10 million unknowns: Is it that big?

IEEE Antennas and Propagation Magazine

Volumn 45, Issue 2, 2003, Pages 43-58

  Velamparambil, Sanjay ^b   Chew, Weng Cho ^a   Song, Jiming ^c  

^a University of Illinois at Urbana Champaign   (United States)

^b Ansoft Corporation   (United States)

^c Iowa State University of Science and Technology   (United States)

Author keywords

Electromagnetic scattering; Fast multiple method; Integral equations; Matrix decomposition; Matrix inversion; Message passing; MLFMA; Parallel algorithms; Radar cross sections

Indexed keywords

DATA COMMUNICATION SYSTEMS; INTEGRAL EQUATIONS; INVERSE PROBLEMS; MATRIX ALGEBRA; PARALLEL ALGORITHMS; PARALLEL PROCESSING SYSTEMS; PROBLEM SOLVING; RADAR CROSS SECTION;

MATRIX DECOMPOSITION; MATRIX INVERSION; MESSAGE PASSING; MULTILEVEL FAST MULTIPOLE ALGORITHM;

ELECTROMAGNETIC WAVE SCATTERING;

EID: 0038383220     PISSN: 10459243     EISSN: None     Source Type: Journal    
DOI: 10.1109/MAP.2003.1203119     Document Type: Article

References (29)

1. J. M. Song, C. C. Lu, and W. C. Chew, "MLFMA for Electromagnetic Scattering from Large Complex Objects," IEEE Transactions on Antennas and Propagation, 45, October 1997, pp. 1488-1493.
2. J. M. Song and W. C. Chew, "The Fast Illinois Solver Code: Requirements and Scaling Properties," IEEE Computational Science and Engineering, 5, 3, 1998, pp. 19-23.
3. V. Kumar, A. Grama, A. Gupta, and G. Karypis, Introduction to parallel Computing: Design and Analysis of Algorithms, Redwood City, CA, The Benjamin/Cummings Publishing Company, Inc., 1994
4. B. Dembart and E. Yip, "A 3D Fast Multipole Method for Electromagnetics with Multiple Levels," 11th Annual Review of Progress in Applied Computational Electromagnetics, Monterey, CA, Volume 1, March 1995, pp. 621-628.
5. B. Dembart and E. Yip, "The Accuracy of Fast Multipole Methods for Maxwell's Equations," IEEE Computational Science and Engineering, 5, 3, 1998, pp. 48-56.
6. M.A. Epton and B. Dembart, "Multipole Translation Theory for the Three Dimensional Laplace and Helmholtz Equations," SIAM Journal of Scientific Computing, 16, July 1995, pp. 865-897.
7. V. Rokhlin, "Diagonal Forms of Translation Operators for the Helmholtz Equation in Three Dimensions," Applied and Computational Harmonic Analysis, 1, 1993, pp. 82-93.
8. R. Coifman, V. Rokhlin, and S. Wandzura, "The Fast Multipole Method for the Wave Equation: A Pedestrian Prescription," IEEE Antennas and Propagation Magazine, 35, June 1993, pp. 7-12.
9. C.-C. Lu and W. C. Chew, "A Multilevel Algorithm for Solving a Boundary Integral Equation of Wave Scattering," Microwave and Optical Technology Letters, 7, July 1994, pp. 466-470.
10. S. Velamparambil and W.C. Chew, "A Fast Polynomial Representation for the Translation Operators of MLFMA," Microwave and Optical Technology Letters, March 2001.
11. J. Song, C. Lu, W. Chew, and S. Lee, "Fast Illinois Solver Code," IEEE Antennas and Propagation Magazine, 40, June 1998, pp. 27-34.
12. S. Velamparambil and W.C. Chew, "Parallelization of Multilevel Fast Multiple Algorithm on Distributed Memory Computers," Tech. Rep. 13-01, Center for Computational Electromagnetics, University of Illinois at Urbana-Champaign, 2001 (under the review of Parallel Computing).
13. S. Velamparambil, W. C. Chew, and L. Hastriter, "Scalable Electromagnetic Scattering Computations," IEEE International Symposium on Antennas and Propagation Digest, volume 3, 2002, pp. 176-179.
14. M. S. Warren, D. J. Becker, M. Goda, J. Salmon, and T. Sterling, "Parallel Supercomputing with Commodity Components," in H. Arbania (ed.), International Conference on Parallel and Distributed Processing Techniques and Applications (PPTA'97), 1997, pp. 1372-1381.
15. J. M. Song and W. C. Chew, "Multilevel Fast Multipole Algorithm for Solving Combined Field Integral Equations of Electromagnetic Scattering," Microwave and Optical Technology Letters, 10, September 1995, pp. 14-19.
16. S. Velamparambil, J. M. Song, and W. C. Chew, "ScaleME: A Portable, Distributed Memory Multilevel Fast Multipole Kernel for Electromagnetic and Acoustic Integral Equation Solvers," Tech. Rep. CCEM-23-99, Center for Computational Electromagnetics, Dept. of Electrical and Computer Engineering, University of Illinois of Urbana-Champaign, Urbana, IL, 1999.
17. S. M. Rao, D. R. Wilton, and A. W. Glisson, "Electromagnetic Scattering by Surfaces of Arbitrary Shape," IEEE Transactions on Antennas and Propagation, 30, May 1982, pp. 409-418.
18. Y. Saad and M. H. Schultz, "GMRES: A Generalised Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems," SIAM Journal of Scientific and Statistical Computing, 7, 1986, pp. 856-869.
19. A. Christie, Murder on the Orient Express, Berkeley Publication Group, 2000.
20. V. Frayssé, L. Giraud, and S. Gratton, "A Set of GMRES Routines for Real and Complex Arithmetics," Tech. Rep. TR/PA/97-49, CERFACS, France, 1997.
21. T. H. Cormen, C. E. Leiserson, and R. L. Rivest, Introduction to Algorithms, New York, McGraw-Hill Book, Company 1990.
22. W. C. Chew, J.-M. Jin, E. Michielssen, and J. M. Song (eds.), Fast and Efficient Algorithms in Computational Electromagnetics, Norwood, MA, Artech House, 2001.
23. H. T. G. Wang, M. L. Sanders, and A. C. Woo, "Radar Cross Section Measurement Data of the VFY 218 Configuration," NAWCWPNS TM 7621, January 1994.
24. S. Velamparambil and W. C. Chew, "Fast Polynomial Representations for the Diagonal Translation Operators of the Three Dimensional Helmholtz Equation," Tech. Rep. CCEM-17-99, Center for Computational Electromagnetics, Dept. of Electrical and Computer Engineering, University of Illinois at Urbana- Champaign, Urbana, IL, 1999.
25. S. Koc, J.M. Song, and W. C. Chew, "Error Analysis for the Numerical Evaluation of the Diagonal Forms of the Scalar Spherical Addition Theorem," SIAM Journal of Numerical Analysis, 36, 3, 1999, pp. 906-921.
26. J. M. Song and W. C. Chew, "Error Analysis for the Truncation of Multipole Expansion of Vector Green's Function," IEEE International Symposium on Antennas and Propagation Digest, Volume 1, 1999, (Orlando, Florida), pp. 628-631.
27. S. V. Velamparambil, J. E. Schutt-Aine, J. G. Nickel, J. M. Song, and W. C. Chew, "Solving Large Scale Electromagnetic Problems Using a Linux Cluster and Parallel MLFMA," IEEE International Symposium on Antennas and Propagation Digest, Volume 1, July 1999, pp. 636-639.
28. U2, Joshua Tree, 1987.
29. J. M. Song and W. C. Chew, "Interpolation of Translation Matrix in MLFMA," Microwave and Optical Technology Letters, 30, July 2001, pp. 109-114.