Recompression techniques for adaptive cross approximation

Journal of Integral Equations and Applications

Volumn 21, Issue 3, 2009, Pages 331-357

  Bebendorf, M ^a   Kunis, S ^b  

^a UNIVERSITY OF BONN   (Germany)

^b CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Adaptive cross approximation; Hierarchical matrices; Integral equations

Indexed keywords

EID: 79952898667     PISSN: 08973962     EISSN: None     Source Type: Journal    
DOI: 10.1216/JIE-2009-21-3-331     Document Type: Article

References (22)

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. Comput., 14, (1993), 159-184.
2. M. Bebendorf, Approximation of boundary element matrices, Numer. Math., 86, (2000), 565-589.
3. B. K. Alpert, Effiziente numerische L̈osung von Randintegralgleichungen unter Verwendung von Niedrigrang-Matrizen PhD thesis, Universiẗat Saarbr̈ucken, (2000). dissertation.de, Verlag im Internet, (2001). ISBN 3-89825-183-7.
4. B. K. Alpert, Hierarchical LU decomposition based preconditioners for BEM. Computing, 74, (2005), 225-247.
5. B. K. Alpert , Hierarchical matrices: a means to efficiently solve elliptic boundary value problems, volume 63 of Lecture Notes in Computational Science and Engineering. Springer, (2008).
6. M. Bebendorf and R. Grzhibovskis, Accelerating Galerkin BEM for Linear Elasticity using Adaptive Cross Approximation, Mathematical Methods in the Applied Sciences, 29, (2006), 1721-1747.
7. M. Bebendorf and S. Rjasanow, Adaptive low-rank approximation of collocation matrices, Computing, 70, (2003), 1-24.
8. S. B̈orm, Construction of data-sparse H2-matrices by hierarchical compression, Technical Report 92, Max-Planck-Institute MiS, Leipzig, (2007), SISC 31 (2009, 1820-1839.
9. S. B̈orm, N. Krzebek, and S. A. Sauter, May the singular integrals in BEM be replaced by zero?, Computer Methods in Applied Mechanics and Engineering, 194, (2005), 383-393.
10. S. B̈orm,M. L̈ohndorf, and J.M. Melenk, Approximation of integral operators by variable-order interpolation, Numer. Math., 99, (2005), 605-643.
11. R. A. DeVore and G. G. Lorentz, Constructive Approximation, Springer- Verlag, Berlin, (1993).
12. S. A. Goreinov, E. E. Tyrtyshnikov, and N. L. Zamarashkin, A theory of pseudoskeleton approximations, Linear Algebra Appl., 261, (1997), 1-21.
13. L. Grasedyck, Adaptive recompression of H-matrices for BEM, Computing, 74 (2005), 205-223.
14. L. Grasedyck and W. Hackbusch, Construction and arithmetics of Hmatrices, Computing, 70, (2003), 295-334.
15. L. F. Greengard and V. Rokhlin, A new version of the fast multipole method for the Laplace equation in three dimensions, In Acta numerica, Cambridge Univ. Press, volume 6, (1997), 229-269.
16. A. Grundmann and H. M. M̈oller, Invariant integration formulas for the n-simplex by combinatorial methods, SIAM J. Numer. Anal., 15 ,(1978), 282-290.
17. W. Hackbusch, A sparse matrix arithmetic based on H-matrices, Part I: Introduction to H-matrices. Computing, 62, (1999), 89108.
18. W. Hackbusch and S. B̈orm, Data-sparse approximation by adaptive H2- matrices, Computing, 69, (2002), 1-35.
19. W. Hackbusch and B. N. Khoromskij, A sparse H-matrix arithmetic, Part II: Application to multi-dimensional problems. Computing, 64, (2000), 21-47.
20. W. Hackbusch, B. N. Khoromskij, and S. A. Sauter, On H2-matrices, In H.-J. Bungartz, R. H. W. Hoppe, and Ch. Zenger, editors, Lectures on Applied Mathematics, pages 9-29. Springer-Verlag, Berlin, (2000).
21. W. Hackbusch and Z. P. Nowak, On the fast matrix multiplication in the boundary element method by panel clustering, Numer. Math., 54, (1989), 463-491.
22. A. Scḧonhage, Approximationstheorie, de Gruyter, Berlin, (1971).