Hierarchical parallelization of the multilevel fast multipole algorithm (MLFMA)

Due to its O(N log N) complexity, the multilevel fast multipole algorithm (MLFMA) is one of the most prized algorithms of computational electromagnetics and certain other disciplines. Various implementations of this algorithm have been used for rigorous solutions of large-scale scattering, radiation, and miscellaneous other electromagnetics problems involving 3-D objects with arbitrary geometries. Parallelization of MLFMA is crucial for solving real-life problems discretized with hundreds of millions of unknowns. This paper presents the hierarchical partitioning strategy, which provides a very efficient parallelization of MLFMA on distributed-memory architectures. We discuss the advantages of the hierarchical strategy over previous approaches and demonstrate the improved efficiency on scattering problems discretized with millions of unknowns.

[1]  J. Fostier,et al.  An Asynchronous Parallel MLFMA for Scattering at Multiple Dielectric Objects , 2008, IEEE Transactions on Antennas and Propagation.

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

[3]  Jan Fostier,et al.  Provably scalable parallel multilevel fast multipole algorithm , 2008 .

[4]  Ozgur Ergul,et al.  Benchmark solutions of large problems for evaluating accuracy and efficiency of electromagnetics solvers , 2011, 2011 IEEE International Symposium on Antennas and Propagation (APSURSI).

[5]  Jiming Song,et al.  Error Analysis for the Numerical Evaluation of the Diagonal Forms of the Scalar Spherical Addition Theorem , 1999 .

[6]  Luis Landesa,et al.  SUPERCOMPUTER AWARE APPROACH FOR THE SOLUTION OF CHALLENGING ELECTROMAGNETIC PROBLEMS , 2010 .

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

[8]  Ozgur Ergul,et al.  Accuracy: The frequently overlooked parameter in the solution of extremely large problems , 2011, Proceedings of the 5th European Conference on Antennas and Propagation (EUCAP).

[9]  Luis Landesa,et al.  MLFMA-FFT PARALLEL ALGORITHM FOR THE SO- LUTION OF LARGE-SCALE PROBLEMS IN ELECTRO- MAGNETICS (INVITED PAPER) , 2010 .

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

[11]  Jian-Ming Jin,et al.  Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies , 1998 .

[12]  L. Gurel,et al.  Accurate solutions of extremely large integral-equation problems in computational electromagnetics , 2013 .

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

[14]  Ozgur Ergul,et al.  Hierarchical parallelisation strategy for multilevel fast multipole algorithm in computational electromagnetics , 2008 .

[15]  L. Gurel,et al.  Rigorous Solutions of Electromagnetic Problems Involving Hundreds of Millions of Unknowns , 2011, IEEE Antennas and Propagation Magazine.

[16]  Jan Fostier,et al.  Full-wave electromagnetic scattering at extremely large 2-D objects , 2009 .

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

[18]  Xiao-Min Pan,et al.  A Sophisticated Parallel MLFMA for Scattering by Extremely Large Targets [EM Programmer's Notebook] , 2008, IEEE Antennas and Propagation Magazine.

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

[20]  J. Fostier,et al.  A fast 2‐D parallel multilevel fast multipole algorithm solver for oblique plane wave incidence , 2011 .

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

[22]  B. Shanker,et al.  A Scalable Parallel Wideband MLFMA for Efficient Electromagnetic Simulations on Large Scale Clusters , 2011, IEEE Transactions on Antennas and Propagation.

[23]  Jan Fostier,et al.  An Open-Source Implementation for Full-Wave 2D Scattering by Million-Wavelength-Size Objects , 2010, IEEE Antennas and Propagation Magazine.

[25]  L. Gurel,et al.  Efficient Parallelization of the Multilevel Fast Multipole Algorithm for the Solution of Large-Scale Scattering Problems , 2008, IEEE Transactions on Antennas and Propagation.

[26]  Xin-Qing Sheng,et al.  On Openmp Parallelization of the Multilevel Fast Multipole Algorithm , 2011 .

[27]  Zaw Zaw Oo,et al.  Parallel multilevel fast multipole method for solving large-scale problems , 2005 .

[28]  L. Gurel,et al.  A Hierarchical Partitioning Strategy for an Efficient Parallelization of the Multilevel Fast Multipole Algorithm , 2009, IEEE Transactions on Antennas and Propagation.