Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects

The fast multipole method (FMM) and multilevel fast multipole algorithm (MLFMA) are reviewed. The number of modes required, block-diagonal preconditioner, near singularity extraction, and the choice of initial guesses are discussed to apply the MLFMA to calculating electromagnetic scattering by large complex objects. Using these techniques, we can solve the problem of electromagnetic scattering by large complex three-dimensional (3-D) objects such as an aircraft (VFY218) on a small computer.

[1]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

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

[3]  V. Rokhlin.  Rapid solution of integral equations of classical potential theory , 1985 .

[4]  Piet Hut,et al.  A hierarchical O(N log N) force-calculation algorithm , 1986, Nature.

[5]  L. Hernquist.  Hierarchical N-body methods , 1987 .

[6]  Leslie Greengard,et al.  A fast algorithm for particle simulations , 1987 .

[7]  Leslie Greengard,et al.  The fast mutipole method for gridless particle simulation. , 1987 .

[8]  V. Rokhlin.  Rapid Solution of Integral Equations of Scattering Theory , 1990 .

[9]  A. Brandt.  Multilevel computations of integral transforms and particle interactions with oscillatory kernels , 1991 .

[10]  Christopher R. Anderson,et al.  An Implementation of the Fast Multipole Method without Multipoles , 1992, SIAM J. Sci. Comput..

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

[12]  Radiation and scattering from complex three-dimensional geometries using a curvilinear hybrid finite element-integral equation approach , 1993 .

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

[14]  W.C. Chew,et al.  A fast algorithm for solving hybrid integral equation , 1993, Proceedings of IEEE Antennas and Propagation Society International Symposium.

[15]  V. Rokhlin.  Diagonal Forms of Translation Operators for the Helmholtz Equation in Three Dimensions , 1993 .

[16]  S. Wandzura,et al.  Scattering computation using the fast multipole method , 1993, Proceedings of IEEE Antennas and Propagation Society International Symposium.

[17]  Weng Cho Chew,et al.  Fast algorithm for solving hybrid integral equations , 1993 .

[18]  Weng Cho Chew,et al.  A ray‐propagation fast multipole algorithm , 1994 .

[19]  Amir Boag,et al.  Multilevel evaluation of electromagnetic fields for the rapid solution of scattering problems , 1994 .

[20]  Weng Cho ChewDepartment.  A Multilevel Algorithm for Solving Boundary Integral Equation , 1994 .

[21]  Jiming Song,et al.  Fast multipole method solution using parametric geometry , 1994 .

[22]  Raj Mittra,et al.  Complex multipole beam approach to electromagnetic scattering problems , 1994 .

[23]  Nicolaos G. Alexopoulos,et al.  Scattering from complex three-dimensional geometries by a curvilinear hybrid finite-element–integral equation approach , 1994 .

[24]  F. Canning.  Solution of impedance matrix localization form of moment method problems in five iterations , 1995 .

[25]  Weng Cho Chew,et al.  Moment method solutions using parametric geometry , 1995 .

[26]  Weng Cho Chew,et al.  A study of wavelets for the solution of electromagnetic integral equations , 1995 .

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

[28]  Fast Multipole Method Solution of Combined Field Integral Equation , 1995 .

[29]  Michael A. Epton,et al.  Multipole Translation Theory for the Three-Dimensional Laplace and Helmholtz Equations , 1995, SIAM J. Sci. Comput..

[30]  J. CARRIERt,et al.  A FAST ADAPTIVE MULTIPOLE ALGORITHM FOR PARTICLE SIMULATIONS * , 2022 .