables and merge them into a single data file. The base name in the case of far-field radiation patterns is "Multi_FF" as pointed out earlier. The name of the resulting consolidated data file is the same as the base name with a "_All" suffix and a ".DAT" file extension. In the case of far-field radiation patterns, it is "Multi_FF_All.DAT". The two "explode" Python functions take a consolidated data file names as "base_name_All.DAT" and break it up into several single-frequency ".RAD" or ".RCS" data files. Finally, the two "average" Python functions take several radiation pattern or RCS files with a common base name in the current project folder, compute their average and save the results to a new data file named "base_name_ave" with a ".RAD" or ".RCS" file extensions, respectively. == Generating the FDTD Mesh in EM.Tempo == === EM.Tempo's Mesh Types === EM.Tempo generates a brick volume mesh for FDTD simulation. The FDTD mesh is a rectangular Yee mesh that extends to the entire computational domain. It is primarily constructed from three mesh grid profiles in the XY, YZ and ZX principal planes. These projections together create a 3D mesh space consisting of a large number of cubic volume cells (voxels) carefully assembled in a way that approximates the shape of the original structure. In EM.Tempo, you can choose one of the three FDTD mesh types: * Adaptive Mesh* Regular Mesh* Fixed-Cell Mesh EM.Tempo's default mesh generator produces an adaptive brick mesh of your physical structure, whose mesh resolution varies with the frequency. As the operating frequency of your project increases, the default '''Adaptive''' FDTD mesh generator creates a larger number of smaller voxels for a given physical structure. The adaptive mesh is optimized in such a way as to capture all the geometric details, curvatures and thin slanted plates or sheets, which often pose a challenge to staircase meshing. It usually provides a reasonably accurate discretization of most complex structures. Occasionally, you may opt for a more regularized FDTD mesh with almost equal grid line spacings everywhere, but still with a frequency-dependent cell size. In that case, you can use EM.Tempo's '''Regular''' FDTD mesh generator, which is indeed a simplified version of its adaptive mesh generator. The regular FDTD mesh enforces only two criteria: minimum mesh density and absolute minimum grid spacing. The grid cell sizes in this mesh are almost uniform in objects of the same material composition or in free-space regions. EM.Tempo also offers a uniform, frequency-independent, '''Fixed-Cell''' FDTD mesh generator. The fixed-cell mesh consists of three uniform grids in the XY, YZ and ZX principal planes. However, the uniform mesh cell dimensions along the three direction, i.e. Δx, Δy and Δz do not have to be equal. The fixed-cell mesh generator tries to fit your physical structure to the mesh grid rather than adapting the mesh to your physical structure. {{Note|When choosing a mesh type for your FDTD simulation, keep in mind that adaptive and regular mesh types are frequency-dependent and their density varies with the highest frequency of your specified bandwidth, while the uniform mesh type is always fixed and independent of your project's frequency settings.}} [[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with Mesh Generator]]'''. [[Image:Info_icon.png|30px]] Click here to learn more about the properties of '''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Adaptive_Yee_Mesh | EM.Tempo's Adaptive Brick Mesh Generator]]'''. [[Image:Info_icon.png|30px]] Click here to learn more about the properties of '''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Fixed-Cell_Brick_Mesh | EM.Tempo's Fixed-Cell Brick Mesh Generator]]'''. <table><tr><td> [[Image:Tempo L11 Fig5.png|thumb|left|550px|A human head model and a cellular phone handset on its side.]] </ptd></tr><tr><td> [[Image:Top_iconTempo L11 Fig7.png|48pxthumb|left|550px|The FDTD mesh of the human head model and the cellular phone handset.]] </td></tr><tr><td> [[Image:Tempo L11 Fig8.png|thumb|left|550px|Another view of the FDTD mesh of the human head model and the cellular phone handset.]] </td></tr></table> === Discretizing the Physical Structure Using the Adaptive Yee Mesh === EM.Tempo's default mesh generator creates an adaptive brick volume mesh that uses a variable staircase profile, where the grid line spacings vary with the curvature (derivative) of the object edges or faces. As a result, a higher mesh resolution is produced at "curved" areas to better capture the geometrical details. The resolution of the adaptive FDTD mesh is driven by the '''Mesh Density''', expressed in cells per effective wavelength. Since FDTD is a time-domain method and the excitation waveform may have a wideband spectral content, the effective wavelength is calculated based on the highest frequency of the project: f<sub>max</sub> = f<sub>0</sub> + Δf/2, where f<sub>0</sub> (or fc) is your project's center frequency and Δf (or bw) is its specified bandwidth. In other words, the effective wavelength in the free space is λ<sub>0,eff</sub> = c / f<sub>max</sub>, c being the speed of light in the free space. The effective wavelength in a dielectric material with relative permittivity ε<sub>r</sub> and permeability μ<sub>r</sub> is given by λ<sub>d,eff</sub> = λ<sub>0,eff</sub> / √ε<sub>r</sub>μ<sub>r</sub>. The adaptive FDTD mesh, by default, produces different grid cell sizes in the free space regions than inside dielectric regions. The effective wavelength in a dielectric material with relative permittivity e<sub>r</sub> and permeability µ<sub>r</sub> is given by λ<sub>d,eff</sub> = λ<sub>0,eff</sub> / √ε<sub>r</sub>μ<sub>r</sub>. Therefore, the average ratio of the cell size in a dielectric region to the cell size in the free space is 1/√(ε<sub>r</sub>μ<sub>r</sub>). The adaptive FDTD mesh generator also takes note of the geometrical features of the objects it discretizes. This is more visible in the case of curved solids, curves surfaces and curved wires or obliquely oriented planes and lines which need to be approximated using a staircase profile. The mesh resolution varies with the slope of the geometrical shapes and tries to capture the curved segments in the best way. Another important feature of the adaptive FDTD mesher is generation of gradual grid transitions between low-density and high-density mesh regions. For example, this often happens around the interface between the free space and high permittivity dielectric objects. Gradual mesh transitions provide better accuracy especially in the case of highly resonant structures. A carefully calculated, "<u>'''Adaptive'''</u>" mesh of your physical structure is generated in order to satisfy the following criteria: * Optimize the number of mesh cells in each dimension. The product of the number of cells in all the three dimension determines the total mesh size. The larger the mesh size, the longer the simulation time, especially with the CPU version of the FDTD engine. Also, a very large mesh size requires more RAM, which may exceed your GPU memory capacity. Set the '''Minimum Mesh Density''' to a moderately low value to keep the mesh size manageable, but be careful not to set it too low (see the next item below).* Ensure simulation accuracy by requiring an acceptable minimum number of cells per wavelength through each object and in the empty (free) space between them and the computational domain boundaries. An effective wavelength is defined for each material at the highest frequency of the project's specified spectrum. We recommend a '''Minimum Mesh Density '''of at least 15-20 cells/ wavelength. But for some resonant structures, 25 or even 30 cells per wavelength may be required to achieve acceptable accuracy. As you reduce the mesh density, the simulation accuracy decreases.* Accurately represent and approximate the boundaries of edges or surfaces that are not grid-aligned by closely adhering to their geometric contours. This is controlled by the '''Minimum Grid Spacing Over Geometric Contours''', which can be specified either as a fraction of the free space grid spacing or as an absolute length value in project units.* Maximize the minimum grid spacing in any dimension inside the computational domain and thus maximize the simulation time step. The time step size is dictated by the CFL stability criterion and is driven by the smallest grid spacing in each dimension. The smaller the time step, the larger the number of time steps required for convergence. This is controlled using the '''Absolute Minimum Grid Spacing''', which can be specified either as a fraction of the free space grid spacing or as an absolute value. It is critical to accurately represent and precisely maintain the object edge/surface boundaries in certain structures like resonant antennas and filters, as the phase of the reflected fields/waves is affected by the object boundary positions. When object boundaries are very close to each other, the mesh needs to represent them by two separate, but very closely spaced, grid lines. To control the minimum allowed grid spacing, use the '''Absolute Minimum Grid Spacing '''settings,* Maintain a smooth grid with no abrupt jumps from low-density to high-density regions. This feature is enabled with the '''Create Gradual Grid Transitions '''check box (always checked by default). When [[EM.Cube]] generates an FDTD mesh, a large number of geometrical considerations are taken into account. These include the bounding box of each object and its corners, the ends of a line, the apex of a cone or pyramid, or the locations of lumped sources, field probes and sensors, vertices of plane wave or far field boxes, to name a few examples. These points are “locked” as fixed grid nodes in the FDTD mesh. [[EM.Cube]] determines these points internally to generate a mesh that best approximates the original structure. As you saw earlier, you can use the FDTD mesh settings to control the shape and resolution of the mesh, for example, around the curved portions of your structure, or on slanted lines or faces, etc. These settings are global and apply to all the objects making up your physical structure. You can control the global mesh more selectively using the Advanced FDTD Mesh Settings Dialog. To open this dialog, click the '''Advanced '''button at the bottom of the FDTD Mesh Settings dialog. For example, you can control the quality of the gradual grid transitions by setting the value of '''Max Adjacent Cell Size Ratio'''. The default value of this parameter is 1.3, which maintains a smooth grid line spacing scheme with no more than 1:1.3 ratio for adjacent cells. By default, grid lines are enforced at all source and observable locations. You have the option to disable this feature and round up source locations to their closest grid lines. You may also uncheck the box labeled "Adapt mesh resolution to material properties". In that case, the same effective wavelength will be used to determine the mesh resolution inside all materials as well as the free-space regions. <table><tr><td> [[Image:FDTD80.png|thumb|left|720px|EM.Tempo's mesh settings dialog.]]</td></tr></table> The figures below compare the three types of the FDTD mesh for a dielectric ellipsoid with ε<sub>r</sub> = 4. Note that the cell size inside the dielectric region is half the cell size in the air region. <table><tr><td> [[Image:FDTD MAN21.png|thumb|left|360px|The geometry of a dielectric ellipsoid with ε<sub>r</sub> = 4.]]</td><td> [[Image:FDTD MAN22.png|thumb|left|360px|The adaptive mesh of the dielectric ellipsoid.]]</td></tr></table> <table><tr><td> [[Image:FDTD MAN18.png|thumb|left|360px|The top view of the adaptive FDTD mesh of the dielectric ellipsoid.]]</td><td> [[Image:FDTD MAN19.png|thumb|left|360px|The top view of the regular FDTD mesh of the dielectric ellipsoid with the same mesh density.]]</td></tr><tr><td> [[Image:FDTD MAN20A.png|thumb|left|360px|The top view of the fixed-cell FDTD mesh of the dielectric ellipsoid using the larger cell size inside the air region.]]</td><td> [[Image:FDTD MAN20.png|thumb|left|360px|The top view of the fixed-cell FDTD mesh of the dielectric ellipsoid using the smaller cell size inside the dielectric region.]]</td></tr></table> The figures below compare the low resolution and high resolution adaptive FDTD meshes of a PEC parabolic reflector. This structure involves both a curved surface and a very thin surface. <table><tr><td> [[Image:FDTD MAN23.png|thumb|left|450px|The geometry of a PEC parabolic reflector.]]</td></tr></table> <table><tr><td> [[Image:FDTD MAN24.png|thumb|left|360px|The low-resolution adaptive mesh of the PEC parabolic reflector.]]</td><td> [[Image:FDTD MAN27.png|thumb|left|360px|The high-resolution adaptive mesh of the PEC parabolic reflector.]]</td></tr><tr><td> [[Image:FDTD MAN26.png|thumb|left|360px|The top (XY) view of the low-resolution adaptive mesh of the PEC parabolic reflector.]]</td><td> [[Image:FDTD MAN25.png|thumb|left|360px|The right (YZ) view of the low-resolution adaptive mesh of the PEC parabolic reflector.]]</td></tr></table> === Adding Fixed Grid Points to the Adaptive Yee Mesh === Adding fixed grid points to an FDTD mesh increases its resolution locally. Each fixed grid point adds three grid lines along the three principal axes passing through that point. You can add as many fixed grid points as you desire and create dense meshes at certain regions. Fixed grid points appear as grey points in the project workspace. To insert a new fixed grid point, follow these steps: * Open the Fixed Grid Points Dialog by selecting '''Menu > Simulate > Discretization > Fixed Grid Points...''' or by right-clicking on the '''FDTD''' '''Mesh''' item of the navigation tree and selecting '''Fixed Grid Points Settings...'''* Click the {{key|Add/Edit}} button to open the "Add Fixed Grid Point" dialog.* Enter the (X, Y, Z) coordinates of the new fixed point in the coordinate boxes and click the {{key|OK}} button.* To modify the coordinates of an existing fixed grid point, select it from the table and click the {{key|Add/Edit}} button.* You can also remove a fix grid point from the FDTD mesh using the {{key|Delete}} button. <table><tr><td> [[Image:FDTD36.png|thumb|left|480px|A user-defined fixed grid point in an FDTD mesh.]] </td></tr><tr><td> [[Image:FDTD38.png|thumb|left|480px|Adding a new fixed grid point in EM.Tempo's fixed grid points settings dialog.]] </td></tr><tr><td> [[Image:FDTD39.png|thumb|left|480px|The "Add Fixed Grid Point" dialog.]] </td></tr></table> According to the Courant-Friedrichs-Levy (CFL) stability criterion, the FDTD time step is determined by the smallest cell size in your FDTD mesh. Occasionally, EM.Tempo's adaptive mesh generator may create extremely tiny grid cells that would result in extremely small time steps. This would then translate into a very long computation time. [[EM.Cube]] offers the "Regular" FDTD mesh generator, which is a simplified version of the adaptive mesh generator. In a regular FDTD mesh, the grid cell sizes stay rather the same in objects of the same material composition. The mesh resolution increases in materials of higher permittivity and/or permeability based on the effective wavelength in exactly the same way as the adaptive mesh. === Profiling the Brick Mesh === A volumetric brick mesh is overwhelming for visualization in the 3D space. For this reason, [[EM.Cube]]'s mesh view shows only the outline of the cells on exterior surface of the (staircased) meshed objects. The mesh grid planes provide a 2D profile of the mesh cells along the principal coordinate planes. To display a mesh grid plane, select '''Menu > Simulate > Discretization > Grid Planes >''' and pick one of the three options: '''XY Plane''', '''YZ Plane''' or '''ZX Plane'''. You may also right click on one of the '''XY Plane''', '''YZ Plane''' or '''ZX Plane''' items in the '''Discretization''' section of the navigation tree and select '''Show''' from the contextual menu. While a mesh grid plane is visible, you can move it back and forth between the two boundary planes at the two opposite sides of the computational domain. You can do this in one of the following four ways: * Using the keyboard's Page Up {{key|PgUp}} key and Page Down {{key|PgDn}} key.* By selecting '''Menu > Simulate > Discretization > Grid Planes > Increment Grid''' or ''' Decrement Grid'''.* By right clicking on one of the '''XY Plane''', '''YZ Plane''' or '''ZX Plane''' items in the '''Discretization''' section of the navigation tree and selecting '''Increment Grid''' or ''' Decrement Grid''' from the contextual menu.* Using the keyboard shortcut {{key|>}} or {{key|<}}. As you “step through” or profile the mesh grid, you can see how the structure is discretized along internal planes of the computational domain. <table><tr><td> [[Image:Tempo L1 Fig11.png|thumb|left|360px|The XY mesh grid plane.]] </td><td> [[Image:Tempo L1 Fig12.png|thumb|left|360px|The YZ mesh grid plane.]] </td></tr></table> === The FDTD Grid Coordinate System (GCS) === When your physical structure is discretized using the brick mesh generator, a second coordinate system becomes available to you. The mesh grid coordinate system allows you to specify any location in the computational domain in terms of node indices on the mesh grid. [[EM.Cube]] displays the total number of mesh grid lines of the simulation domain (N<sub>x</sub> × N<sub>y</sub> × N<sub>z</sub>) along the three principal axes on the '''Status Bar'''. Therefore, the number of cells in each direction is one less than the number of grid lines, i.e. (N<sub>x</sub>-1)× (N<sub>y</sub>-1) × (N<sub>z</sub>-1). The lower left front corner of the domain box (Xmin, Ymin, Zmin) becomes the origin of the mesh grid coordinate system (I = 0, J = 0, K = 0). The upper right back corner of the domain box (Xmax, Ymax, Zmax) therefore becomes (I = N<sub>x</sub>-1, J = N<sub>y</sub>-1, K = N<sub>z</sub>-1). [[EM.Cube]] allows you to navigate through the mesh grid and evaluate the grid points individually. Every time you display one of the three mesh grid planes, the "'''Grid Coordinate System (GCS)'''" is automatically activated. On the Status Bar, you will see [[Image:statusgrid.png]] instead of the default [[Image:statusworld.png]]. This means that the current coordinates reported on Status Bar are now expressed in grid coordinate system. The current grid point is displayed by a small white circle on the current mesh grid plane, and it always starts from (I = 0, J = 0, K = 0). Using the keyboard's '''Arrow Keys''', you can move the white circle through the mesh grid plane and read the current node's (I, J, K) indices on the status bar. You can switch back to the "'''World Coordinate System (WCS)'''" or change to the "'''Domain Coordinate System'''" by double-clicking the status bar box that shows the current coordinate system and cycling through the three options. The domain coordinate system is one that establishes its origin at the lower left front corner of the computational domain and measure distances in project unit just like the WCS. <table><tr><td> [[Image:FDTD35(1).png|thumb|left|480px|The grid cursor on the XY grid plane and its grid coordinates (I, J, K) displayed on the status bar.]]</td></tr></table> == Running FDTD Simulations in EM.Tempo == === EM.Tempo's Simulation Modes === Once you build your physical structure in the project workspace and define an excitation source, you are ready to run an FDTD simulation. The simulation engine will run even if you have not defined any observables. Obviously, no simulation data will be generated in that case. [[EM.Tempo]] currently offers several different simulation modes as follows: {| class="wikitable"|-! scope="col"| Simulation Mode! scope="col"| Usage! scope="col"| Number of Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[#An_EMRunning a Wideband FDTD Analysis | Wideband Analysis]]| style="width:270px;" | Simulates the physical structure "As Is"| style="width:100px;" | Single run| style="width:200px;" | Generates data for many frequency samples| style="width:150px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Tempo_Primer Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]| style="width:270px;" | Varies the value(s) of one or more project variables| style="width:100px;" | Multiple runs| style="width:200px;" | Runs at the center frequency fc| style="width:150px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Performing_Optimization_in_EM.Cube | Optimization]]| style="width:270px;" | Optimizes the value(s) of one or more project variables to achieve a design goal | style="width:100px;" | Multiple runs | style="width:200px;" | Runs at the center frequency fc| style="width:150px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Generating_Surrogate_Models | HDMR Sweep]]| style="width:270px;" | Varies the value(s) of one or more project variables to generate a compact model| style="width:100px;" | Multiple runs | style="width:200px;" | Runs at the center frequency fc| style="width:150px;" | None|-| style="width:120px;" | [[#Running a Dispersion Sweep in EM.Tempo | Dispersion Sweep]]| style="width:270px;" | Varies the value of wavenumber in a periodic structure | style="width:100px;" | Multiple runs | style="width:200px;" | Runs at multiple frequency points corresponding to constant wavenumber values| style="width:150px;" | Only for periodic structures excited by a plane wave source|} === Running a Wideband FDTD Analysis === The FDTD method is one of the most versatile numerical techniques for solving electromagnetic modeling problems. Choosing the right settings and optimal values for certain numerical parameters will have a significant impact on both accuracy and computational efficiency of an FDTD simulation. Below are a number of steps that you should typically follow by order when planning your FDTD simulation: * Identify material types and proper domain boundary conditions.* Identify the source type and excitation mechanism.* Define the project observables.* Mesh the physical structure and examine the quality of the generated mesh and it geometric fidelity.* Determine the proper temporal waveform.* Select the simulation mode and run the FDTD engine. Wideband analysis is [[EM.Tempo]]'s simplest and most straightforward simulation mode. It runs the FDTD time marching loop once. At the end of the simulation, the time-domain field data are transformed into the frequency domain using a discrete Fourier transform (DFT). As a result, you can generate wideband frequency data from a single time-domain simulation run. The other simulation modes will be explained later in this manual. To open the Simulation Run Dialog, click the '''Run''' [[Image:run_icon.png]] button of the '''Simulate Toolbar''' or select the menu item '''Simulate → Run...''' from the menu bar or use the keyboard shortcut {{key|Ctrl+R}}. To start the FDTD simulation, click the {{key|Run}} button at the bottom of this dialog. Once the simulation starts, the "Output Message Window" pops up and reports messages during the different stages of the FDTD simulation. During the FDTD time marching loop, after every 10th time step, the output window updates the values of the time step, elapsed time, the engine performance in Mega-cells per seconds, and the value of the convergence ratio U<sub>n</sub>/U<sub>max</sub> in dB. An [[EM.Tempo]] simulation is terminated when the ratio U<sub>n</sub>/U<sub>max</sub> falls below the specified power threshold or when the maximum number of time steps is reached. You can, however, terminate the FDTD engine earlier by clicking the '''Abort Simulation''' button. <table><tr><td> [[Image:Tempo L1 Fig13.png|thumb|left|480px|EM.Tempo's simulation run dialog.]]</td></tr><tr><td> [[Image:Tempo L1 Fig15.png|thumb|left|550px|EM.Tempo's output message window.]]</td></tr></table> === The FDTD Simulation Engine Settings === An FDTD simulation involves a number of numerical parameters that can be accessed and modified from the FDTD Engine Settings Dialog. To open this dialog, select '''Menu > Simulate > Simulation Engine Settings... '''or open the '''Run Dialog''', and click the {{key|Settings}} button next to the engine dropdown list. In the " '''Convergence''' " section of the dialog, you can set the '''Termination Criterion''' for the FDTD time loop. The time loop must stop after a certain point in time. If you use a decaying waveform like a Gaussian pulse or a Modulated Gaussian pulse, after certain number of time steps, the total energy of the computational domain drops to very negligible values, and continuing the time loop thereafter would not generate any new information about your physical structure. By contrast, a sinusoidal waveform will keep pumping energy into the computational domain forever, and you have to force the simulation engine to exit the time loop. [[EM.Tempo]] provides two mechanism to terminated the time loop. In the first approach, an energy-like quantity defined as U<sub>n</sub> = Σ [ ε<sub>0</sub>|'''E<sub>i,n</sub>'''|<sup>2</sup> + μ<sub>0</sub>|'''H<sub>i,n</sub>'''|<sup>2</sup> ].ΔV<sub>i</sub> is calculated and recorded at a large random set of points in the computational domain. Here i is the space index and n is the time index. The quantity U<sub>n</sub> has a zero value at t = 0 (i.e. n = 0), and its value starts to build up over time. With a Gaussian or Modulated Gaussian pulse waveform, U<sub>n</sub> reach a maximum value U<sub>max</sub> at some time step and starts to decline thereafter. The ratio 10.log( U<sub>n</sub>/ U<sub>max</sub>) expressed in dB is used as the convergence criterion. When its value drops below certain '''Power Threshold''', the time loop is exited. The default value of Power Threshold is -30dB, meaning that the FDTD engine will exit the time loop if the quantity U<sub>n</sub> drops to 1/1000 of its maximum value ever. The second termination criterion is simply reaching a '''Maximum Number of Time Steps''' , whose default value set to 10,000. A third option, which is [[EM.Tempo]]'s default setting (labeled "'''Both'''"), terminates the simulation as soon as either of the first two criteria is met first. {{Note|Keep in mind that for highly resonant structures, you may have to increase the maximum number of time steps to very large values above 20,000.}} The "'''Acceleration'''" section of the FDTD Simulation Engine Settings dialog give three options for the FDTD kernel: # Serial CPU Solver# Multi-Core CPU Solver# GPU Solver The serial CPU solver is [[EM.Tempo]]'s basic FDTD kernel that run the time marching loop on a single central processing unit (CPU) of your computer. The default option is the multi-core CPU solver. This is a highly parallelized version of the FDTD kernel based on the Open-MP framework. It takes full advantage of a multi-core, multi-CPU architecture, if your computer does have one. The GPU solver is a hardware-accelerated FDTD kernel optimized for CUDA-enabled graphical processing unit (GPU) cards. If your computer has a fast NVIDIA GPU card with enough onboard RAM, the GPU kernel can speed up your FDTD simulations up to 50 times or more over the single CPU solver. For structures excited with a plane wave source, there are two standard FDTD formulations: '''Scattered Field '''(SF) formulation and '''Total Field - Scattered Field''' (TF-SF) formulation. [[EM.Tempo]] offers both formulations. The TF-SF solver is the default choice and is typically much faster than the SF solver for most problems. In two cases, when the structure has periodic boundary conditions or infinite CPML boundary conditions (zero domain offsets), only the SF solver is available. <table><tr><td> [[Image:FDTD58.png|thumb|left|720px|EM.Tempo's simulation engine settings dialog.]]</td></tr></table> ==Modeling 3D Periodic Structures in EM.Tempo== [[EM.Tempo]] allows you to simulate doubly periodic structures with periodicities along the X and Y directions. In the FDTD method, this is accomplished by applying periodic boundary conditions (PBC) at the side walls of the computational domain. {{Note| [[EM.Tempo]] can only handle regular, non-skewed periodic lattices with no secondary offsets.}} [[Image:Info_icon.png|30px]] Click here to learn more about the theory of '''[[Basic_Principles_of_The_Finite_Difference_Time_Domain_Method#Time_Domain_Simulation_of_Periodic_Structures | Time Domain Simulation of Periodic Structures]]'''. ===Defining a Periodic Structure in EM.Tempo=== By default, your physical structure in the project workspace is not periodic, and you have to instruct [[EM.Tempo]] to turn it into a periodic structure using its Periodicity Dialog. By designating a structure as periodic, you enforce periodic boundary conditions (PBC) on the side walls of its computational domain. Your structure in the project workspace then turns into a periodic unit cell. The periodic side walls are displayed with dashed blues lines. To define a periodic structure, follow these steps: * Select '''Menu > Simulate > Computational Domain > Periodicity Settings...''' or right click on the '''Periodicity''' item in the '''Computational Domain''' section of the Navigation Tree and select '''Periodicity Settings...''' from the contextual menu. This open up the Periodicity Settings Dialog.* Check the box labeled '''Periodic Structure''' and click the '''Apply''' button of this dialog. The default domain box initially shrinks to the edges of the physical structure in the project workspace. The default periods along the X and Y axes appear in the dialog, which are equal to the dimensions of the structure's bounding box.* Enter new values for '''X Spacing''' and '''Y Spacing '''in project units and close the dialog.* Periodic boundary conditions (PBC) are established on the ±X and ±Y faces of the domain box. You still have to designate the boundary conditions on the ±Z faces of the computational domain. These are CPML by default. But you can change them to PEC or PMC. <table><tr><td> [[Image:FDTD134.png|thumb|360px|EM.Tempo's periodicity settings dialog.]]</td></tr></table> ===Exciting Periodic Structures as Radiators in EM.Tempo=== In [[EM.Tempo]], a periodic structure can be excited using various source types. Exciting the unit cell structure using a lumped source, a waveguide source, or a distributed source, you can model an infinite periodic antenna array. For most practical antenna types, you excite your periodic structure with a lumped source or waveguide source. In this case, you can define a port for the lumped source or waveguide source and calculate the S<sub>11</sub> parameter or input impedance of the periodic antenna array. You can also compute the near-field and far-field data. [[EM.Tempo]]'s periodic FDTD simulator uses periodic boundary conditions (PBC) to model an infinite periodic array. All the periodic replicas of the unit cell structure are excited. In this case, you can impose a phase progression across the infinite array to steer its beam. You can do this from the property dialog of the lumped source or waveguide source. At the bottom of the '''Lumped Source Dialog''' or '''Waveguide Source Dialog''', there is a section titled '''Periodic Beam Scan Angles'''. This section is grayed out when the project structure is not periodic. You can enter desired beam scan angle values for both '''Theta''' and '''Phi''' in degrees. To visualize the radiation pattern of the beam-steered array, you have to define a finite-sized array factor. You do this in the "Impose Array Factor" section of the '''Radiation Pattern Dialog'''. {{Note|For large θ scan angles, the periodic FDTD time marching loop may take far more time steps to converge.}} <table><tr><td> [[Image:Period1.png|thumb|350px|Setting periodic scan angles in EM.Tempo's Lumped Source dialog.]] </td></tr></tr></table> <table><tr><tr><td> [[Image:Period2.png|thumb|720px|Setting the array factor in EM.Tempo's Radiation Pattern dialog.]] </td></tr></table> <table><tr><td> [[Image:Period3.png|thumb|360px|Radiation pattern of an 8×8 finite-sized periodic wire dipole array with 0° phi and theta scan angles.]] </td><td> [[Image:Period4.png|thumb|360px|Radiation pattern of a beam-steered 8×8 finite-sized periodic wire dipole array with 45° phi and theta scan angles.]] </td></tr></table> ===Exciting Periodic Structures Using Plane Waves in EM.Tempo=== Using a plane wave source to excite a periodic structure in [[EM.Tempo]], you can model frequency selective surfaces, electromagnetic band-gap (EBG) structures, metamaterials, etc. Exciting periodic structures with plane wave sources requires careful attention. [[EM.Tempo]]'s FDTD simulation engine uses the direct spectral domain FDTD or constant transverse wavenumber method for analyzing periodic structures. In this technique, instead of a plane wave box, one defines a plane wave surface parallel to the X-Y plane. At the end of the FDTD simulation of a periodic structure with plane wave excitation, the reflection and transmission coefficients of the structure are calculated and saved into ASCII data files. <table><tr><td> [[Image:Period11.png|thumb|380px|Geometry of a periodic printed strip FSS in EM.Tempo.]] </td><td> [[Image:Period12.png|thumb|340px|Define a custom periodic plane wave box in EM.Tempo.]] </td></tr></table> Using a plane wave source to excite a periodic structure in [[EM.Tempo]], you can model frequency selective surfaces, electromagnetic band-gap (EBG) structures, metamaterials, etc. Exciting periodic structures with plane wave sources requires careful attention. [[EM.Tempo]]'s FDTD simulation engine uses the direct spectral domain FDTD or constant transverse wavenumber method for analyzing periodic structures. In this technique, instead of a plane wave box, one defines a plane wave surface parallel to the X-Y plane. If the plane wave source illuminates the periodic unit cell from the top (90° < θ < 180°), the excitation surface is placed above the structure's bounding box. If the plane wave source illuminates the periodic unit cell from the bottom up (0° < θ < 90°), the excitation surface is placed below the structure's bounding box. In either case, the plane wave must intercept the excitation surface before hitting the unit cell's physical structure. It is highly recommended that you accept [[EM.Tempo]]'s default settings for the plane wave box of periodic structures. Nevertheless, you can change the location of the excitation surface if you wish. To do so, you have to open the '''Plane Wave Dialog'''. In the Excitation Box section of the dialog, select the '''Size: Custom''' option. Only the '''Z Coordinate''' of '''Corner 1''' is available for editing. The rest of the coordinates are enforced by the periodic domain. You can enter the incidence angles '''Theta''' and '''Phi''' in degrees. For periodic structures, only the '''TM<sub>z</sub>''' and '''TE<sub>z</sub>''' polarization options are available. One of the pitfalls of the direct spectral FDTD method is the possibility of horizontal resonances, which may lead to indefinite oscillation or even divergence of field values during the time marching loop. This happens in the case of oblique plane wave incidence when θ > 0°. [[EM.Cube]]'s FDTD engine automatically detects such cases and avoids those resonances by shifting the modulation frequency of the modulated Gaussian pulse waveform away from the resonant frequency. However, in some cases, the size of oscillations may still remain large after a large number of time steps. Occasionally, a late-time diverging behavior may appear. To avoid situations like these, it is highly recommended that you place a time-domain field probe above your structure and monitor the temporal field behavior during the time marching loop as shown in the figure below. {{Note|It is very important to keep in mind that only in the case of normal incidence does [[EM.Cube]] compute the reflection and transmission coefficients over the entire specified bandwidth of the project. At oblique incidences when θ > 0, the computed R/T coefficients after the discrete Fourier transformation are valid only at the center frequency of the project for the given value of the incident θ<sub>0</sub> angle. In other words, the computed R/T coefficients at all the other frequencies away from the center frequency correspond to different values of the incident θ angle. As a result, [[EM.Cube]] only saves the reflection and transmission coefficients at the center frequency into the output data files "reflection_coefficient.CPX" and "transmission_coefficient.CPX".}} === Running a Dispersion Sweep in EM.Tempo === The '''Dispersion Sweep '''option of the Simulation Mode drop-down list performs a sweep of constant k<sub>l</sub> wavenumber values. This is a specialized sweep for the constant transverse wavenumber method that [[EM.Tempo]] uses to model periodic structures illuminated by a plane wave source. The real advantage of a dispersion sweep is that through a one-dimensional sweep of k<sub>li</sub>, you can find the reflection and transmission coefficients for all combinations of frequency f<sub>j</sub> and incident angle θ<sub>j</sub> such that (2π/c) . f<sub>j</sub>. sin θ<sub>j</sub> = k<sub>li</sub>. This provides a complete picture of the dispersion behavior of your periodic structure. The sweep data can be graphed as a wavenumber-frequency intensity plot (also known as beta-k diagram) that projects the eigenvalues of the periodic structure. The horizontal axis represents the constant transverse wavenumber k<sub>l</sub> (or beta). The vertical axis represents frequency. Sometimes, the free space wave number k<sub>0</sub> = (2π/c).f is used as the vertical axis, hence, the term beta-k diagram. However, [[EM.Cube]] plots frequency vs. wavenumber. Both the horizontal and vertical axes start from 0 and extend to f<sub>max</sub> and k<sub>l,max</sub>, respectively, where f<sub>max</sub> = f<sub>0</sub> + Δf/2, and Δf is the specified bandwidth of the project. For this sweep option you have to specify the number of wavenumber samples. Note that the dispersion sweep is run for a fixed given value of the plane wave incident angle φ as specified in [[EM.Tempo]]'s Plane Wave Dialog. <table><tr><td>[[Image:KBT Settings.png|thumb|360px| [[EM.Tempo]]'s Dispersion Sweep Settings dialog.]]</td></tr></table> <table><tr><td>[[Image:KBT R.png|thumb|360px|A typical reflection coefficient dispersion diagram of a periodic structure.]]</td><td>[[Image:KBT T.png|thumb|360px|A typical transmission coefficient dispersion diagram of a periodic structure.]]</td></tr></table> <br /> <hr> [[Image:Top_icon.png|30px]] '''[[EM.Tempo#Product_Overview | Back to the Top of the Page]]'''
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