Approximate moment matrix decomposition in wavelet Galerkin BEM

Computer Methods in Applied Mechanics and Engineering

Volumn 197, Issue 45-48, 2008, Pages 4000-4006

  Xiao, Jinyou ^a   Tausch, Johannes ^b   Wen, Lihua ^a  

^a NORTHWESTERN POLYTECHNICAL UNIVERSITY   (China)

^b SOUTHERN METHODIST UNIVERSITY   (United States)

Author keywords

Galerkin BEM; Matrix compression; Non standard form; Quasi vanishing moments; Wavelets

Indexed keywords

BOUNDARY ELEMENT METHOD; CANNING; GALERKIN METHODS; INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; SINGULAR VALUE DECOMPOSITION; STANDARDS; WAVELET DECOMPOSITION;

ASYMPTOTIC CONVERGENCE; CUT-OFF; GALERKIN; GALERKIN BEM; GALERKIN SCHEME; INTEGRAL OPERATORS; LAYER POTENTIALS; MATRIX COMPRESSION; MEMORY USAGE; MOMENT MATRIX; NON-STANDARD FORM; NUMERICA L RESULTS; OPTIMAL CONVERGENCE RATE; POLYNOMIAL MOMENTS; QUASI-VANISHING MOMENTS; SINGULAR VALUE DECOMPOSITIONS; SINGULAR VALUES; SPARSE REPRESENTATIONS; STANDARD FORM; VANISHING MOMENTS; VARIABLE ORDER; WAVELET METHODS; WAVELETS;

CONVERGENCE OF NUMERICAL METHODS;

EID: 50049110846     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2008.03.015     Document Type: Article

References (17)

1. Beylkin G., Coifman R., and Rokhlin V. Fast wavelet transforms and numerical algorithms. Commun. Pure Appl. Math. 37 (1991) 141-183
2. Bebendorf M., and Rjasanow S. Adaptive low-rank approximation of collocation matrices. Computing 70 (2003) 1-24
3. Tausch J. A variable order wavelet method for the sparse representation of layer potentials in the non-standard form. J. Numer. Math. 12 3 (2004) 233-254
4. Greengard L., and Rokhlin V. A fast algorithm for particle simulations. J. Comput. Phys. 73 (1987) 325-348
5. Tausch J., and White J. Multiscale bases for the sparse representation of boundary integral operators on complex geometry. SIAM J. Sci. Comput. 24 5 (2003) 1610-1629
6. Tausch J. The variable order fast multipole method for boundary integral equations of the second kind. Computing 72 (2004) 267-291
7. Tausch J. Sparse BEM for potential theory and Stokes flow using variable order wavelets. Comput. Mech. 32 4-6 (2003) 312-319
8. Tausch J., and White J. Second-kind integral formulations for the capacitance problem. Adv. Comput. Math. 9 1 (1998) 217-232
9. 2-matrix approximation of integral operators by interpolation. Appl. Numer. Math. 43 (2002) 129-143
10. Harbrecht H., Kähler U., and Schneider R. Wavelet Galerkin BEM on unstructured meshes. Comput.Visual Sci. 8 (2005) 189-199
11. Schmidlin G., and Schwab C. Wavelet Galerkin BEM on unstructured meshes by aggregation. Multiscale and Multiresolution Methods. Lecture Notes in Computer Science and Engineering vol. 20 (2002), Springer, Berlin 359-378
12. Hackbusch W., and Nowak Z.P. On the fast matrix multiplication in the boundary element method by panel clustering. Numer. Math. 54 (1989) 463-491
13. von Petersdorff T., and Schwab C. Fully discrete multiscale Galerkin BEM. In: Dahmen W., Kurdila P., and Oswald P. (Eds). Wavelet Analysis and its Applications vol. 6 (1997), Academic Press, New York 287-346
14. Lage C., and Schwab C. Wavelet Galerkin algorithms for boundary integral equations. SIAM J. Sci. Comput. 20 (1999) 2195-2222
15. Dahmen W., Harbrecht H., and Schneider R. Compression techniques for boundary integral equations - optimal complexity estimates. SIAM J. Numer. Anal. 43 6 (2006) 2251-2271
16. Harbrecht H., and Schneider R. Wavelet Galerkin schemes for boundary integral equations - implementation and quadrature. SIAM J. Sci. Comput. 27 4 (2006) 1347-1370
17. Elschner J. The double-layer potential over polyhedral domains II: Spline Galerkin methods. Math. Methods Appl. Sci. 15 (1992) 23-27