Solution to 3-D electromagnetic problems discretized by a hybrid FEM/MOM method

Li, Liang; Huang, Ting‐Zhu; Cheng, Guanghui; Jing, Yan-Fei; Ren, Zhigang; Li, Hong

doi:10.1016/j.cpc.2012.08.017

Cited by 7 publications

(5 citation statements)

References 28 publications

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“…Because of problems described above, dominant approach for coupling of BEM with FEM in computational electromagnetics is method of moments (MoM) coupled with edge‐element FEM 33–40 . MoM is a method in computational electromagnetics that relies on boundary integral equation, 41–43 and it is equivalent to BEM.…”

Section: Introductionmentioning

confidence: 99%

On the edge element boundary element method/finite element method coupling for time harmonic electromagnetic scattering problems

Dodig

Poljak

Cvetković

2021

Numerical Meth Engineering

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Over recent decades coupled MoM/FEM formulation emerged as dominant method for solving EM scattering problems over inhomogeneous domains. Initial efforts on coupling of edge element BEM with edge element FEM have lost momentum and somehow disappeared from recent literature, possibly because of mathematical and other issues. This article, however, presents correct coupling of edge element BEM with edge element FEM. Such coupling is convenient because edge basis functions are used for modeling both the surface and the interior of the problem. We show that singularity extraction is simpler when compared with singularity extraction in MoM/FEM. Because BEM part of edge element BEM/FEM formulation uses simpler Green's function, the method is easier to implement than MoM/FEM which uses Dyadic Green's functions. The accuracy of the method is demonstrated by comparison with Mie series and with MoM/FEM and MoM/VSIE methods. Convergence of the method with respect to number of surface and interior edges was investigated by comparing 20 computational models with Mie series. Computational results suggest that edge‐element BEM/FEM performs well for scattering problems involving objects with sharp corners. Finally, the ability of the method to cope with relatively large number of elements was demonstrated on the example of human head illuminated by 3.5 GHz EM plane wave.

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Section: Introductionmentioning

confidence: 99%

On the edge element boundary element method/finite element method coupling for time harmonic electromagnetic scattering problems

Dodig

Poljak

Cvetković

2021

Numerical Meth Engineering

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“…Electric fields e ∈ H(curl, Ω − ) that satisfy (27) ∀ψ ∈ H(curl, Ω − ) are exact solutions to the Maxwell equations in the heterogeneous domain. In the finite element method, e and ψ are restricted to a finitedimensional finite element space V h ⊂ H(curl, Ω − ), with h > 0 denoting the characteristic size of the mesh 6 elements, i.e., we are interested in approximate solutions e ∈ V h such that (27) holds ∀ψ ∈ V h .…”

Section: Finite Element Schur Complement Discretizationmentioning

confidence: 99%

“…With the bases {b j i } 1≤j≤Ni and {b j b } 1≤j≤N b of characteristic functions corresponding to the degrees of freedom in V h i and V h b , respectively, denote e i ∈ C Ni such that e i = j (e i ) j b j i (and likewise for e b ). This reduces (27), with e, ψ ∈ V h , to the following linear system:…”

Section: Finite Element Schur Complement Discretizationmentioning

confidence: 99%

“…In the finite element method, e and ψ are restricted to a finitedimensional finite element space V h ⊂ H(curl, Ω − ), with h > 0 denoting the characteristic size of the mesh 6 elements, i.e., we are interested in approximate solutions e ∈ V h such that (27) holds ∀ψ ∈ V h . Let us denote the subspace of finite elements with vanishing tangential trace as V h i = {e ∈ V h :n × e| Γ = 0}, which contains the finite elements associated to the N i = dim(V h i ) interior degrees of freedom, and a subspace denoted V h b , containing the finite elements associated to the N b = dim(V h b ) boundary degrees of freedom and isomorphic to the quotient space V h /V h i .…”

Section: Finite Element Schur Complement Discretizationmentioning

confidence: 99%

“…A wide class of preconditioners for hybrid FEM-BEM formulations exists [24][25][26][27][28], with an important subset of them relying on domain decomposition methods [29,30]. For the first time, a Calderón multiplicative preconditioner is applied to a reduced hybrid FEM-BEM formulation for electromagnetic scattering at a heterogeneous obstacle, and is compatible with existing matrix vector product acceleration schemes, such as the multilevel fast multipole algorithm (MLFMA) [31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

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A Calderón multiplicative preconditioner for the electromagnetic Poincaré–Steklov operator of a heterogeneous domain with scattering applications

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Zutter

Hese

et al. 2015

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In the context of hybrid formulations, the Poincaré-Steklov operator acting on traces of solutions to the vector Helmholtz equation in a heterogeneous interior domain with a smooth boundary is regularized by a well-known boundary integral operator related to the homogeneous exterior domain. For the first time, this property allows us to simultaneously construct a Calderón multiplicative preconditioner for the discretized operator and for a 3-D hybrid finite/boundary element method formulation, applicable to electromagnetic scattering problems. Numerical examples demonstrate the effectiveness of this novel preconditioning scheme, even for heterogeneous domains with non-smooth boundaries.

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Solution to 3-D electromagnetic problems discretized by a hybrid FEM/MOM method

Cited by 7 publications

References 28 publications

On the edge element boundary element method/finite element method coupling for time harmonic electromagnetic scattering problems

On the edge element boundary element method/finite element method coupling for time harmonic electromagnetic scattering problems

A Calderón multiplicative preconditioner for the electromagnetic Poincaré–Steklov operator of a heterogeneous domain with scattering applications

Modeling of Microwave Waveguide Systems of Complex Structure in Nonlinear Media

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