[[Image:Splash-generic2.jpg|right|800px720px]]
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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 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.
* '''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 question often asked in conjunction with electromagnetic modeling is: "Does one really need to use 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 solution than the others. Full-wave techniques provide the most accurate solution of 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 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) method 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"
| 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: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:40px;" | [[image:po-ico.png | link=[[EM.Illumina]]]]
| style="width:80px;" | [[EM.Illumina]]
| style="width:40px;" | [[Theory_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
|-
| style="width:40px;" | [[image:static-ico.png | link=[[EM.Ferma]]]]
| 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: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
|}
{{Note|Among [[EM.Cube]]'s computational modules, [[EM.Tempo]] serves as a general-purpose electromagnetic simulator than can handle most types of modeling problems involving arbitrary geometries and complex material variations in both time and frequency domains.}}
== Geometrical Construction of the Physical Structure ==
| style="width:40px;" | [[image:prop-ico.png | link=[[EM.Terrano]]]]
| [[EM.Terrano]]
| style="width:450px;" | General solid & surface objects - no curve objects
|-
| style="width:40px;" | [[image:po-ico.png | link=[[EM.Illumina]]]]
| [[EM.Illumina]]
| style="width:450px;" | General solid & surface objects - no curve objects
|-
| [[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 ==
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.
<table>
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[[Image:MAT1_newMAT1 Head.png|thumb|left|350px400px|A structure made up of two PEC plates a human head (lossy dielectric) and objects made of different dielectric materialsa 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 (ε) having units of F/m
* Electric conductivity (σ) having units of S/m
* Magnetic conductivity (σ<sub>m</sub>) having units of Ω/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 ε<sub>0</sub> = 8.854e-12 F/m, μ<sub>r</sub> = 1.257e-6 H/m, and ε<sub>r</sub> and μ<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>jωt</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 ω = 2πf, 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"| ε<sub>r</sub>
! scope="col"| μ<sub>r</sub>
! scope="col"| σ
! scope="col"| σ<sub>m</sub>
|-
| Free Space
| 1.0
| 1.0
| 0.0
| 0.0
|-
| Perfect Electric Conductor (PEC)
| 1.0
| 1.0
| ∞
| 0.0
|-
| Perfect Magnetic Conductor (PMC)
| 1.0
| 1.0
| 0.0
| ∞
|}
[[EM.Cube]] offers a large variety of material types listed in the table below:
|-
| style="width:320px;" | Perfect Electric Conductor (PEC)
| [[EM.Tempo]], [[EM.IlluminaFerma]], [[EM.FermaPicasso]], [[EM.PicassoLibera]], [[EM.LiberaIllumina]]
|-
| style="width:320px;" | Thin Wire
|-
| 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.Tempo]]
|-
| style="width:320px;" | Voxel DatabaseGyrotropic Material (Ferrite, Magnetoplasma)
| [[EM.Tempo]]
|}
| style="width:40px;" | [[image:fdtd-ico.png | link=[[EM.Tempo]]]]
| [[EM.Tempo]]
| style="width:450px;" | PEC, thin wire, PMC, dielectric, anisotropic, dispersive, voxel database gyrotropic
|-
| style="width:40px;" | [[image:prop-ico.png | link=[[EM.Terrano]]]]
| [[EM.Terrano]]
| style="width:450px;" | Material surfaces, thin walls and material volumes
|-
| style="width:40px;" | [[image:po-ico.png | link=[[EM.Illumina]]]]
| [[EM.Illumina]]
| style="width:450px;" | PEC, PMC, impedance surfaces
|-
| style="width:40px;" | [[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.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|40px30px]] 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 ==
| [[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
|-
| style="width:40px;" | [[image:po-ico.png | link=[[EM.Illumina]]]]
| [[EM.Illumina]]
| style="width:350px;" | Open-boundary free space
| style="width:250px;" | Radiation BC
|-
| [[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]]]]
| 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
| 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]]
|-
| 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 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
|-
| Volume Charge
| style="width:250px;" | Used as a distributed eelctric electric charge source
| style="width:250px;" | Requires drawing geometric objects
| style="width:200px;" | [[EM.Ferma]]
| Permanent Magnet
| 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]]
| style="width:40px;" | [[image:fdtd-ico.png | link=[[EM.Tempo]]]]
| [[EM.Tempo]]
| style="width:350px;" | Lumpedsource, distributedsource, microstrip, COWCPW, coaxial and waveguide port sources, Hertzian dipole, wire current source, plane wave, Gaussian beam, Huygens source, arbitrary waveform | style="width:250px;" | Resistor, capacitor, inductor and , series RL, parallel RC, nonlinear diode , active lumped one-port and two-port devices, active distributed one-port and 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|-| 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
|-
| style="width:40px;" | [[image:static-ico.png | link=[[EM.Ferma]]]]
| [[EM.Ferma]]
| style="width:270px;" | Volume charge, volume current, wire current and , permanent magnet, volume heat source
| style="width:250px;" | N/A
|-
| style="width:350px;" | Strip 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|40px30px]] 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 Excitation Materials, Sources, Devices & Other Physical Object Types]]'''.
== Defining Simulation Observables in EM.Cube ==
| 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
| style="width:250px;" | Far-Field Radiation Patterns
| Far-Field Radiation Pattern
| style="width:250px;" | [[EM.Tempo]], [[EM.Terrano|Em.TerranoPicasso]], [[EM.IlluminaLibera]], [[EM.PicassoIllumina]], [[EM.LiberaTerrano]]
|-
| style="width:250px;" | Radiation Characteristics (D0, HPBW, SLL, AR, etc.)
| Far-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)
| 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)
| style="width:250px;" | [[EM.Tempo]], [[EM.Picasso]]
|-
| style="width:250px;" | Temporal Electric and Magnetic Energies and Dissipated Power| Energy-Power| Domain style="width:250px;" | [[EM.Tempo]]|-| 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
| style="width:250px;" | [[EM.Ferma]]
|-
| style="width:250px;" | Resistance, Capacitance, Self-Inductanceand 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]]
|-
| style="width:250px;" | Channel Path Loss
| Receiver Set
| style="width:250px;" | [[EM.Terrano]]
| style="width:250px;" | [[EM.Terrano]]
|-
| style="width:250px;" | Channel Path Loss 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]]
| 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 |-| style="width:40px;" | [[image:po-ico.png | link=[[EM.Illumina]]]] | [[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|40px30px]] 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
#Volume Mesh
The linear mesh, also known as the wireframe mesh, 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 discretize surface geometric objects as well as the surface of solid 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. They are generated by a three-dimensional arrangement of grid lines along the X, Y and Z axes. [[EM.Tempo]] offers an "Adaptive" brick mesh as well as a "Fixed-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>
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 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 very much on the quality and resolution of the generated mesh. As a rule of thumb, a mesh density of about 10-30 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. Also, the The particular simulation data that 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:
| 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
|-
| style="width:40px;" | [[image:po-ico.png | link=[[EM.Illumina]]]]
| [[EM.Illumina]]
| style="width:450px;" | Triangular surface mesh
|-
| style="width:40px;" | [[image:static-ico.png | link=[[EM.Ferma]]]]
| [[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|40px30px]] Click here to access '''[[Glossary of EM.Cube's Mesh GeneratorsSimulation-Related Operations]]'''. <br /> <hr>
<p> </p>[[Image:Top_icon.png|48px30px]] '''[[Numerical_Modeling_of_Electromagnetic_Problems_Using_EM.Cube#A Review of Computational Electromagnetics An_Overview_of_Computational_Electromagnetics | Back to the Top of the Page]]'''
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