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Nested multigrid vector and scalar potential finite element method for three‐dimensional time‐harmonic electromagnetic analysis
Author(s) -
Zhu Yu,
Cangellaris Andreas C.
Publication year - 2002
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/2001rs002484
Subject(s) - multigrid method , preconditioner , finite element method , scalar (mathematics) , solver , iterative method , conjugate gradient method , mathematics , computational electromagnetics , mixed finite element method , computer science , mathematical analysis , mathematical optimization , electromagnetic field , partial differential equation , geometry , physics , quantum mechanics , thermodynamics
A new finite element methodology is presented for fast and robust numerical simulation of three‐dimensional electromagnetic wave phenomena. The new methodology combines nested multigrid techniques with the ungauged vector and scalar potential formulation of the finite element method. The finite element modeling is performed on nested meshes over the computational domain of interest. The iterative solution of the finite element matrix on the finest mesh is performed using the conjugate gradient method, while the nested multigrid vector and scalar potential algorithm acts as the preconditioner for the iterative solver. Numerical experiments from the application of the new methodology to three‐dimensional electromagnetic scattering are used to demonstrate its superior numerical convergence and efficient memory usage.