Adaptive recompression of ℋ-matrices for BEM

Computing (Vienna/New York)

Volumn 74, Issue 3, 2005, Pages 205-223

  Grasedyck, L ^a,b  

^a Max Planck Institut für Mathematik in den Naturwissenschaften ^*

^b MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

Author keywords

Boundary elements; Data sparse approximations; Fast solvers; Formatted matrix operations; Hierarchical matrices; Preconditioning

Indexed keywords

BOUNDARY ELEMENTS; DATA-SPARSE APPROXIMATIONS; FAST SOLVERS; FORMATTED MATRIX OPERATIONS; HIERARCHICAL MATRICES; PRECONDITIONING;

ALGORITHMS; APPROXIMATION THEORY; BOUNDARY ELEMENT METHOD; FINITE ELEMENT METHOD; FUNCTIONS; HIERARCHICAL SYSTEMS; INTEGRAL EQUATIONS; LAPLACE TRANSFORMS; MATHEMATICAL OPERATORS;

MATRIX ALGEBRA;

EID: 18844454548     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00607-004-0103-1     Document Type: Conference Paper

References (21)

1. Bebendorf, M.: Approximation of boundary element matrices. Numer. Math. 86(4), 565-589 (2000).
2. Bebendorf, M.: Hierarchical LU decomposition based preconditioned for BEM. Technical Report 28, Max-Planck-Institute for Mathematics in the Sciences, 2004.
3. Bebendorf, M., Rjasanov, S.: Adaptive low-rank approximation of collocation matrices. Computing 70, 1-24 (2003).
4. 2-matrices, 1999. Available at http://www.hlib.org.
5. Börm, S., Grasedyck, L.: Low-rank approximation of integral operators by interpolation. Computing 72, 325-332 (2004).
6. Börm, S., Grasedyck, L., Hackbusch, W.: Introduction to hierarchical matrices with applications. Engineering Analysis with Boundary Elements 27, 405-422 (2003).
7. Dahmen. W., Schneider, R.: Wavelets on manifolds I: Construction and domain decomposition. SIAM J. Math Anal. 31, 184-230 (1999).
8. Sauter, S. A., Erichsen, S.: Efficient automatic quadrature in 3-D Galerkin BEM. Comput. Meth. Appl. Mech. Eng. 757, 215-224 (1998).
9. Grasedyck, L.: Theorie und Anwendungen hierarchischer Matrizen. PhD thesis, Universität Kiel 2001.
10. Grasedyck, L., Hackbusch, W.: Construction and arithmetics of ℋ-matrices. Computing 70, 295-334 (2003).
11. Greengard, L., Rokhlin, V.: A new version of the fast multipole method for the Laplace in three dimensions. In: Acta Numerica 1997, pp. 229-269. Cambridge University Press.
12. Hackbusch, W.: A sparse matrix arithmetic based on ℋ-matrices. Part I: Introduction to ℋ-matrices. Computing 62, 89-108 (1999).
13. Hackbusch, W., Khoromskij, B.: A sparse matrix arithmetic based on ℋ-matrices. Part II: Application to multi-dimensional problems. Computing 64, 21-47 (2000).
14. Hackbusch, W., Khoromskij, B., Kriemann, R.: Hierarchical matrices based on a weak admissibility criterion. Technical Report 2, Max-Planck-Institute for Mathematics in the Sciences 2003.
15. Computing 73, 207-243 (2004).
16. Hackbusch, W., Nowak, Z. P.: On the fast matrix multiplication in the boundary element method by panel clustering. Numer. Math. 54. 463-491 (1989).
17. Lintner, M.: The eigenvalue problem for the 2D Laplacian in ℋ-matrix arithmetic and application to the heat and wave equation. Computing 72. 293-323 (2004).
18. Rokhlin, V.: Rapid solution of integral equations of classical potential theory. J. Comput. Phys. 60, 187-207 (1985).
19. Saad, Y., Schultz, M.: GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist, Computing 7, 856-869 (1986).
20. Sauter, S. A.: Variable order panel clustering (extended version). Technical Report 52, Max-Planck-Institute for Mathematics in the Sciences, Leipzig, Germany. 1999.
21. Tyrtyshnikov, E.: Incomplete cross approximation in the mosaic-skeleton method. Computing 64, 367-380 (2000).