An adaptive fast direct solver for boundary integral equations in two dimensions

Applied and Computational Harmonic Analysis

Volumn 31, Issue 3, 2011, Pages 346-369

  Kong, Wai Yip ^a   Bremer, James ^b   Rokhlin, Vladimir ^a  

^a YALE UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Boundary value problems; Fast solvers; Integral equations; Laplace's equation; Layer potentials

Indexed keywords

ASYMPTOTIC COMPLEXITY; DIRECT SOLUTION; DIRECT SOLVERS; DISCRETIZATIONS; FAST SOLVERS; LAPLACE'S EQUATIONS; LAYER POTENTIALS; LINEAR ALGEBRAIC SYSTEMS; NUMERICAL EXAMPLE; PARAMETER SPACES; POTENTIAL THEORY; TWO-DIMENSION; TWO-POINT;

ALGORITHMS; BOUNDARY VALUE PROBLEMS; INTEGRAL EQUATIONS; LAPLACE EQUATION; LAPLACE TRANSFORMS;

BOUNDARY INTEGRAL EQUATIONS;

EID: 80052954708     PISSN: 10635203     EISSN: 1096603X     Source Type: Journal    
DOI: 10.1016/j.acha.2011.01.008     Document Type: Article

References (27)

1. Å. Björck Numerical Methods for Least Squares Problems 1996 SIAM Philadelphia
2. J. Carrier, L. Greengard, and V. Rokhlin A fast adaptive multipole algorithm for particle simulations SIAM J. Sci. Stat. Comput. 9 4 1988 669 686
3. G. Chandler Galkerin's method for boundary integral equations on polygonal domains J. Aust. Math. Soc., Ser. B 26 1984 1 13
4. S. Chandrasekaran, M. Gu, and T. Pals A fast ULV decomposition solver for hierarchically semi-separable representations SIAM J. Matrix Anal. Appl. 28 3 August 2006 603 622 (Pubitemid 47109352)
5. Y. Chen A fast direct algorithm for the Lippmann-Schwinger integral equation in two dimensions Adv. Comput. Math. 16 2-3 2002 175 190 (Pubitemid 37130931)
6. n 2 algorithm for the multiple scattering solution of n scatterers Micro. Optical Tech. Lett. 2 1989 380 383 (Pubitemid 20632596)
7. R. Coifman, and Y. Meyer Wavelets: Calderón-Zygmund and Multilinear Operators 1997 Cambridge University Press
8. G. Folland Introduction to Partial Differential Equations 1976 Princeton University Press Princeton, NJ
9. D. Gines, G. Beylkin, and J. Dunn LU factorization of non-standard forms and direct multiresolution solvers Appl. Comput. Harmon. Anal. 5 2 1998 156 201 MR99c:65087 (Pubitemid 128419936)
10. G. Golub, and C.V. Loan Matrix Computations second edition 1989 Johns Hopkins University Press Baltimore
11. L. Greengard, and V. Rokhlin A fast algorithm for particle simulations J. Comput. Phys. 73 1987 325 348
12. Ming Gu, and Stanley C. Eisenstat Efficient algorithms for computing a strong rank-revealing QR factorization SIAM J. Sci. Comput. 17 4 1996 848 869 MR 97h:65053 (Pubitemid 126621180)
13. W. Hackbusch A sparse matrix arithmetic based on H-matrices. I. Introduction to H-matrices Computing 62 2 1999 89 108 MR 2000c:65039
14. H 2-matrices Computing 69 1 2002 1 35 MR 1 954 142
15. J. Helsing, and R. Ojala Corner singularities for elliptic problems: Integral equations, graded meshes, quadrature, and compressed inverse preconditioning J. Comput. Phys. 227 2008
16. T. Hrycak, and V. Rokhlin An improved fast multipole algorithm for potential fields SIAM J. Sci. Comput. 19 6 1998 1804 1826 (Pubitemid 128614420)
17. O. Kellog Foundations of Potential Theory 1953 Dover New York
18. C. Kenig Elliptic boundary value problems on Lipschitz domains Beijing Lectures in Harmonic Analysis Ann. of Math. Stud. 112 1986 131 183
19. R. Kress A Nyström method for boundary integral equations in domains with corners Numer. Math. 58 1990 145 161
20. R. Kress Integral Equations 1999 Springer-Verlag New York
21. P.G. Martinsson, and V. Rokhlin A fast direct solver for boundary integral equations in two dimensions J. Comput. Phys. 205 2005 1 23
22. S. Mikhlin Integral Equations 1957 Pergamon Press New York
23. V. Rokhlin Rapid solution of integral equations of classical potential theory J. Comput. Phys. 60 1983 187 207
24. P. Starr, and V. Rokhlin On the numerical solution of two-point boundary value problems II Comm. Pure Appl. Math. 47 1994 1117 1159
25. J. Stoer, and R. Bulirsch Introduction to Numerical Analysis second edition 1993 Springer-Verlag
26. G. Verchota Layer potentials and boundary value problems for Laplace's equation in Lipschitz domains J. Funct. Anal. 59 1984 572 611
27. F. Woolfe, E. Liberty, V. Rokhlin, and M. Tygert A fast randomized algorithm for the approximation of matrices Appl. Comput. Harmon. Anal. 25 2008 335 366