Multiwavelets for second-kind integral equations

SIAM Journal on Numerical Analysis

Volumn 34, Issue 6, 1997, Pages 2212-2227

  Von Petersdorff, Tobias ^a   Schwab, Christoph ^b   Schneider, Reinhold ^c  

^a Bldg 142   (United States)

^b ETH ZURICH   (Switzerland)

^c DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Boundary element methods; Integral equations; Wavelets

Indexed keywords

EID: 0001100395     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142994272957     Document Type: Article

References (33)

1. 2 for the sparse representation of integral operators, SIAM J. Math. Anal., 24 (1993), pp. 246-262.
2. B. ALPERT, G. BEYLKIN, R. COIFMAN, AND V, ROKHLIN, Waveletlike bases for the fast solution of second-kind integral equations, SIAM J. Sci. Statist. Comput., 14 (1993), pp. 159-184.
3. G. BBYLKIN, R. COIFMAN, AND V. ROKHLIN, Fast wavelet transforms and numerical algorithms I, Comm. Pure and Appl. Math., 44 (1991), pp. 141-183.
4. A. BRANDT AND A.A. LUBRECHT, Multilevel matrix multiplication and fast solution of integral equations, J. Comp. Phys., 90 (1991), pp. 348-370.
5. C.K. CHUI, An Introduction to Wavelets, Academic Press, New York, 1992.
6. A. COHEN, I. DAUBECHIES, AND J.-C. FEAUVEAU, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math., 45 (1992), pp. 485-560.
7. R. COIFMAN, Adapted multiresolution analysis, computation, signal processing and operator theory, in Proc. Internat. Congress of Mathematicians, Kyoto, Japan, 1990, pp. 879-887.
8. M. COSTABEL, Principles of boundary element methods, Comp. Phys. Reports, 6 (1987), pp. 243-274.
9. M. COSTABEL AND W.L. WENDLAND, Strongly elliptic boundary integral equations, J. Reine Angew. Math., 372 (1986), pp. 34-63.
10. W. DAHMEN AND A. KUNOTH, Multilevel preconditioning, Numer. Math., 63 (1992), pp. 315-344.
11. W. DAHMEN, S. PRÖSSDORF, AND R. SCHNEIDER, Wavelet approximation methods for pseudodifferential equations I: Stability and convergence, Math. Z., 215 (1994), pp. 583-620.
12. W. DAHMEN, S. PRÖSSDORF, AND R. SCHNEIDER, Wavelet approximation methods for pseudodifferential equations II: Matrix compression and fast solution, Adv. Comput. Math., 1 (1993), pp. 259-335.
13. W. DAHMEN, S. PRÖSSDORF, AND R. SCHNEIDER, Multiscale methods for pseudo-differential equations, in Wavelet Anal. Appl. 3, L.L. Schumaker and G. Webb, eds., Academic Press, Boston, 1994, pp. 191-235.
14. W. DAHMEN, B. KLEEMANN, S. PRÖSSDORF, AND R. SCHNEIDER, A multiscale method for the double layer potential equation on a polyhedron, in Advances in Computational Mathematics, H.P. Dikshit and C.A. Micchelli, eds., World Scientific, Singapore, 1994, pp. 15-57.
15. I. DAUBECHIES, Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics 61, SIAM, Philadelphia, PA, 1992.
16. R.A. DEVORE AND B.J. LUCIER, Wavelets, Acta Numerica, 1 (1991), pp. 1-56.
17. J. ELSCHNER, The double layer potential operator over polyhedral domains II: Spline Galerkin methods, Math. Meth. Appl. Sci., 15 (1992), pp. 23-37.
18. S. JAFFARD, Wavelet methods for fast resolution of elliptic problems, SIAM J. Numer. Anal., 29 (1992), pp. 965-987.
19. W. HACKBUSCH AND Z.P. NOWAK, On the fast matrix multiplication in the boundary element method by panel clustering, Numer. Math., 54 (1989), pp. 463-491.
20. A. HARTEN AND I. YAD-SHALOM, Fast Multiresolution Algorithm for Matrix-Vector Multiplication, ICASE Report No. 92-55, Hampton, VA, 1992.
21. S. HILDEBRANDT AND E. WIENHOLTZ, Constructive proofs of representation theorems in separable Hilbert spaces, Comm. Pure Appl. Math., 17 (1964), pp. 369-373.
22. L. HÖRMANDER, The Analysis of Linear Partial Differential Operators III, Grundlehren Math. Wiss., Springer-Verlag, Berlin, 1985.
23. J. KOHN AND L. NIRENBERG, On the algebra of pseudo-differential operators, Comm. Pure Appl. Math., 18 (1965), pp. 269-305.
24. H. KUMANO-GO, Pseudodifferential Operators, MIT Press, Boston, 1981.
25. Y. MEYER, Ondelettes et opérateurs. Vol. 1: Ondelettes, Vol. 2: Opérateurs de Caldéron-Zygmund, Hermann and Cie., Paris, 1990.
26. Y. MEYER AND R.R. COIFMAN, Ondelettes et opérateurs. Vol. 3: Opérateurs multilinéaires, Hermann and Cie., Paris, 1991.
27. P. OSWALD: On function spaces related to finite element approximation theory, Z. Anal. Anwendungen, 9 (1990), pp. 43-64.
28. T. VON PETERSDORFF, AND C. SCHWAB, Wavelet approximation for first kind boundary integral equations on polygons, Numer. Math., 74 (1996), pp. 479-516.
29. A. RATHSFELD, A wavelet algorithm for the solution of the double layer potential equation over polygonal boundaries, J. Int. Equations Oper. Theory, 7 (1995), pp. 47-98.
30. V. ROKHLIN, Rapid solution of integral equation equations of classical potential theory, J. Comp. Phys., 60 (1985), pp. 187-207.
31. M.A. SHUBIN, Pseudodifferential Operators and Spectral Theory, Springer-Verlag, Berlin, 1985.
32. M.E. TAYLOR, Pseudodifferential Operators, Princeton University Press, Princeton, NJ, 1981.
33. W.L. WENDLAND, On asymptotic error analysis and underlying mathematical principles for boundary element methods, in Boundary Element Techniques in Computer Aided Engineering, C.A. Brebbia, ed., NATO ASI Series E 84, Martinus Nijhoff, Dordrecht, Boston, Lancaster, 1984, pp. 417-436.