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<strong><font color="#961717" size="4">Fast Multi-Core Multicore & GPU-Accelerated FDTD Solvers for Simulating the Most Complex Electromagnetic Modeling Problems</font></strong>

[[EM.Tempo]] is a powerful 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 the key to a thorough understanding of the interaction of electromagnetic waves with complex media such as anisotropic composites, metamaterials or biological environments or with passive and active devices and nonlinear circuits.

[[EM.Tempo]] has undergone several evolutionary development cycles since its inception in 2004. The original simulation engine utilized an FDTD formulation based on the uniaxial perfectly matched layer (UPML) boundary termination. Subsequently, a more advanced boundary termination based on the convolutional perfectly matched layer (CPML) was implemented 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 using CPML walls that touch material media. A novel formulation of periodic boundary conditions was 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 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.

[[EM.Tempo]] is a general-purpose EM simulator than can solve most types of electromagnetic modeling problems involving arbitrary geometries and complex material variations in both time and frequency domains. It has also been integrated within the [[EM.Cube]] simulation environment as its full-wave "FDTD Module". [[EM.Tempo]] shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as [[Building Geometrical Constructions in CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.

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 structureto reduce the total size of the computational domain.

[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Domain_Settings | Domain SettingSettings]]'''.

=== Advanced CMPL CPML Setup ===

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.

{{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.}}

Before you can run an FDTD simulation, you have to define a source to excite your project’s physical structure. [[EM.Tempo]] offers a variety of excitation mechanisms for your physical structure depending on your particular type of modeling problem or application:

A lumped source is the most commonly used way of exciting a structure in [[EM.Tempo]]. A lumped source is a voltage 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, you can simulate a variety of transmission line structures including filters, couplers or antenna feeds. This approach may become less accurate at higher frequencies when the details of the feed structure become important and can no longer be modeled with highly localized lumped ports. In such cases, it is recommended to use “Distributed Sources”, which utilize accurate modal field distributions at the ports for calculation of the incident and reflected waves. Waveguide source is used to excite the dominant TE₁₀ 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 0.2&lambda;₀ 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).

Ports are used to order and index sources for circuit parameter calculations like S/Y/Z parameters. In [[EM.Tempo]], you can define ports at the location of the following types of sources:

If your physical structure has two or more sources, but you have not defined any ports, all the sources will excite the structure simultaneously during the simulation. However, when you assign N ports to the sources, then you have a multiport structure that is characterized by an N×N scattering matrix, an N×N impedance matrix, and an N×N admittance matrix. To calculate these matrices, [[EM.Tempo]] uses a binary excitation scheme in conjunction with the principle of linear superposition. In this binary scheme, the structure is analyzed a total of N times. Each time one of the N port-assigned sources is excited, and all the other port-assigned sources are turned off. In other words, the FDTD solver runs a "port sweep" internally. When the ''j''th port is excited, all the S_ij parameters are calculated together based on the following definition:

In summary, to analyze an N-port structure, [[EM.Tempo]] runs N separate FDTD time marching loops. The S/Z/Y parameters are frequency-domain quantities. The port voltages and currents are Fourier-transformed to the frequency domain over the frequency range [fc-bw/2, fc+bw/2], where fc is the center frequency and bw is the bandwidth of your project. You can reduce the frequency range of the Fourier transform by settings new values for '''Start''' and '''End''' frequencies in the "Port Definition" dialog as long as these are within the range [fc-bw/2, fc+bw/2]. By default, 200 frequency samples are taken over the specified frequency range. This number can be modified from the FDTD simulation engine settings dialog.

{{Note|In order to obtain correct results, the port impedance must equal the characteristic impedance of the transmission line on which the port is established. This is not automatically taken care of by [[EM.Tempo]].}}

When an FDTD simulation starts, your project's source starts pumping energy into the computational domain at t > 0. 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:

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 &rarr; &infin;, but it has a lowpass frequency spectrum which is concentrated around f = 0. A modulated Gaussian pulse decays exponentially as t &rarr; &infin;, 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|30px]] Click here to learn more about [[EM.Tempo]]'s '''[[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]]'''.

In some time-domain applications, you may want to simulate the propagation of a certain kind of waveform in a circuit or structure. In addition to the default waveforms, [[EM.Tempo]] allows you to define custom waveforms by either time or frequency specifications for each individual source in your project. If you open up the property dialog of any source type in [[EM.Tempo]], you will see an {{key|Excitation Waveform...}} button located in the "Source Properties" section of the dialog. Clicking this button opens up [[EM.Tempo]]'s Excitation Waveform dialog. From this dialog, you can override [[EM.Tempo]]'s default waveform and customize your own temporal waveform. The Excitation Waveform dialog offers three different options for defining the waveform:

| style="width:300px;" | Computing the 3D radiation pattern in spherical coordinates and additional radiation characteristics such as directivity, axial ratio, side lobe levels, etc.

| style="width:150px;" | Far-Field Scattering CharacteristicsPatterns

| style="width:250px;" | Requires a plane wave or Gaussian beam source

| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Cartesian_Data_Observable 3D_Cartesian_Data_Observable |3D Cartesian Data]]

<td> [[Image:FDTD_FF3.png|thumb|left|480px600px|EM.Tempo's Radar Cross Section dialog.]] </td>

</tr></tr></table> <table><tr><tr><td> [[Image:Period2.png|thumb|350px720px|Setting the array factor in EM.Tempo's Radiation Pattern dialog.]] </td>