Multipole Fast Algorithm for the Least-Squares Approach of the Method of Fundamental Solutions for Three-dimensional Harmonic Problems

Numerical Methods for Partial Differential Equations

Volumn 19, Issue 6, 2003, Pages 828-845

  Saavedra, I ^a   Power, H ^b  

^a UNIVERSIDAD CENTRAL DE VENEZUELA   (Venezuela)

^b UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

3D harmonic problem; Method of fundamental solution; Multipole fast algorithm

Indexed keywords

EID: 0242340540     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/num.10071     Document Type: Article

References (32)

1. 1 M. A. Golberg and C. S. Chen, The method of fundamental solutions for potential, Helmholtz and diffusion problems, M. Goldberg, editor, Boundary integral methods numerical and mathematical aspects, WIT Press Computational Mechanics Publications, Southampton, 1999.
2. 2 V. D. Kupradze and M. A. Aleksidze, The method of functional equations for the approximate solution of certain boundary value problems, U.S.S.R. Computat Math Math Phys 4 ( 1964), 82–126.
3. 3 A. Bogomolny, Fundamental solutions method for elliptic boundary value problems, SIAM J Numer Anal 22 ( 1985), 644–669.
4. 4 R. L. Johnston and G. Fairweather, The method of fundamental solutions for problems in potential flow, Appl Math Modelling 8 ( 1984), 265–270.
5. 5 M. Katsurada and H. Okamoto, The collocation points of the fundamental solution method for the potential problem, Comput Math Appl 31 (1) ( 1996), 123–137.
6. 6 P. S. Han, M. D. Olsen, and R. L. Johnson, An adaptive boundary element method, Intl J Numer Methods Eng 24 ( 1987), 1187–1202.
7. 7 M. A. Golberg and C. S. Chen, Discrete projection methods for integral equations, Computational Mechanics Publications, Southampton, 1996.
8. 8 T. Kitagawa, On the numerical stability of the method of fundamental solutions applied to Dirichlet problem, Jpn J Appl Math 35 ( 1988), 507–518.
9. 9 T. Kitagawa, Asymptotic stability of the fundamental solution method, J Comput Appl Math 38 ( 1991), 263–269.
10. 10 M. A. Golberg, C. S. Chen, and S. R. Karur, Improved multiquadric approximation for partial differential equations, Eng Anal Boundary Elements 18 ( 1996), 9–17.
11. 11 T. F. Chan and D. Foulser, Effectively well‐conditioned linear systems, SIAM J Sci Stat Comput 9 ( 1988), 963–969.
12. 12 R. S. C. Cheng, Delta‐trigonometric and spline methods using the single layer potential representation, Ph.D. dissertation, University of Maryland, 1987.
13. 13 M. Katsurada and H. Okamoto, A mathematical study of the charge simulation method, Journal of the Faculty of Science, University of Tokyo, Section 1A 35 ( 1988), 507–518.
14. 14 M. Katsurada, Asymptotic error analysis of the charge simulation method in a Jordan region with an analytic boundary, Journal of the Faculty of Science, University of Tokyo, Section 1A 37 ( 1990), 635–657.
15. 15 V. Rokhlin, Rapid solution of integral equations of classical potential theory, J Comput Phys 60 ( 1985), 187–207.
16. 16 Y. Saad and M. H. Shultz, GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J Sci Stat Comput 7 (3) ( 1986), 856–869.
17. 17 J. E. Gomez and H. Power, A multipole direct and indirect BEM for 2D cavity flow at low Reynolds number, Eng Anal Boundary Elements 19 ( 1997), 17–31.
18. 18 A. A. Mammoli and M. S. Ingber, Stokes flow around cylinders in a bounded two‐dimensional domain using multipole‐accelerated boundary element methods', Intl J Numer Methods Eng 44 (7) ( 1999), 897–917.
19. 19 V. Popov and H. Power, An O(N) Taylor series multipole boundary element method for three‐dimensional elasticity problems, Eng Anal Boundary Elements 25 ( 2001), 7–18.
20. 20 J. E. Barnes and P. Hut, A hierarchical O(N Log N) force calculation algorithm, Nature 324 (4) ( 1986), 446–449.
21. 21 L. Greengard and V. Rokhlin, A fast algorithm for particle simulation, J Comput Phys 73 ( 1987), 325–348.
22. 22 J. F. Leathrum and J. A. Board, The parallel fast multipole algorithm in three dimensions, Technical Report 92‐001, Duke University Department of Electrical Engineering, 1992.
23. 23 J. A. Board, Z. S. Hakura, W. S. Elliot, and W. T. Rankin, Scalable variants of multipole‐accelerated algorithms for molecular dynamics, Technical Report 94‐006, Duke University Dept of Electrical Engineering, 1994.
24. 24 J. A. Board and W. S. Elliot, Fast fourier transform accelerated fast multipole algorithm, Technical Report 94‐001, Duke University Dept of Electrical Engineering, 1994.
25. 25 W. D. Elliott, Multipole algorithms for molecular dynamics simulation on high performance computers, Technical Report 95‐003, Duke University Department of Electrical Engineering, 1995.
26. 26 A. Z. Zinchenko and R. H. Davis, Shear flow of highly concentrated emulsions of deformable drops by numerical simulations, J Fluid Mech 455 ( 2002), 21–62.
27. 27 G. H. Golub and C. F. Van Loan, Matrix computations, 3rd ed., Johns Hopkins Series in the Mathematical Sciences, Johns Hopkins University Press, 1996.
28. 28 W. H. Press, S. A. Teukolsky, and W. T. Vetterling, Numerical recipes in Fortran, Cambridge University Press, Cambridge, Chap. 2, 15, 1992.
29. 29 Å. Björck, Numerical methods for least squares problems, SIAM Society for Industrial & Applied Mathematics, 1996.
30. 30 C. Paige and M. Saunders, LSQR, an algorithm for sparse linear equations and sparse least squares, ACM Transactions on Mathematical Software 8 (1) ( 1982), 43–71.
31. 31 L. Greengard, The rapid evaluation of potential fields in particle systems, MIT Press, Cambridge, MA, 1988.
32. 32 L. Greengard, M. C. Kropiniski, and A. Mayo, Integral methods for Stokes flow and isotropic elasticity in the plane, J Comput Phys 125 ( 1996), 403–414.