Fast multipole method as an efficient solver for 2D elastic wave surface integral equations

摘要

The fast multipole method (FMM) is very effi- cient in solving integral equations. This paper applies the method to solve large solid-solid boundary integral equations for elastic waves in two dimensions. The scat- tering problem is first formulated with the boundary ele- ment method. FMM is then introduced to expedite the solution process. By using the FMM technique, the num- ber of floating-point operations of the matrix-vector multiplication in a standard conjugate gradient algorithm is reduced from O(N~2) to O(N~1.5), where N is the number of unknowns. The matrix-filling time and the memory requirement are also of the order N~1.5.