Parallel hierarchical solvers and preconditioners for boundary element methods

SIAM Journal on Scientific Computing

Volumn 20, Issue 1, 1998, Pages 337-358

  Grama, Ananth ^a   Kumar, Vipin ^b   Sameh, Ahmed ^a  

^a Purdue University   (United States)

^b University of Minnesota   (United States)

Author keywords

Barnes Hut method; Boundary element method; Dense iterative solver; Fast multipole method; Hierarchical dense matrix vector product; Parallel treecode; Preconditioning boundary element methods

Indexed keywords

BARNES-HUT METHOD; FAST MULTIPOLE METHODS; HIERARCHICAL APPROXIMATION TECHNIQUES; PARALLEL HIERARCHICAL SOLVERS;

APPROXIMATION THEORY; BOUNDARY ELEMENT METHOD; COMPUTATIONAL COMPLEXITY; CONVERGENCE OF NUMERICAL METHODS; GREEN'S FUNCTION; INTEGRAL EQUATIONS; METHOD OF MOMENTS; PARALLEL PROCESSING SYSTEMS;

ITERATIVE METHODS;

EID: 0032131422     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827596313322     Document Type: Article

References (31)

1. B. K. ALPERT, G. BEYLKIN, R. COIFMAN, AND V. ROKHLIN, Wavelet-like bases for the fast solution of second-kind integral equations, SIAM J. Sci. Statist. Comput., 14 (1993), pp. 159-184.
2. A. W. APPEL, An efficient program for many-body simulation, SIAM J. Sci. Statist. Computing, 6 (1985), pp. 85-103.
3. J. BARNES AND P. HUT, A hierarchical O(n log n) force calculation algorithm, Nature, 324 (1986), pp. 446-449.
4. G. BEYLKIN, R. COIFMAN, AND V. ROKHLIN, Fast wavelet transforms and numerical algorithms i, Comm. Pure Appl. Math., 44 (1991) pp. 141-183.
5. S. BINDIGANAVALE AND J. L. VOLAKIS, Guidelines for using the fast multipole method to calculate the RCS of large objects, Microwave and Optical Tech. Letters, 11 (1996).
6. J. A. BOARD, J. W. CAUSEY, J. F. LEATHRUM, A. WINDEMUTH, AND K. SCHULTEN, Accelerated molecular dynamics with the fast multipole algorithm, Chem. Phys. Let., 198 (1992), p. 89.
7. A. BRANDT AND A. A. LUBRECHT, Multilevel matrix multiplication and fast solution of integral equations, J. Comput. Phys., 90 (1990), pp. 348-370.
8. A. BRANDT, Multilevel computations of integral transforms and particle interactions with oscillatory kernels, Comput. Phys. Comm., 65 (1991), pp. 24-38.
9. F. X. CANNING, Sparse approximation for solving integral equations with oscillatory kernels, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 71-87.
10. A. GRAMA, V. KUMAR, AND A. SAMEH, Parallel iterative solvers and preconditioners using approximate hierarchical methods, in Proc. Copper Mountain Conference on Iterative Methods, Copper Mountain, CO, 1996.
11. A. GRAMA, V. KUMAR, AND A. SAMEH, Scalable parallel formulations of the Barnes-Hut method for n-body simulations, in Proc. Supercomputing '94, Washington, DC, 1994.
12. A. GRAMA, V. KUMAR, AND A. SAMEH, Parallel hierarchical solvers and preconditioners for boundary element methods, in Proc. Supercomputing '96, Pittsburgh, PA, 1996. Best student paper award finalist at Supercomputing '96.
13. A. GRAMA, V. KUMAR, AND A. SAMEH, Parallel matrix-vector product using hierarchical methods, in Proc. Supercomputing '95, San Diego, CA, 1995.
14. A. GRAMA, V. KUMAR, AND A. SAMEH, On n-body simulations using message passing parallel computers, in Proc. SIAM Conference on Parallel Processing, San Francisco, 1995.
15. L. GREENGARD AND W. GROPP, A parallel version of the fast multipole method, Comput. Math. Appl., 20 (1990), pp. 63-71.
16. L. GREENGARD AND V. ROKHLIN, A fast algorithm for particle simulations, J. Comput. Physics, 73 (1987), pp. 325-348.
17. L. GREENGARD AND J. STRAIN, A fast algorithm for the evaluation of heat potentials, Comm. Pure Appl. Math, 43 (1990), pp. 949-963.
18. V. KUMAR, A. GRAMA, A. GUPTA, AND G. KARYPIS, Introduction to Parallel Computing: Algorithm Design and Analysis, Benjamin Cummings/Addison-Wesley, Redwood City, CA, 1994.
19. J. F. LEATHRUM AND J. A. BOARD, Mapping the adaptive fast multipole algorithm into mimd systems, in Unstructured Scientific Computation on Scalable Multiprocessors, P. Mehrotra and J. Saltz, eds., MIT Press, Cambridge, MA, 1992.
20. K. NABORS, S. KIM, AND J. WHITE, Fast capacitance extraction, of general three dimensional structures, IEEE Trans. Microwave Theory and Techniques, 40 (1992), pp. 1496-1506.
21. K. NABORS, F. T. KORSMEYER, F. T. LEIGHTON, AND J. WHITE, Preconditioned, adaptive, multipole-accelerated iterative methods for three-dimensional first-kind integral equations of potential theory, SIAM J. Sci. Comput, 15 (1994), pp. 713-735.
22. V. ROKHLIN, Rapid solution of integral equations of classical potential theory, J. Comput. Phys., 60 (1985), pp. 187-207.
23. V. ROKHLIN, Rapid solutions of integral equations of scattering theory in two dimensions, J. Comput. Phys., 86 (1990), pp. 414-439.
24. Y. SAAD AND M. SCHULTZ, GMRES: A generalized minimal residual algorithm for solving non-symmetrical linear systems, SIAM J. Sci. Statist. Comput., 3 (1986), pp. 856-869.
25. K. E. SCHMIDT AND M. A. LEE, Implementing the fast multipole method in three dimensions, J. Statist. Phys., 63 (1991) p. 1120.
26. J. SINGH, C. HOLT, T. TOTSUKA, A. GUPTA, AND J. HENNESSY, Load balancing and data locality in adaptive hierarchical n-body methods: Barnes-Hut, fast multipole, and radiosity, Journal of Parallel and Distributed Computing, 27 (1995), pp. 118-141.
27. J. M. SONG AND W. C. CHEW, Fast multipole method solution of three dimensional integral equation, in IEEE Antennas and Propagation Society International Symposium 1995 Digest, IEEE, Piscataway, NJ, 1995.
28. J. M. SONG AND W.C. CHEW, Multilevel fast multipole algorithm for solving combined field integral equation of electromagnetic scattering, Microwave and Optical Tech. Letters, 10 (1995) pp. 14-19.
29. M. S. WARREN AND J. K. SALMON, Astrophysical N-body simulations using hierarchical tree data structures, in Proc. Supercomputing '92, Minneapolis, MN, 1992, IEEE Comp. Soc. Press, Los Alamitos, CA, 1992, pp. 570-576.
30. M. S. WARREN AND J. K. SALMON, A parallel hashed oct-tree N-body algorithm, in Proc. Supercomputing '93, Washington, DC, 1993, IEEE Comp. Soc. Press', Los Alamitos, CA, 1993, pp. 12-21.
31. F. ZHAO AND S. L. JOHNSSON, The parallel multipole method on the connection machine, SIAM J. Sci. Stat. Comput., 12 (1991), pp. 1420-1437.