A domain decomposition approach for non-conformal couplings between finite and boundary elements for unbounded electromagnetic problems in R3

This paper presents a symmetric FEM-BEM formulation for solving unbounded three-dimensional electromagnetic problems. The approach is based on domain decomposition method that decomposes original problem into FEM and BEM domains. Two domains communicate through Robin transmission condition enforced on the interface between these two domains. The meshes on the interface are non-matching (non-conformal), thus two domains can be modularly treated. The resulting system matrix is symmetric and free of internal resonances. To accelerate the convergence of iterative solvers, three Schwarz type preconditioners are proposed. An ad hoc proof of convergence for the proposed Robin interface between FEM and BEM is also included for spherical outer boundaries. The efficiency and performance of the proposed approach with three different preconditioners are demonstrated through a few numerical examples.

[1]  X. Yuan.  Three-dimensional electromagnetic scattering from inhomogeneous objects by the hybrid moment and finite element method , 1990 .

[2]  D. Hoppe,et al.  A hybrid symmetric FEM/MOM formulation applied to scattering by inhomogeneous bodies of revolution , 1994 .

[3]  Din-Kow Sun,et al.  Construction of Nearly Orthogonal Nedelec Bases for Rapid Convergence with Multilevel Preconditioned Solvers , 2001, SIAM J. Sci. Comput..

[4]  Ralf Hiptmair,et al.  Symmetric Coupling for Eddy Current Problems , 2002, SIAM J. Numer. Anal..

[5]  Jin-Fa Lee,et al.  p-Type multiplicative Schwarz (pMUS) method with vector finite elements for modeling three-dimensional waveguide discontinuities , 2004 .

[6]  J. Nédélec.  Mixed finite elements in ℝ3 , 1980 .

[7]  J. D. Collins,et al.  A finite-element-boundary-integral method for scattering and radiation by two- and three-dimensional structures , 1991, IEEE Antennas and Propagation Magazine.

[8]  Jin-Fa Lee,et al.  A symmetric FEM-IE formulation with a single-level IE-QR algorithm for solving electromagnetic radiation and scattering problems , 2004, IEEE Transactions on Antennas and Propagation.

[9]  Bruno Stupfel,et al.  A hybrid finite element and integral equation domain decomposition method for the solution of the 3-D scattering problem , 2001 .

[10]  Jin-Fa Lee,et al.  Analysing microwave devices using a symmetric coupling of finite and boundary elements , 2005 .

[11]  Jin-Fa Lee,et al.  A non-overlapping domain decomposition method with non-matching grids for modeling large finite antenna arrays , 2005 .

[12]  Sergej Rjasanow,et al.  Adaptive Low-Rank Approximation of Collocation Matrices , 2003, Computing.

[13]  Jianming Jin,et al.  A novel hybridization of higher order finite element and boundary integral methods for electromagnetic scattering and radiation problems , 2001 .

[14]  Martin Costabel,et al.  Symmetric Methods for the Coupling of Finite Elements and Boundary Elements (Invited contribution) , 1987 .

[15]  T. Cwik.  Coupling finite element and integral equation solutions using decoupled boundary meshes [electromagn , 1992 .

[16]  Jin-Fa Lee,et al.  A fast IE-FFT algorithm for solving PEC scattering problems , 2005 .

[17]  M. Vouvakis,et al.  The adaptive cross approximation algorithm for accelerated method of moments computations of EMC problems , 2005, IEEE Transactions on Electromagnetic Compatibility.

[18]  X. Yuan,et al.  Coupling of finite element and moment methods for electromagnetic scattering from inhomogeneous objects , 1990 .

[19]  D. Wilton,et al.  Electromagnetic scattering by surfaces of arbitrary shape , 1980 .

[20]  Ralf Hiptmair,et al.  Coupling of Finite Elements and Boundary Elements in Electromagnetic Scattering , 2003, SIAM J. Numer. Anal..

[21]  W. Chew.  Waves and Fields in Inhomogeneous Media , 1990 .

[22]  Jian-Ming Jin,et al.  Fast and Efficient Algorithms in Computational Electromagnetics , 2001 .

[23]  Jin-Fa Lee,et al.  Adaptive mesh refinement, h-version, for solving multiport microwave devices in three dimensions , 2000 .

[24]  Jian-Ming Jin,et al.  A highly effective preconditioner for solving the finite element-boundary integral matrix equation of 3-D scattering , 2002 .

[25]  R. Hiptmair,et al.  Galerkin Boundary Element Methods for Electromagnetic Scattering , 2003 .