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| THE FMM-MFS SOLUTON TO TWO-DIMENSINAL SCATTERING OF ELASTIC WAVES |
| This paper presents a new algorithm of the fast multipole fundamental solution method（FMM-MFS）for calculating two-dimensional elastic wave scattering problems. It avoids the singularity of the matrix by placing the line sources of compressional wave and shear wave on a virtual boundary based on single layer potential theory. Additionally, there is no need of elements discretization on the boundary. Combining with the FMM, MFS can solve large-scale problems of wave scattering by greatly reducing the computation and the memory requirement. Taking the two-dimensional scattering of P, SV waves around a cavity in elastic full-space as an example, the implement procedure are presented in detail, and up to millions DOF’s scattering problem are solved successfully on a personal computer. Based on the test of accuracy and efficiency of FMM-MFS, the scattering of plane waves by a cavity as well as random distributed group cavities in full-space are solved. Finally, several important conclusions about scattering of elastic waves around cavity(cavities) are obtained. |
1.Department of Civil Engineering, Tianjin Chengjian University, Tianjin 300384, China;
2.Key Laboratory of Soft Soils and Engineering Environmental of Tianjin Province, Tianjin 300384, China
3.Department of Civil Engineering, Tianjin University, Tianjin 300072, China |
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Abstract This paper presents a new algorithm of the fast multipole fundamental solution method（FMM-MFS）for calculating two-dimensional elastic wave scattering problems. It avoids the singularity of the matrix by placing the line sources of compressional wave and shear wave on a virtual boundary based on single layer potential theory. Additionally, there is no need of elements discretization on the boundary. Combining with the FMM, MFS can solve large-scale problems of wave scattering by greatly reducing the computation and the memory requirement. Taking the two-dimensional scattering of P, SV waves around a cavity in elastic full-space as an example, the implement procedure are presented in detail, and up to millions DOF’s scattering problem are solved successfully on a personal computer. Based on the test of accuracy and efficiency of FMM-MFS, the scattering of plane waves by a cavity as well as random distributed group cavities in full-space are solved. Finally, several important conclusions about scattering of elastic waves around cavity(cavities) are obtained.
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Received: 30 December 2013
Published: 15 March 2015
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