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/* Defining the Computational Domain & Boundary Conditions in EM.Cube */
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<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.CUBECube]] [[image:cad-ico.png | link=Building Geometrical Constructions in CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:postatic-ico.png | link=EM.IlluminaFerma]] [[image:staticplanar-ico.png | link=EM.FermaPicasso]] [[image:planarmetal-ico.png | link=EM.PicassoLibera]] [[image:metalpo-ico.png | link=EM.LiberaIllumina]] </td>
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[[Image:Back_icon.png|40px30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''== A Review An Overview of Computational Electromagnetics ==
Mathematically speaking, all electromagnetic modeling problems require solving some form of Maxwell's equations in conjunction with subject to certain initial and boundary conditions. Radiation and scattering problems are defined over an unbounded domain. Circuit and device problems are often formulated as shielded structures within finite domains. Aside from a few well-known canonical problems, there are no closed-form solutions available for most electromagnetic problems due to the complexity of their domains and boundaries. Numerical analysis, therefore, is the only way to solve such problems.
The numerical techniques used in computational electromagnetics (CEM) are generally divided into three categories:
* '''Asymptotic Techniques''': These techniques assume quasi-optical or high-frequency conditions, and solve the asymptotic forms of Maxwell'e equations. These methods are effective in solving structures or scenes with very large electrical dimensions. All the ray tracing techniques like the shoot-and Bounce-Rays (SBR) method fall into this category. Another example is the physical optics (PO) method.
[[Image:Info_icon.png|40px30px]] Click here for a brief review of '''[[A Review of Maxwell's Equations | Maxwell's Equations& Computational Electromagnetics (CEM)]]'''.
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[[Image:ship_image1ART GOLF Fig title.png|thumb|left|600px450px|The electric field excited above modified radiation pattern of a battleship illuminated by patch antenna installed on the front hood of a plane Volkswagen Golf automobile computed using the full-wave sourceFDTD technique.]]
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== Typical Steps of Computer Simulation of an Electromagnetic Problem ==
Using a numerical method to solve a certain electromagnetic modeling problem typically involves a recurring sequence of steps:
*#Geometrical construction of the physical structure *#Material assignment to geometric objects*#Definition of the computational domain and boundary conditions*#Definition of excitation sources*#Definition of simulation observables*#Geometrical reduction and mesh generation#Running the numerical solver#Post-processing and visualization of the output data
The above steps reduce first transform your original physical modeling problem to into a numerical computational problem, which must be solved using an appropriate numerical solver. Verifying and benchmarking different techniques in the same simulation environment helps you better strategize, formulate and validate a definitive solution.
A ubiquitous question surfaces very often asked in conjunction with electromagnetic modelingis: "Does one really need more than one simulation engine? " Different numerical techniques have different strengths and weaknesses with respect to modeling versatility and breadth of scope, modeling accuracy and computational efficiency. There is no single numerical technique that can solve all the electromagnetic problems at all frequencies and involving all length scales from microns to miles. A true challenge of electromagnetic modeling is the right choice of numerical technique for any given problem. Depending on the electrical length scales and the physical nature of your problem, some modeling techniques may provide a more accurate or computationally more efficient solutions solution than the others. Full-wave techniques provide the most accurate solution of [[Maxwell's Equations|Maxwell's equations]] in general. In the case of very large-scale problems, asymptotic methods sometimes offer the only practical solution. On the other hand, static or quasi-static methods may provide more stable solutions for extremely small-scale problems. Having access to multiple simulation engines in a unified modeling environment provides many advantages beyond getting the best solver for your a particular problem. Some complex problems involve dissimilar length scales which cannot be compromised in favor of one or another. In such cases, a hybrid simulation using different techniques for different parts of the larger problem can lead to a reasonable solution. In addition, verifying and benchmarking different solvers in the same simulation environment helps you better strategize, formulate and validate a definitive solution.
== A Functional Comparison of EM.Cube's Numerical Solvers ==
* Finite Different Time Domain (FDTD) method
* ShootShooting-and-BounceBouncing-Rays (SBR) method* Physical Optics Finite Difference (POFD) method: Geometrical Optics for electrostatic, magnetostatic and steady- Physical Optics (GO-PO) method and Iterative Physical Optics (IPO) emthod state thermal Laplace/Poisson equations* Mixed Potential Integral Equation (MPIE) method for multilayer planar structures also known as [[Planar Method of Moments|Planar method of Moments]] (PMOM)
* Wire Method of Moments (WMOM) based on Pocklington integral equation
* Surface Method of Moments (SMOM) with Adaptive Integration Equation (AIM) accelerator
* Finite Difference Physical Optics (FDPO) method: Geometrical Optics - Physical Optics (GO-PO) method solution of electrostatic and magnetostatic Laplace/Poisson equationsIterative Physical Optics (IPO) method
 Of [[EM.Cube]]'s computational modules, [[EM.Tempo]] serves as a general-purpose electromagnetic simulator that can handle most types of modeling problems involving arbitrary geometries and complex material variations in both time and frequency domains. The table below compares [[EM.Cube]]'s computational modules and its simulation engines with regards to modeling accuracy, frequency limitations and the type of numerical solution they offer:
{| class="wikitable"
|-
! scope="col"|
! scope="col"| Module Name
! scope="col"| Simulation Engine(s)
! scope="col"| Applications
|-
| style="width:40px;" | [[image:fdtd-ico.png | link=[[EM.Tempo]]]]
| style="width:80px;" | [[EM.Tempo]]
| style="width:40px;" | [[Basic_FDTD_Theory Basic_Principles_of_The_Finite_Difference_Time_Domain_Method | FDTD]]
| style="width:30px;" | Full-wave
| style="width:90px;" | 3D volumetric solver
| style="width:200px;" | General-purpose field simulator capable of handling complex geometrical and material variations
|-
| style="width:40px;" | [[image:prop-ico.png | link=[[EM.Terrano]]]]
| style="width:80px;" | [[EM.Terrano]]
| style="width:40px;" | [[SBR_Method Basic_Principles_of_SBR_Ray_Tracing | SBR]]
| style="width:30px;" | Asymptotic
| style="width:90px;" | 3D ray tracer
| style="width:80px;" | High-frequency harmonic
| style="width:150px;" | Electric field fields and ray tubes & power received at receiver locations
| style="width:200px;" | Radio wave propagation in very large scenes
|-
| style="width:80px40px;" | [[EMimage:static-ico.Illumina]]png | stylelink="width:40px;" | [[Theory_of_Physical_Optics | GO-PO & IPOEM.Ferma]]]]| style="width:30px;" | Asymptotic| style="width:90px;" | 3D surface solver| style="width:80px;" | High-frequency harmonic | style="width:150px;" | Electric and magnetic currents on surfaces| style="width:200px;" | Scattering from very large surface structures & antenna-platform combinations|-
| style="width:80px;" | [[EM.Ferma]]
| style="width:40px;" | [[Electrostatic_and_Magnetostatic_Methods Electrostatic_%26_Magnetostatic_Field_Analysis | FD]]
| style="width:30px;" | Static or quasi-static
| style="width:90px;" | 3D volumetric solver
| style="width:80px;" | DC or low-frequency
| style="width:150px;" | Electric or magnetic fields or temperature in the entire domain
| style="width:200px;" | Small-scale devices and structures
|-
| style="width:40px;" | [[image:planar-ico.png | link=[[EM.Picasso]]]]
| style="width:80px;" | [[EM.Picasso]]
| style="width:40px;" | [[Planar_Method_of_Moments Basic_Principles_of_The_Method_of_Moments | MPIE (PMOM)]]
| style="width:30px;" | Full-wave
| style="width:90px;" | 2.5D planar solver
| style="width:200px;" | Multilayer planar circuits, antennas & arrays, FSS, homogeneous substrates
|-
| style="width:40px;" | [[image:metal-ico.png | link=[[EM.Libera]]]]
| style="width:80px;" | [[EM.Libera]]
| style="width:40px;" | [[3D_Method_of_Moments Basic_Principles_of_The_Method_of_Moments | WMOM & SMOM]]
| style="width:30px;" | Full-wave
| style="width:90px;" | 3D wire & surface solvers
| style="width:150px;" | Electric and magnetic currents on surfaces or wires
| style="width:200px;" | Radiation and scattering problems involving metals and homogeneous dielectric materials
|-
| style="width:40px;" | [[image:po-ico.png | link=[[EM.Illumina]]]]
| style="width:80px;" | [[EM.Illumina]]
| style="width:40px;" | [[Basic_Principles_of_Physical_Optics | GO-PO & IPO]]
| style="width:30px;" | Asymptotic
| style="width:90px;" | 3D surface solver
| style="width:80px;" | High-frequency harmonic
| style="width:150px;" | Electric and magnetic currents on surfaces
| style="width:200px;" | Scattering from very large surface structures & antenna-platform combinations
|}
== The Geometrical Construction of the Physical Structure ==
A physical structure in [[EM.Cube]] in is typically made up of one or more geometric objects, which you either draw in its project workspace or import from an external CAD model file. In [[EM.Cube]], geometric objects are generally categorized into solids, surfaces, curves and special objects, which include points and fractal trees.
When you start the [[EM.Cube]] application, you land in its [[Building Geometrical Constructions in CubeCAD | CubeCAD]] module by default. [[Building Geometrical Constructions in CubeCAD | CubeCAD]] is a comprehensive, parametric, 3D CAD modeler along with integrated mesh generation, data processing and visualization capabilities and a powerful Python scripting environment. With the click of a few buttons, you can build complex 3D models and structures in seconds using a large variety of intuitive mouse-based object creation and transformation tools. Import of standard CAD formats allows you to fly in external CAD models with utmost ease. Imported structures can easily be augmented with your own geometrical constructions created using the native [[Standard Objects|standard geometric objects]].
All of [[EM.Cube]]'s computational modules use [[Building Geometrical Constructions in CubeCAD | CubeCAD]] together with individually customized navigation trees as their graphical user interface and geometry definition utility. Once you have mastered the basics of [[Building Geometrical Constructions in CubeCAD | CubeCAD]], using the other modules will be very straightforward.
[[image:cad-ico.png | link=Building Geometrical Constructions in CubeCAD]] Click here to learn more about '''[[Building Geometrical Constructions in CubeCAD | CubeCAD]]'''.
{| class="wikitable"
|-
! scope="col"|
! scope="col"| Module Name
! scope="col"| Geometry Types
|-
| style="width:40px;" | [[image:fdtd-ico.png | link=[[EM.Tempo]]]]
| [[EM.Tempo]]
| style="width:450px;" | General solid, surface & curve objects
|-
| style="width:40px;" | [[image:prop-ico.png | link=[[EM.Terrano]]]]
| [[EM.Terrano]]
| style="width:450px;" | General solid & surface objects - no curve objects
|-
| [[EM.Illumina]]| style="width:450px40px;" | General solid & surface objects [[image:static- no curve objectsico.png |-link=[[EM.Ferma]]]]
| [[EM.Ferma]]
| style="width:450px;" | General solid, surface & curve objects
|-
| style="width:40px;" | [[image:planar-ico.png | link=[[EM.Picasso]]]]
| [[EM.Picasso]]
| style="width:450px;" | Planar surface objects only - no solid or curve objects (vias are automatically constructed from cross-sectional planar objects as vertical prisms)
|-
| style="width:40px;" | [[image:metal-ico.png | link=[[EM.Libera]]]]
| [[EM.Libera]]
| style="width:450px;" | General solid & surface objects for Surface MoM solver, general curve objects and wireframe structures for Wire MoM solver
|-
| style="width:40px;" | [[image:po-ico.png | link=[[EM.Illumina]]]]
| [[EM.Illumina]]
| style="width:450px;" | General solid & surface objects - no curve objects
|}
== The Material Composition of the Physical Structure ==
A physical structure in [[EM.Cube]] in made up of a number of geometric objects you either draw in the project workspace or import from an external CAD model file. In [[Building Geometrical Constructions in CubeCAD | CubeCAD]], geometric objects are simply grouped together by their color. They do not have any physical properties. However, in In all of [[EM.Cube]]'s computational modules, however, you need to assign physical properties to each geometric object. In From an electromagnetic modeling point of view, the difference between a material block and a free-space region is the constitutive relations that govern the electric and magnetic fields in these media and/or their boundary conditions. In [[EM.Cube]]'s computational modules, geometric objects are grouped together by their common physical properties as well as their color. The types of physical properties may differ in different computational modules, but they are typically related to the material properties or boundary conditions.
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[[Image:MAT1_newMAT1 Head.png|thumb|left|350px400px|A structure made up of a PEC plate and different human head (lossy dielectric materials) and a handheld radio unit with plastic and metallic parts.]]
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From an electromagnetic modeling point of view, materials are categorized by the constitutive relations or boundary conditions that relate electric and magnetic fields. In general, an isotropic material medium is macroscopically characterized by four constitutive parameters:
* Permittivity (&epsilon;) having units of F/m
* Electric conductivity (&sigma;) having units of S/m
* Magnetic conductivity (&sigma;<sub>m</sub>) having units of &Omega;/m
 
The permittivity and permeability of a material are typically related to the permittivity and permeability of the free space as follows:
 
:<math> \epsilon = \epsilon_r \epsilon_0 </math>
 
:<math> \mu = \mu_r \mu_0, \quad \quad </math>
 
where &epsilon;<sub>0</sub> = 8.854e-12 F/m, &mu;<sub>r</sub> = 1.257e-6 H/m, and &epsilon;<sub>r</sub> and &mu;<sub>r</sub> are called relative permittivity and permeability of the material, respectively.
 
The constitutive parameters relate the field quantities in the material medium:
 
:<math> \mathbf{D} = \epsilon \mathbf{E}, \quad \quad \mathbf{J} = \sigma \mathbf{E} </math>
 
:<math> \mathbf{B} = \epsilon \mathbf{H}, \quad \quad \mathbf{M} = \sigma_m \mathbf{H} </math>
 
where '''E''' and '''H''' are the electric and magnetic fields, respectively, '''D''' is the electric flux density, also known as the electric displacement vector, '''B''' is the magnetic flux density, also known as the magnetic induction vector, and '''J '''and '''M '''are the electric and magnetic current densities, respectively.
 
The electric conductivity and magnetic conductivity parameters represent the material losses. In frequency-domain simulations under a time-harmonic (e<sup>j&omega;t</sup>) field assumption, it is often convenient to define a complex relative permittivity and a complex relative permeability in the following manner:
 
:<math> \epsilon_r = \epsilon^{\prime}_r -j\epsilon^{\prime\prime}_r = \epsilon^{\prime}_r -j\frac{\sigma}{\omega \epsilon_0} = \epsilon^{\prime}_r (1 - j \tan \delta ) </math>
 
:<math> \mu_r = \mu^{\prime}_r -j\mu^{\prime\prime}_r = \mu^{\prime}_r - j\frac{\sigma_m}{\omega \mu_0} = \mu^{\prime}_r (1 - j \tan \delta_m)</math>
 
where &omega; = 2&pi;f, and f is the operational frequency, and the electric and magnetic loss tangents are defined as follows:
 
:<math> \tan \delta = \epsilon^{\prime\prime}_r / \epsilon^{\prime}_r </math>
 
:<math> \tan \delta_m = \mu^{\prime\prime}_r / \mu^{\prime}_r </math>
 
Three special media are frequently encountered in electromagnetic problems:
{| class="wikitable"
|-
! scope="col"| Medium
! scope="col"| &epsilon;<sub>r</sub>
! scope="col"| &mu;<sub>r</sub>
! scope="col"| &sigma;
! scope="col"| &sigma;<sub>m</sub>
|-
| Free Space
| 1.0
| 1.0
| 0.0
| 0.0
|-
| Perfect Electric Conductor (PEC)
| 1.0
| 1.0
| &infin;
| 0.0
|-
| Perfect Magnetic Conductor (PMC)
| 1.0
| 1.0
| 0.0
| &infin;
|}
 
[[EM.Cube]] offers a large variety of material types listed in the table below:
! scope="col"| Supporting Module(s)
|-
| style="width:320px;" | Perfect Electric Conductor (PEC)| [[EM.Tempo]], [[EM.IlluminaFerma]], [[EM.FermaPicasso]], [[EM.PicassoLibera]], [[EM.LiberaIllumina]]
|-
| style="width:320px;" | Thin Wire
| [[EM.Tempo]], [[EM.Libera]]
|-
| style="width:320px;" | Perfect Magnetic Conductor (PMC)| [[EM.Tempo]], [[EM.IlluminaPicasso]], [[EM.PicassoIllumina]]
|-
| style="width:320px;" | Perfect Thermal Conductor (PTC)| [[EM.Ferma]]|-| style="width:320px;" | Dielectric(or Magnetic) Material
| [[EM.Tempo]], [[EM.Ferma]], [[EM.Picasso]], [[EM.Libera]], [[EM.Terrano]]
|-
| style="width:320px;" | Insulator Material| [[EM.Ferma]]|-| style="width:320px;" | Impedance Surface
| [[EM.Illumina]]
|-
| style="width:320px;" | Conductive Sheet
| [[EM.Picasso]]
|-
| style="width:320px;" | Anisotropic Material
| [[EM.Tempo]]
|-
| style="width:320px;" | Dispersive Material(Debye, Drude, Lorentz, Generalized Metamaterial)
| [[EM.Tempo]]
|-
| Inhomogeneous style="width:320px;" | Gyrotropic Material(Ferrite, Magnetoplasma)
| [[EM.Tempo]]
|}
 
[[Image:Info_icon.png|40px]] Click here to access '''[[Glossary of EM.Cube's Materials & Physical Object Types]]'''.
 
The table below compares [[EM.Cube]]'s computational modules with regards to their material variety:
{| class="wikitable"
|-
! scope="col"|
! scope="col"| Module Name
! scope="col"| Material Types
|-
| style="width:40px;" | [[image:fdtd-ico.png | link=[[EM.Tempo]]]]
| [[EM.Tempo]]
| style="width:450px;" | PEC, thin wire, PMC, dielectric, anisotropic, dispersive, complex materials gyrotropic
|-
| style="width:40px;" | [[image:prop-ico.png | link=[[EM.Terrano]]]]
| [[EM.Terrano]]
| style="width:450px;" | Material surfaces, thin walls and material volumes
|-
| [[EM.Illumina]]| style="width:450px40px;" | PEC, PMC, impedance surfaces|[[image:static-ico.png | link=[[EM.Ferma]]]]
| [[EM.Ferma]]
| style="width:450px;" | PEC, PTC, dielectric or magnetic or insulator materials
|-
| style="width:40px;" | [[image:planar-ico.png | link=[[EM.Picasso]]]]
| [[EM.Picasso]]
| style="width:450px;" | PEC and slot traces, short vias, infinite substrate layers
|-
| style="width:40px;" | [[image:metal-ico.png | link=[[EM.Libera]]]]
| [[EM.Libera]]
| style="width:450px;" | PEC, thin wire, homogeneous dielectric |-| style="width:40px;" | [[image:po-ico.png | link=[[EM.Illumina]]]] | [[EM.Illumina]]| style="width:450px;" | PEC, PMC, impedance surfaces
|}
 
[[Image:Info_icon.png|30px]] Click here for a more detailed discussion of '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Assigning_Material_Properties_to_the_Physical_Structure | Assigning Material Properties to the Physical Structure]]'''.
 
[[Image:Info_icon.png|30px]] Click here to access '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]]'''.
== Defining the Computational Domain & Boundary Conditions in EM.Cube ==
{| class="wikitable"
|-
! scope="col"|
! scope="col"| Module Name
! scope="col"| Domain Type
! scope="col"| Domain Boundary Conditions
|-
| style="width:40px;" | [[image:fdtd-ico.png | link=[[EM.Tempo]]]]
| [[EM.Tempo]]
| style="width:350px;" | Finite box
| style="width:250px;" | PEC, PMC, PML , Periodic
|-
| style="width:40px;" | [[image:prop-ico.png | link=[[EM.Terrano]]]]
| [[EM.Terrano]]
| style="width:350px;" | Open-boundary free space with optional half-space ground
| style="width:250px;" | Radiation BC
|-
| [[EM.Illumina]]| style="width:350px40px;" | Open[[image:static-boundary free space ico.png | stylelink="width:250px;" | Radiation BC|-[[EM.Ferma]]]]
| [[EM.Ferma]]
| style="width:350px;" | Finite box
| style="width:250px;" | Dirichlet & Neuman , Neumann, Adiabatic and Convective (for thermal simulation)
|-
| style="width:40px;" | [[image:planar-ico.png | link=[[EM.Picasso]]]]
| [[EM.Picasso]]
| style="width:350px;" | Open-boundary with multilayer background medium
| style="width:250px;" | Radiation BC
|-
| style="width:40px;" | [[image:metal-ico.png | link=[[EM.Libera]]]]
| [[EM.Libera]]
| style="width:350px;" | Open-boundary free space
| style="width:250px;" | Radiation BC
|-
| style="width:40px;" | [[image:po-ico.png | link=[[EM.Illumina]]]]
| [[EM.Illumina]]
| style="width:350px;" | Open-boundary free space
| style="width:250px;" | Radiation BC
|}
 
For more information, refer to the manuals of individual computational modules.
== Exciting a Physical Structure Using Sources or Devices in EM.Cube ==
In order to perform an electromagnetic simulation in any of [[EM.Cube]]'s computational modules, you need to excite your physical structure using some kind of source. In most cases, you can define more than one source if necessary.  *In [[EM.Tempo]], a source pumps energy into your FDTD computational domain in the form of a temporal waveform varying as a function time. *In the MoM-based modules, [[EM.Picasso|EM.picasso]] and [[EM.Libera]], a source provides the "right-hand-side (RHS)" vector of the MoM linear system resulting from the integral equation formulation of your boundary value problem. *In [[EM.IlluuminaIllumina]], a source is used to illuminate your surfaces, and the scattrering of the incident fields from those surfaces are then computed. *In [[EM.Terrano]], a source acts as a transmitter that launches the broadcast signal into the free space. The transmitter rays travel in the free space until they reach a receiver or are intercepted by an obstructing surface. *In [[EM.Ferma]], you need either an electric or magnetic sources like volume charges and volume currents provide the source to term for the Poisson equation, while fixed-potential PEC objects set the boundary conditions for the Laplace equation or provide the source term for the Poisson equation.
In each module, you should choose the right source type depending on the purpose of your simulation and based on the observables you define for your project. For example, for computing the radar cross section (RCS) of a target, you need a plane wave source. If you are interested in computing the S/Z/Y parameters of your structure, then you have to choose a source type like a gap or lumped source that supports a "Port Definition" observable.
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<td> [[Image:Source12_new.png|thumb|left|360px|Current distribution on a metallic plate excited by a plane wave source.]] </td><td> [[Image:Source13_new.png|thumb|left|360px|Current distribution on a metallic plate excited by a short horizontal dipole source above it.]] </td>
</tr>
</table>
|-
! scope="col"| Source Type
! scope="col"| Applications
! scope="col"| Restrictions
! scope="col"| Supporting Module(s)
|-
| Lumped Source
| [[EM.Tempo]]style="width:250px;" |General-purpose point voltage source| Waveguide Sourcestyle="width:250px;" | Associated with a PEC or thin wire line| style="width:200px;" | [[EM.Tempo]]
|-
| Distributed Source
| style="width:250px;" | General-purpose distributed voltage source| style="width:250px;" | Associated with a virtual rectangle strip| style="width:200px;" | [[EM.Tempo]]
|-
| Gap Microstrip Port Source| style="width:250px;" | Used for S-parameter computations| style="width:250px;" | Associated with a PEC rectangle strip| style="width:200px;" | [[EM.Picasso]], [[EM.LiberaTempo]]
|-
| Probe CPW Port Source| style="width:250px;" | Used for S-parameter computations| style="width:250px;" | Associated with a PEC rectangle strip| style="width:200px;" | [[EM.PicassoTempo]]
|-
| DeCoaxial Port Source| style="width:250px;" | Used for S-parameter computations| style="width:250px;" | Associated with a PEC Cylinder| style="width:200px;" | [[EM.Tempo]]|-| Waveguide Port Source| style="width:250px;" | Used for S-parameter computations| style="width:250px;" | Associated with a hollow PEC box| style="width:200px;" | [[EM.Tempo]]|-| Wire Current Source| style="width:250px;" | General-purpose current source| style="width:250px;" | Stand-alone source| style="width:200px;" | [[EM.Tempo]]|-| Wire Gap Circuit Source| style="width:250px;" | General-purpose point voltage source| style="width:250px;" | Associated with a PEC or thin wire line| style="width:200px;" | [[EM.Libera]]|-| Strip Gap Circuit Source| style="width:250px;" | General-purpose point voltage source| style="width:250px;" | Associated with a PEC rectangle strip| style="width:200px;" | [[EM.Picasso]], [[EM.Libera]]|-| Probe Gap Circuit Source| style="width:250px;" | Used for modeling short coaxial probes | style="width:250px;" | Associated with a PEC embedded via | style="width:200px;" | [[EM.Picasso]] |-| Scattering Wave Port Source| style="width:250px;" | Used for S-parameter computations| style="width:250px;" | Associated with a PEC rectangle strip| style="width:200px;" | [[EM.Picasso]]
|-
| Hertzian Dipole Source
| style="width:250px;" | General-purpose short filament current source| style="width:250px;" | Stand-alone source| style="width:200px;" | [[EM.Tempo]], [[EM.IlluminaTerrano]], [[EM.Picasso]], [[EM.Libera]], [[EM.TerranoIllumina]]
|-
| Plane Wave Source
| style="width:250px;" | Used for scattering computations| style="width:250px;" | Stand-alone source| style="width:200px;" | [[EM.Tempo]], [[EM.IlluminaPicasso]], [[EM.PicassoLibera]], [[EM.LiberaIllumina]]
|-
| Gaussian Beam Source
| style="width:250px;" | Used for modeling focused beams | style="width:250px;" | Stand-alone source| style="width:200px;" | [[EM.Tempo]]
|-
| Huygens Source
| style="width:250px;" | Used as a distributed equivalent | style="width:250px;" | Imported from a Huygens data file| style="width:200px;" | [[EM.IlluminaTempo]], [[EM.Terrano]], [[EM.Picasso]], [[EM.Libera]], [[EM.Illumina]]
|-
| Point Transmitter Set| style="width:250px;" | Used as a point source with an imported radiation pattern | style="width:250px;" | Associated with a point or point array| style="width:200px;" | [[EM.Terrano]]
|-
| Fixed-Potential PEC with Nonzero Voltage| style="width:250px;" | Used as a distributed DC voltage source | style="width:250px;" | Requires drawing geometric objects| style="width:200px;" | [[EM.Ferma]]
|-
| Volume Charge Source| style="width:250px;" | Used as a distributed electric charge source | style="width:250px;" | Requires drawing geometric objects| style="width:200px;" | [[EM.Ferma]]
|-
| Wire Current Source| style="width:250px;" | Used as a linear filament current source | style="width:250px;" | Requires drawing geometric objects| style="width:200px;" | [[EM.Ferma]]
|-
| Volume Current Source| style="width:250px;" | Used as a distributed elctric current source | style="width:250px;" | Requires drawing a line or polyline| style="width:200px;" | [[EM.Ferma]]
|-
| Permanent Magnet with Nonzero Magnetization| style="width:250px;" | Used as a distributed magnetization source | style="width:250px;" | Requires drawing geometric objects| style="width:200px;" | [[EM.Ferma]]|-| Fixed-Temperature PTC| style="width:250px;" | Used as an isothermal surface heat source for thermal simulation| style="width:250px;" | Requires drawing geometric objects| style="width:200px;" | [[EM.Ferma]]|-| Volume Heat Source| style="width:250px;" | Used as a distributed volume heat source for thermal simulation | style="width:250px;" | Requires drawing geometric objects| style="width:200px;" | [[EM.Ferma]]
|}
 
 
[[Image:Info_icon.png|40px]] Click here to access '''[[Glossary of EM.Cube's Excitation Sources]]'''.
 
The table below compares [[EM.Cube]]'s computational modules with regards to their excitation source and lumped device types:
{| class="wikitable"
|-
! scope="col"|
! scope="col"| Module Name
! scope="col"| Excitation/Sources
! scope="col"| Lumped Devices
|-
| style="width:40px;" | [[image:fdtd-ico.png | link=[[EM.Tempo]]]]
| [[EM.Tempo]]
| style="width:350px;" | Lumped and source, distributed source, microstrip, CPW, coaxial and waveguide port sources, Hertzian dipole, wire current source, plane wave, Gaussian beam, Huygens source, arbitrary waveform | style="width:250px;" | Passive and activeResistor, capacitor, inductor, series RL, parallel RC, linear and nonlinear diode, active lumped one-port and two-port devices , active distributed one-port and circuits two-port devices
|-
| style="width:40px;" | [[image:prop-ico.png | link=[[EM.Terrano]]]]
| [[EM.Terrano]]
| style="width:350px;" | TransmittersPoint transmitter set, Hertzian dipoles| style="width:250px;" | N/A|-| [[EM.Illumina]]| style="width:350px;" | Hertzian dipole, plane wave, Huygens source
| style="width:250px;" | N/A
|-
| style="width:40px;" | [[image:static-ico.png | link=[[EM.Ferma]]]]
| [[EM.Ferma]]
| style="width:270px;" | ChargeVolume charge, volume current and , wire current, permanent magnet, volume heat source
| style="width:250px;" | N/A
|-
| style="width:40px;" | [[image:planar-ico.png | link=[[EM.Picasso]]]]
| [[EM.Picasso]]
| style="width:350px;" | Gap sourceStrip and probe gap circuit sources, scattering wave port, Hertzian dipole, plane wave, Huygens source
| style="width:250px;" | Simple passive RLC lumped elements
|-
| style="width:40px;" | [[image:metal-ico.png | link=[[EM.Libera]]]]
| [[EM.Libera]]
| style="width:350px;" | Gap sourceStrip and wire gap circuit sources, Hertzian dipole, plane wave, Huygens source
| style="width:250px;" | Simple passive RLC lumped elements
|-
| style="width:40px;" | [[image:po-ico.png | link=[[EM.Illumina]]]]
| [[EM.Illumina]]
| style="width:350px;" | Hertzian dipole, plane wave, Huygens source
| style="width:250px;" | N/A
|}
 
[[Image:Info_icon.png|30px]] Click here for a more detailed discussion of '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Defining_an_Excitation_Source | Defining an Excitation Source]]'''.
 
[[Image:Info_icon.png|30px]] Click here to access '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]]'''.
== Defining Simulation Observables in EM.Cube ==
! scope="col"| Supporting Module(s)
|-
| style="width:250px;" | Electric and Magnetic Field Distributions
| Field Sensor
| style="width:250px;" | [[EM.Tempo]], [[EM.Terrano|Em.Terrano]], [[EM.IlluminaFerma]], [[EM.FermaPicasso]], [[EM.PicassoLibera]], [[EM.LiberaIllumina]]
|-
| style="width:250px;" | Electric and Magnetic Current Distributions
| Current Distribution
| style="width:250px;" | [[EM.IlluminaPicasso]], [[EM.PicassoLibera]], [[EM.LiberaIllumina]]
|-
| style="width:250px;" | Temporal Fields
| Field Probe
| style="width:250px;" | [[EM.Tempo]]|-| style="width:250px;" | Far-Field Radiation Patterns| Far-Field Radiation Pattern| style="width:250px;" | [[EM.Tempo]], [[EM.Picasso]], [[EM.Libera]], [[EM.Illumina]], [[EM.Terrano]]
|-
| Far-Field style="width:250px;" | Radiation PatternsCharacteristics (D0, HPBW, SLL, AR, etc.)| Far Fields - Field Radiation Pattern| style="width:250px;" | [[EM.Tempo]], [[EM.Terrano|Em.TerranoPicasso]], [[EM.IlluminaLibera]], [[EM.PicassoIllumina]], [[EM.LiberaTerrano]]
|-
| style="width:250px;" | Radar Cross Section (RCS)| Far Fields - RCS| style="width:250px;" | [[EM.Tempo]], [[EM.IlluminaPicasso]], [[EM.PicassoLibera]], [[EM.LiberaIllumina]]
|-
| style="width:250px;" | Huygens Surface Data
| Huygens Surface
| style="width:250px;" | [[EM.Tempo]], [[EM.Terrano|Em.TerranoPicasso]], [[EM.IlluminaLibera]], [[EM.PicassoIllumina]], [[EM.LiberaTerrano]]
|-
| style="width:250px;" | Port Characteristics (S/Z/Y Parameters)
| Port Definition
| style="width:250px;" | [[EM.Tempo]], [[EM.Picasso]], [[EM.Libera]]
|-
| style="width:250px;" | Port Voltags, Currents & Powers| Port Definition| style="width:250px;" | [[EM.Tempo]]|-| style="width:250px;" | Periodic Reflection and Transmission Coefficients
| No Observables Required
| style="width:250px;" | [[EM.Tempo]], [[EM.Picasso]]
|-
| style="width:250px;" | Temporal Electric and Magnetic EnergyEnergies and Dissipated Power| Domain Energy-Power| style="width:250px;" | [[EM.FermaTempo]]
|-
| style="width:250px;" | Electric and Magnetic Field Densities and Dissipated Power Density | Field Sensor & Energy-Power| style="width:250px;" | [[EM.Tempo]], [[EM.Ferma]]|-| style="width:250px;" | Specific Absorption Rate (SAR) Density| Field Sensor & Energy-Power| style="width:250px;" | [[EM.Tempo]]|-| style="width:250px;" | Complex Poynting Vector| Field Sensor & Energy-Power| style="width:250px;" | [[EM.Tempo]]|-| style="width:250px;" | Static Electric and Magnetic Energy & Ohmic Losses
| Field Integral
| style="width:250px;" | [[EM.Ferma]]
|-
| style="width:250px;" | Voltage and Current
| Field Integrals
| style="width:250px;" | [[EM.Ferma]]
|-
| style="width:250px;" | Electric and Magnetic Flux
| Field Integrals
| style="width:250px;" | [[EM.Ferma]]
|-
| style="width:250px;" | Resistance, Capacitance, Self-Inductance and Mutual Inductance
| Field Integrals
| style="width:250px;" | [[EM.Ferma]]
|-
| style="width:250px;" | Temperature and heat flux distributions| Field Sensor| style="width:250px;" | [[EM.Ferma]]|-| style="width:250px;" | Thermal energy density | Field Sensor| style="width:250px;" | [[EM.Ferma]]|-| style="width:250px;" | Thermal Flux and Thermal Energy| Field Integrals| style="width:250px;" | [[EM.Ferma]]|-| style="width:250px;" | Received Power
| Receiver Set
| style="width:250px;" | [[EM.Terrano]]
|-
| Singal-to-Noise Ratio (SNR) style="width:250px;" | Channel Path Loss
| Receiver Set
| style="width:250px;" | [[EM.Terrano]]
|-
| Channel Path Loss style="width:250px;" | Singal-to-Noise Ratio (SNR)
| Receiver Set
| style="width:250px;" | [[EM.Terrano]]|-| style="width:250px;" | E<sub>b</sub>/N<sub>0</sub> | Receiver Set| style="width:250px;" | [[EM.Terrano]]|-| style="width:250px;" | Bit Error Rate (BER) | Receiver Set| style="width:250px;" | [[EM.Terrano]]|-| style="width:250px;" | Power Delay Profile | Receiver Set| style="width:250px;" | [[EM.Terrano]]|-| style="width:250px;" | Angles of Arrival and Departure | Receiver Set| style="width:250px;" | [[EM.Terrano]]
|}
<table><tr><td> [[Image:Info_iconSource14_new.png|40pxthumb|left|360px|The radar cross section of a metallic plate illuminated by a plane wave source.]] Click here to access '''</td><td> [[Glossary Image:Source15_new.png|thumb|left|360px|The radiation pattern of EMa short horizontal dipole above a metallic plate.Cube's Simulation Observables]]'''. </td></tr></table>
The table below compares [[EM.Cube]]'s computational modules with regards to their observable types:
{| class="wikitable"
|-
! scope="col"|
! scope="col"| Module Name
! scope="col"| Observables
|-
| style="width:40px;" | [[image:fdtd-ico.png | link=[[EM.Tempo]]]]
| [[EM.Tempo]]
| style="width:450px600px;" | Near-fielddistributions, far-fieldradiation patterns and characteristics, RCS, periodic R/Tcoefficients, temporal waveforms, S/Z/Y parameters, port current/voltage/power, electric and magnetic field densities, dissipated power density, SAR density, complex Poynting vector, temporal domain electric and magnetic energies and dissipated power
|-
| style="width:40px;" | [[image:prop-ico.png | link=[[EM.Terrano]]]]
| [[EM.Terrano]]
| style="width:450px600px;" | Far-Received power coverage, field & received distributions, SNR, E<sub>b</sub>/N<sub>0</sub>, BER, ray information (delay and angles of arrival and departure, ray fields, ray power |-| [[EM.Illumina]]| style="width:450px;" | Far-field & RCS)
|-
| style="width:40px;" | [[image:static-ico.png | link=[[EM.Ferma]]]]
| [[EM.Ferma]]
| style="width:450px600px;" | Electric or magnetic field fields & potentialpotentials, electric and magnetic energy densities, dissipated power density, voltage, current, electric and magnetic energy, Ohmic power loss, electric and magnetic flux, capacitance, inductance, resistance, temperature, heat flux density, thermal energy density, thermal flux and energy
|-
| style="width:40px;" | [[image:planar-ico.png | link=[[EM.Picasso]]]]
| [[EM.Picasso]]
| style="width:450px600px;" | Current distributiondistributions, exterior near-field distributions, far-fieldradiation patterns and characteristics, RCS, periodic R/T, S/Z/Y parameters
|-
| style="width:40px;" | [[image:metal-ico.png | link=[[EM.Libera]]]]
| [[EM.Libera]]
| style="width:450px600px;" | Current distributiondistributions, exterior near-field distributions, far-fieldradiation patterns and characteristics, RCS, S/Z/Y parameters|-| style="width:40px;" | [[image:po-ico.png | link=[[EM.Illumina]]]] | [[EM.Illumina]]| style="width:600px;" | Current distributions, exterior near-field distributions, far-field radiation patterns and characteristics, RCS
|}
 
[[Image:Info_icon.png|30px]] Click here to access '''[[Glossary of EM.Cube's Simulation Observables & Graph Types]]'''.
== Discretizing a Physical Structure Using a Mesh Generator in EM.Cube ==
In order to transform a physical modeling problem into a computational problem that can be solved using a numerical technique, your physical structure must first be discretized into simple canonical elements or mesh cells.[[EM.Cube]]'s computational modules use a number of different mesh generation schemes to discretize your physical structurestructures. Even [[Building Geometrical Constructions in CubeCAD | CubeCAD]] provides several tools for object discretization. In general, all of [[EM.Cube]]'s mesh generation schemes can be grouped into three categories representing their based on dimensionality:
# Linear Mesh# Surface Mesh# Volume Mesh
The linear mesh is , also known as the wireframe mesh and , is used by [[EM.Libera]] to discretize the physical structure for Wire MoM simulation. [[EM.Cube]] offer offers two types of surface mesh types: triangular surface mesh and hybrid surface mesh. As its name implies, a triangular surface mesh is made up of interconnected triangular cells. [[EM.Terrano]], [[EM.Illumina]], [[EM.Libera]] and [[EM.Picasso]] all use triangular surface mesh generators to discretized discretize surface CAD geometric objects and as well as the surface of solid CAD geometric objects. The hybrid surface mesh is [[EM.Picasso]]'s default mesh. It combines rectangular and triangular cells to discretize planar structures. The hybrid surface mesh generator tries to produce as many identical rectangular cells as possible in rectangular regions of your planar structure.
[[EM.Cube]] provides two types of brick meshes mesh, also known as voxel mesh, to discretize the volume of your computational domain. Brick meshes are entire-domain volume meshes and are made up of cubic cells. Brick meshes They are indeed generated by a three-dimensional arrangement of grid lines along the X, Y and Z dimensionsaxes. [[EM.Tempo]] offers an "Adaptive " brick mesh as well as a fixed"Fixed-cell Cell" brick mesh for the FDTD simulation of your physical structure. [[EM.Ferma]] offers only a fixed-mesh brick mesh for the solution of electrostatic and magnetostatic Laplace/Poisson equations.
<table>
<tr>
<td> [[Image:Mesh1_new.png|thumb|left|240px|The geometry of a metallic torus.]] </td><td> [[Image:Mesh2_new.png|thumb|left|240px|The brick volume mesh of the metallic torus.]] </td><td> [[Image:Mesh3_new.png|thumb|left|240px|The triangular surface mesh of the metallic torus.]] </td>
</tr>
</table>
The objects of your physical structure are discretized based on a specified mesh density. The default mesh densities of [[EM.Tempo]], [[EM.Picasso]], [[EM.Libera]] and [[EM.Illumina]] are expressed as the number of cells per effective wavelength. Therefore, the resolution of the default mesh in these modules are is frequency-dependent. You can also define the mesh resolution using a fixed cell size or fixed edge length specified in project units. The mesh density of [[EM.Terrano]] is always expressed in terms of cell edge length. The mesh resolution of [[EM.Ferma]] is always specified as the fixed cell size. All of [[EM.Cube]]'s computational modules have default mesh settings that usually work well for most simulations.  The accuracy of the numerical solution of an electromagnet problem depends greatly on the quality and resolution of the generated mesh. As a rule of thumb, a mesh density of about 10-30 cells per effective wavelength usually yields satisfactory results. Yet, for structures with lots of fine geometrical details or for highly resonant structures, higher mesh densities may be required. Also, the particular simulation data that you seek in a project also influence your choice of mesh resolution. For example, far field characteristics like radiation patterns are less sensitive to the mesh density than the near-field distributions on a structure with a highly irregular shape and a rugged boundary.  [[Image:Info_icon.png|40px]] Click here to access '''[[Glossary of EM.Cube's Mesh Generators]]'''.
The accuracy of the numerical solution of an electromagnet problem depends very much on the quality and resolution of the generated mesh. As a rule of thumb, a mesh density of about 10-25 cells per effective wavelength usually yields satisfactory results. Yet, for structures with lots of fine geometrical details or for highly resonant structures, higher mesh densities may be required. The particular simulation data you seek in a project also influences your choice of mesh resolution. For example, far-field characteristics like radiation patterns are less sensitive to the mesh density than the near-field distributions on a structure with a highly irregular shape and a rugged boundary.
The table below compares [[EM.Cube]]'s computational modules with regards to their mesh generator types:
{| class="wikitable"
|-
! scope="col"|
! scope="col"| Module Name
! scope="col"| Mesh Type
|-
| style="width:40px;" | [[image:fdtd-ico.png | link=[[EM.Tempo]]]]
| [[EM.Tempo]]
| style="width:450px;" | Adaptive and fixed-cell volumetric brick (voxel) mesh
|-
| style="width:40px;" | [[image:prop-ico.png | link=[[EM.Terrano]]]]
| [[EM.Terrano]]
| style="width:450px;" | Triangular facet mesh
|-
| [[EM.Illumina]]| style="width:450px40px;" | Triangular surface mesh|[[image:static-ico.png | link=[[EM.Ferma]]]]
| [[EM.Ferma]]
| style="width:450px;" | Fixed-cell volumetric brick mesh
|-
| style="width:40px;" | [[image:planar-ico.png | link=[[EM.Picasso]]]]
| [[EM.Picasso]]
| style="width:450px;" | Hybrid rectangular-triangular surface mesh
|-
| style="width:40px;" | [[image:metal-ico.png | link=[[EM.Libera]]]]
| [[EM.Libera]]
| style="width:450px;" | Wireframe and triangular surface mesh
|-
| style="width:40px;" | [[image:po-ico.png | link=[[EM.Illumina]]]]
| [[EM.Illumina]]
| style="width:450px;" | Triangular surface mesh
|}
[[Image:Info_icon.png|30px]] Click here to access '''[[Glossary of EM.Cube's Simulation-Related Operations]]'''. <pbr />&nbsp; </phr> [[Image:Top_icon.png|48px30px]] '''[[Numerical_Modeling_of_Electromagnetic_Problems_Using_EM.Cube#Computational_Electromagnetics An_Overview_of_Computational_Electromagnetics | Back to the Top of the Page]]'''
[[Image:Back_icon.png|40px30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''
Kazem Sabet
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