Fast solution of problems with multiple load cases by using wavelet-compressed boundary element matrices

This paper presents a fast approach for rapidly solving problems with multiple load cases using the boundary element method (BEM). The basic idea of this approach is to assemble the BEM matrices separately and to compress them using fast wavelet transforms. Using a technique called ‘virtual assembly...

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Bibliographic Details
Published in:Communications in numerical methods in engineering 2003-05, Vol.19 (5), p.387-399
Main Authors: Bucher, Henrique F., Wrobel, Luiz C., Mansur, Webe J., Magluta, Carlos
Format: Article
Language:English
Subjects:
boundary element method
Boundary-integral methods
Computational techniques
Exact sciences and technology
fast solvers
Mathematical methods in physics
matrix compression
Physics
wavelet transforms
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Summary:This paper presents a fast approach for rapidly solving problems with multiple load cases using the boundary element method (BEM). The basic idea of this approach is to assemble the BEM matrices separately and to compress them using fast wavelet transforms. Using a technique called ‘virtual assembly’, the matrices are then combined inside an iterative solver according to the boundary conditions of the problem, with no need for recompression each time a new load case is solved. This technique does not change the condition number of the matrices—up to a small variation introduced by compression—so that previous theoretical convergence estimates are still valid. Substantial savings in computer time are obtained with the present technique. Copyright © 2003 John Wiley & Sons, Ltd.
ISSN:1069-8299
1099-0887
DOI:10.1002/cnm.598