An IE‐ODDM Scheme Combined With Efficient Direct Solver for 3D Scattering Problems

An improved scheme of integral equation-based overlapped domain decomposition method combined with an efficient direct solver based on hierarchical LU (H-LU) decomposition is proposed for the three-dimensional (3D) scattering problems. In this scheme, the H-LU direct method is utilized to solve the self-impedance matrix equation in each extended subdomain; simultaneously, the multilevel fast multipole algorithm is applied to complete the matrix vector product operation of mutual-impedance matrix between different subdomains. In the H-LU operation, a recompressed adaptive cross approximation technique is used to generate the low-rank approximations of the far-field matrices. After integrating all the techniques, the proposed scheme is very efficient especially for 3D electromagnetic scattering problems with multiple incident fields such as the computation of the monostatic radar cross section. Some examples are provided to demonstrate its accuracy and efficiency. © 2013 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:2027–2033, 2013

[1]  K. Michalski,et al.  Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media. I. Theory , 1990 .

[2]  Sabine Le Borne,et al.  H-matrix Preconditioners in Convection-Dominated Problems , 2005, SIAM J. Matrix Anal. Appl..

[3]  R. Coifman,et al.  The fast multipole method for the wave equation: a pedestrian prescription , 1993, IEEE Antennas and Propagation Magazine.

[4]  Jiming Song,et al.  Multilevel fast‐multipole algorithm for solving combined field integral equations of electromagnetic scattering , 1995 .

[5]  Dan Jiao,et al.  An H-matrix-based method for reducing the complexity of integral-equation-based solutions of electromagnetic problems , 2008, 2008 IEEE Antennas and Propagation Society International Symposium.

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

[7]  Hou-Xing Zhou,et al.  Integral equation‐based overlapped domain decomposition method for the analysis of electromagnetic scattering of 3D conducting objects , 2007 .

[8]  Hou-Xing Zhou,et al.  An IE-ODDM-MLFMA Scheme With DILU Preconditioner for Analysis of Electromagnetic Scattering From Large Complex Objects , 2008, IEEE Transactions on Antennas and Propagation.

[9]  Wolfgang Hackbusch,et al.  Construction and Arithmetics of H-Matrices , 2003, Computing.

[10]  Mario Bebendorf,et al.  Approximation of boundary element matrices , 2000, Numerische Mathematik.

[11]  Dan Jiao,et al.  A complexity-reduced H-matrix based direct integral equation solver with prescribed accuracy for large-scale electrodynamic analysis , 2010, 2010 IEEE Antennas and Propagation Society International Symposium.

[12]  M. Benzi.  Preconditioning techniques for large linear systems: a survey , 2002 .

[13]  V. Rokhlin,et al.  The fast multipole method (FMM) for electromagnetic scattering problems , 1992 .

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

[15]  Allen W. Glisson,et al.  Electromagnetic Scattering by Surface of Arbitrary Shape. , 1980 .

[16]  Jiming Song,et al.  Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects , 1997 .

[17]  Krzysztof A. Michalski,et al.  Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media. II. Implementation and results for contiguous half-spaces , 1990 .

[18]  W. Hackbusch.  A Sparse Matrix Arithmetic Based on $\Cal H$-Matrices. Part I: Introduction to ${\Cal H}$-Matrices , 1999, Computing.

[19]  Weng Cho Chew,et al.  A multilevel algorithm for solving a boundary integral equation of wave scattering , 1994 .

[20]  Sabine Le Borne,et al.  ℋ-matrices for Convection-diffusion Problems with Constant Convection , 2003, Computing.

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

[22]  W. Hong,et al.  A Cube-Based Scheme of IE-ODDM-MLFMA for Electromagnetic Scattering Problems , 2009, IEEE Antennas and Wireless Propagation Letters.

[23]  Xiao Qing Hu,et al.  Hierarchical LU decomposition‐based direct method with improved solution for 3D scattering problems in FEM , 2011 .

[24]  Stefan Kurz,et al.  The adaptive cross-approximation technique for the 3D boundary-element method , 2002 .