Numerical Modeling of Electromagnetic Problems Using EM.Cube

Computational Electromagnetics

The electric field excited above a battleship illuminated by a plane wave source.

Mathematically speaking, all electromagnetic modeling problems require solving some form of Maxwell's equations in conjunction with 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.

Click here for a brief review of Maxwell's Equations.

Click here to learn more about Numerical Techniques for Solving Maxwell's Equations.

Using a numerical method to solve a certain electromagnetic modeling problem typically involves a recurring sequence of steps:

• Geometrical construction of the physical structure and material assignments
• Definition of the computational domain and boundary conditions
• Definition of excitation sources
• Definition of observables
• Geometrical reduction and mesh generation

The above steps reduce your original physical problem to a numerical 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 in electromagnetic modeling: "Does one really need more than one simulation engine? A true challenge of electromagnetic modeling is the right choice of numerical technique for any given problem. Depending on the electrical length scales and physical nature of your problem, some modeling techniques may provide more accurate or computationally more efficient solutions 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 your 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.

EM.Tempo is EM.Cube's general-purpose EM simulator than can handle most types of modeling problems involving arbitrary geometries and complex material variations in both time and frequency domains.

An Overview of EM.Cube's Numerical Solvers

EM.Cube uses a number of computational electromagnetic (CEM) techniques to solve your modeling problems. All of these techniques are based on a fine discretization of your physical structure into a set of elementary cells or elements. A discretized form of Maxwell's equations or some variations of them are then solved numerically over these smaller cells. From the resulting numerical solution, the quantities of interest are derived and computed.

The numerical techniques used by EM.Cube are:

• Finite Different Time Domain (FDTD) method
• Shoot-and-Bounce-Rays (SBR) method
• Physical Optics (PO) method: Geometrical Optics - Physical Optics (GO-PO) method and Iterative Physical Optics (IPO) emthod
• Mixed Potential Integral Equation (MPIE) method for multilayer planar structures
• Wire Method of Moments (WMOM) based on Pocklington integral equation
• Surface Method of Moments (SMOM) with Adaptive Integration Equation (AIM) accelerator
• Finite Difference (FD) method solution of electrostatic and magnetostatic Laplace/Poisson equations

Module Name	Simulation Engine(s)	Solver Type	Modeling Accuracy	Frequency Range	Fundamental Solution
EM.Tempo	FDTD	Volumetric solver	Full-wave	Ultra-wideband time-domain	Electric and magnetic fields in the entire domain
EM.Terrano	SBR	Ray tracer	Asymptotic	High-frequency harmonic	Electric field ray tubes and power received at receiver locations
EM.Illumina	GO-PO & IPO	Surface solver	Asymptotic	High-frequency harmonic	Electric and magnetic currents on surfaces
EM.Ferma	FD	Volumetric solver	Static or quasi-static	DC or low-frequency	Electric or magnetic fields in the entire domain
EM.Picasso	MPIE	Planar solver	Full-wave	Arbitrary harmonic	Electric and magnetic currents on traces
EM.Libera	WMOM & SMOM	Surface & wire solvers	Full-wave	Arbitrary harmonic	Electric and magnetic currents on surfaces or wires

Module Name	Material Capability	Excitation/Sources	Lumped Devices
EM.Tempo	PEC, PMC, dielectric, anisotropic, dispersive, complex materials	Lumped and distributed sources, plane wave, Gaussian beam, arbitrary waveform	Passive and active, linear and nonlinear devices and circuits
EM.Terrano	Material surfaces, thin walls and material volumes	Transmitters, Hertzian dipoles	N/A
EM.Illumina	PEC, PMC, impedance surfaces	Hertzian dipole, plane wave, Huygens source	N/A
EM.Ferma	PEC, dielectric or magnetic materials	Charge, current and permanent magnet	N/A
EM.Picasso	PEC and slot traces, short vias, infinite substrate layers	Gap source, wave port, Hertzian dipole, plane wave, Huygens source	Simple passive RLC lumped elements
EM.Libera	PEC, homogeneous dielectric	Gap source, Hertzian dipole, plane wave, Huygens source	Simple passive RLC lumped elements

Module Name	Observables	Applications
EM.Tempo	Near-field, far-field, RCS, periodic R/T, S/Z/Y parameters, port current/voltage/power	General-purpose field simulator capable of handling complex geometrical and material variations
EM.Terrano	Far-field & received power	Radio wave propagation in very large scenes
EM.Illumina	Far-field & RCS	Scattering from very large surface structures & antenna-platform combinations
EM.Ferma	Electric or magnetic field & potential, voltage, current, energy, power	Small-scale devices and structures
EM.Picasso	Current distribution, far-field, periodic R/T, S/Z/Y parameters	Multilayer planar circuits, antennas & arrays, FSS, homogeneous substrates
EM.Libera	Current distribution, far-field, RCS, S/Z/Y parameters	Radiation and scattering problems involving metals and homogeneous dielectric materials