Fast wavelet BEM for 3d electromagnetic shaping

Applied Numerical Mathematics

Volumn 54, Issue 3-4, 2005, Pages 537-554

  Eppler, Karsten ^a   Harbrecht, Helmut ^b  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

^b UNIVERSITY OF KIEL   (Germany)

Author keywords

Boundary element methods; Shape optimization; Wavelets

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; ELECTROMAGNETISM; FOURIER TRANSFORMS; GRADIENT METHODS; HARMONIC ANALYSIS; LEVITATION MELTING; LIQUID METALS; MAGNETIC FIELDS; OPTIMIZATION; WAVELET TRANSFORMS;

ELECTROMAGNETIC SHAPING; FOURIER SERIES; SHAPE OPTIMIZATION; WAVELETS;

BOUNDARY ELEMENT METHOD;

EID: 20444507207     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2004.09.018     Document Type: Conference Paper

References (23)

1. M. Bebendorf, and S. Rjasanow Adaptive low-rank approximation of collocation matrices Computing 70 1 2003 1 24
2. O. Colaud, and A. Henrot Numerical approximation of a free boundary problem arising in electromagnetic shaping SIAM J. Numer. Anal. 31 1994 1109 1127
3. D. Colton, and R. Kress Integral Equation Methods in Scattering Theory Pure and Applied Mathematics 1983 Wiley Chichester
4. M. Crouzeix Variational approach of magnetic shaping problem European J. Mech. B Fluids 10 1991 527 536
5. M. Crouzeix, Ph. Feat, and F.-J. Sayas Theoretical and numerical study of a free boundary problem by boundary integral methods Modél. Math. Anal. Numér. 35 6 2001 1137 1158
6. W. Dahmen, H. Harbrecht, R. Schneider, Compression techniques for boundary integral equations - Optimal complexity estimates, Preprint SFB 393/02-06, TU Chemnitz, 2002, SIAM J. Numer. Anal., submitted for publication
7. W. Dahmen, A. Kunoth, and K. Urban Biorthogonal spline-wavelets on the interval - stability and moment conditions Appl. Comput. Harm. Anal. 6 1999 259 302
8. K. Eppler, and H. Harbrecht Numerical solution of elliptic shape optimization problems using wavelet-based BEM Optim. Methods Software 18 2003 105 123
9. K. Eppler, H. Harbrecht, 2nd order shape optimization using wavelet BEM, Preprint 06-2003, TU Berlin, 2003, Optim. Methods Software, submitted for publication
10. K. Eppler, H. Harbrecht, Exterior electromagnetic shaping using wavelet BEM, Preprint 13-2003, TU Berlin, 2003, Math. Methods Appl. Sci., in press
11. P.E. Gill, W. Murray, and M.H. Wright Practical Optimization 1981 Academic Press New York
12. L. Greengard, and V. Rokhlin A fast algorithm for particle simulation J. Comput. Phys. 73 1987 325 348
13. Ch. Grossmann, and J. Terno Numerik der Optimierung 1993 Teubner Stuttgart
14. 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
15. H. Harbrecht, Wavelet Galerkin Schemes for the Boundary Element Method in Three Dimensions, Ph.D. Thesis, Technische Universität Chemnitz, Germany, 2001
16. H. Harbrecht, R. Schneider, Wavelet Galerkin schemes for boundary integral equations - Implementation and quadrature, Preprint SFB 393/02-21, Technische Universität Chemnitz, Germany, 2002, SISC, submitted for publication
17. H. Harbrecht, and R. Schneider Biorthogonal wavelet bases for the boundary element method Math. Nach. 269-270 2004 167 188
18. A. Henrot, and M. Pierre About existence of equilibria in electromagnetic casting Quart. Appl. Math. 49 3 1991 563 575
19. A. Novruzi, Contribution en Optimisation des Formes et Applications, Ph.D. Thesis, Nancy, 1997
20. A. Novruzi, J.-R. Roche, Second derivatives, Newton method, application to shape optimization, INRIA-report No. 2555, 1995
21. M. Pierre, and J.-R. Roche Numerical Simulation of tridimensional electromagnetic shaping of liquid metals Numer. Math. 65 1993 203 217
22. R. Schneider Multiskalen- und Wavelet-Matrixkompression: Analysisbasierte Methoden zur Lösung großer vollbesetzter Gleichungssysteme 1998 Teubner Stuttgart
23. J. Sokolowski, and J.-P. Zolesio Introduction to Shape Optimization 1992 Springer Berlin