A Sophisticated Parallel MLFMA for Scattering by Extremely Large Targets [EM Programmer's Notebook]

The development of the MLFMA for realistic targets is currently at the stage where clever implementation, using a series of tricks based on the characteristics of the MLFMA and current computer technology, is required. A sophisticated parallel MLFMA for use on distributed-memory computers is presented as a whole picture of developing the program using a style of multilevel development in this paper. A series of implementation tricks for the parallel MLFMA are analyzed and compared. Particularly, a novel trick for reducing the truncation numbers is presented for extremely large targets, in the paper. These tricks are integrated into a sophisticated parallel MLFMA. The memory requirement and the CPU time for each part in each level are analyzed numerically by typical numerical experiments. The capability of this sophisticated parallel MLFMA is demonstrated by computing scattering by a sphere with a diameter of 480 wavelengths, containing around 130 million unknowns, and for a plane model with a fuselage of more than 1000 wavelengths, containing more than 72 million unknowns. These are the largest scattering problems ever solved by full-wave numerical methods, to our knowledge.

[1]  Julien Langou,et al.  Algorithm 842: A set of GMRES routines for real and complex arithmetics on high performance computers , 2005, TOMS.

[2]  Ozgur Ergul,et al.  Fast and accurate solutions of extremely large integral-equation problems discretised with tens of millions of unknowns , 2007 .

[3]  S. Velamparambil,et al.  Analysis and performance of a distributed memory multilevel fast multipole algorithm , 2005, IEEE Transactions on Antennas and Propagation.

[4]  X. Sheng,et al.  A Highly Efficient Parallel Approach of Multi-level Fast Multipole Algorithm , 2006 .

[5]  P. Havé.  A parallel implementation of the fast multipole method for Maxwell's equations , 2003 .

[6]  Michael S. Warren,et al.  Skeletons from the treecode closet , 1994 .

[7]  Eric Jui-Lin Lu,et al.  A massively parallel fast multipole algorithm in three dimensions , 1996, Proceedings of 5th IEEE International Symposium on High Performance Distributed Computing.

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

[9]  Ananth Grama,et al.  Scalable parallel formulations of the Barnes-Hut method for n-body simulations , 1994, Proceedings of Supercomputing '94.

[10]  S. Velamparambil,et al.  10 million unknowns: is it that big? [computational electromagnetics] , 2003, IEEE Antennas and Propagation Magazine.

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

[12]  Weng Cho Chew,et al.  A fast polynomial representation for the translation operators of an MLFMA , 2001 .

[13]  Weng Cho Chew,et al.  Scalable electromagnetic scattering computations , 2002, IEEE Antennas and Propagation Society International Symposium (IEEE Cat. No.02CH37313).

[14]  W.C. Chew,et al.  Solving large scale electromagnetic problems using a Linux cluster and parallel MLFMA , 1999, IEEE Antennas and Propagation Society International Symposium. 1999 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.99CH37010).

[15]  Jianming Jin,et al.  A higher order parallelized multilevel fast multipole algorithm for 3-D scattering , 2001 .

[16]  Jiming Song,et al.  Fast Illinois solver code (FISC) , 1998 .

[17]  Jian-Ming Jin,et al.  A novel implementation of multilevel fast multipole algorithm for higher order Galerkin's method , 2000 .

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

[19]  Lawrence Carin,et al.  Multilevel fast-multipole algorithm for scattering from conducting targets above or embedded in a lossy half space , 2000, IEEE Trans. Geosci. Remote. Sens..

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