Time domain boundary element method for semi-infinite domain problems using CSR storage method

Abstract

The time domain boundary element method (TDBEM) is suitable for dealing with dynamic problems in the semi-infinite domain (such as the propagation of seismic waves). The fundamental solution in the TDBEM is an impulse function with time terms, and the formed coefficient matrix is sparse. In this paper, a TDBEM using the compressed storage algorithm based on Compressed Sparse Row (CSR) format is proposed to solve the semi-infinite domain dynamics problems. The coefficient matrix is stored in the CSR format, and the generation method of the coefficient matrix elements and the matrix operation scheme based on CSR format in the TDBEM are given. The GMRES algorithm is also modified to make it suitable for TDBEM of CSR format to improve the efficiency of iterative solution. The provided semi-infinite domain dynamics examples show that the TDBEM of CSR format proposed in this paper can greatly reduce the storage space and improve the efficiency and scale of the solution.