Electromagnetics and Multiphysics
Modeling and Simulation
Thermal Expansion of RF Solenoid
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There are many numerical methods that have been developed to solve
Maxwell’s equations. The three most-widely used methods are:
◆ Method of Moments (MoM) / Boundary Element Method (BEM)
◆ Finite Element Method (FEM)
◆ Finite-Difference Time-Domain (FDTD) Method
Many commercial CEM codes have been developed around particular methods, and, of course, each method has its strengths and weaknesses. Historically,
the codes themselves had their strengths and weaknesses that were
associated with the strengths and weaknesses of underlying numerical
Recognizing these differences, software developers have been addressing the shortcomings of their numerical techniques of choice. This work has led to an effective blurring of the differences between various commercial simulation packages. Furthermore, many companies started to apply multiple methods
in their packages, sometimes combining two or more methods into hybrid methods. In addition, complementary simulation techniques have been
developed to address the weaknesses of some methods, most notably,
effective formulation of unbounded (open) problems.
As a result, detailed comparison of the various methods, which used to be an important factor in selecting software packages, is much less important now. Below is a reference list of various numerical methods used for solving
Generalized Multipole Technique (GMT)
Similar to MOM/BEM, but the basis functions are chosen to satisfy Maxwell's equations at some distance away from the boundaries, rather than on the boundaries.
Time-Domain Method of Moments (TD-MoM)
Essentially, MoM formulated in time domain rather than in frequency domain.
Finite-Volume Time-Domain (FVTD) Technique
The FVTD technique is based on the integral form of Maxwell's curl equations.
The FVTD method solves the equations numerically by integrating them over
a volume that has been meshed into arbitrarily-shaped elements;
consequently, the resulting meshes can be unstructured. FVTD combines the strengths of both FDTD and FEA methods. Unbounded problems can be
are two main varieties of this technique: (1) the time-dependent Maxwell’s equations are discretized which leads to a generalization for FDTD method for unstructured meshes, (2) one of the field variables is eliminated from the Maxwell’s equations which leads to second-order (curl-curl) equations which
in turn are discretized.
Finite-Difference Frequency-Domain (FDFD) Technique
Physical Optics (PO)
Uniform Theory of Diffraction (UTD)
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