FAST SOLUTION OF BEM SYSTEMS FOR ELASTICITY PROBLEMS USING WAVELETS

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EBRAHIMNEZHAD L.; ATARNEZHAD R.

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Journal: Year:2008 | Volume:41 | Issue:6 (108) Page(s): 663-673

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Title

FAST SOLUTION OF BEM SYSTEMS FOR ELASTICITY PROBLEMS USING WAVELETS

Author(s)

EBRAHIMNEZHAD L. | ATARNEZHAD R. | Issue Writer Certificate

Keywords

BOUNDARY ELEMENT METHODQ2

ELASTICITY PROBLEMSQ3

GMRES SOLVERQ3

WAVELET TRANSFORMQ3

Abstract

This paper describes a fast approach for solving ELASTICITY PROBLEMS using BOUNDARY ELEMENT METHOD. The key idea is based on compressing matrices, to sparsify them, using fast WAVELET TRANSFORMs. Wavelet compression technique is successfully used to overcome the main drawback of BEM, dense and fully populated matrices. Compactly supported orthogonal wavelets have been used to compress matrices arising from applying BEM to practical engineering problems, which could be added as a black box to existing BEM codes. Dense and fully populated matrices arising from BEM have been changed to semi banded sparse matrices by applying wavelets and permutation matrices at the same time. Applying permuted wavelets converts dense matrices arising from BEM to semi-banded and sparse ones like what are encountered in FEM. Transforming matrices from the physical variables to wavelet basis needs much less computational effort than that saved by solving sparse linear system. Transformed linear system is solved by iterative GMRES SOLVER. Numerical results including a precise study on threshold parameter, solution accuracy for displacements and stresses and savings in computer time and memory are presented. High speed-ups are achieved for large problems without significant loss of accuracy. Compression ratio is tested by different thresholding parameter to optimize the method. The proposed method works on the final linear algebraic system then, it could be used in any other numerical method, which leads to linear equations. The results demonstrate the competence of the method in terms of both computation time and memory requirements and since wavelet technique is used as a black box in the existing BEM code, the results encourage application of the combined wavelet-BEM codes to analyze practical engineering problems.

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APA: Copy

EBRAHIMNEZHAD, L., & ATARNEZHAD, R.. (2008). FAST SOLUTION OF BEM SYSTEMS FOR ELASTICITY PROBLEMS USING WAVELETS. JOURNAL OF FACULTY OF ENGINEERING (UNIVERSITY OF TEHRAN), 41(6 (108)), 663-673. SID. https://sid.ir/paper/14103/en

Vancouver: Copy

EBRAHIMNEZHAD L., ATARNEZHAD R.. FAST SOLUTION OF BEM SYSTEMS FOR ELASTICITY PROBLEMS USING WAVELETS. JOURNAL OF FACULTY OF ENGINEERING (UNIVERSITY OF TEHRAN)[Internet]. 2008;41(6 (108)):663-673. Available from: https://sid.ir/paper/14103/en

IEEE: Copy

L. EBRAHIMNEZHAD, and R. ATARNEZHAD, “FAST SOLUTION OF BEM SYSTEMS FOR ELASTICITY PROBLEMS USING WAVELETS,” JOURNAL OF FACULTY OF ENGINEERING (UNIVERSITY OF TEHRAN), vol. 41, no. 6 (108), pp. 663–673, 2008, [Online]. Available: https://sid.ir/paper/14103/en

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