A high order kernel independent fast multipole boundary element method for elastodynamics

In this paper, a highly accurate kernel-independent fast multipole boundary element method (BEM) is developed for solving large-scale elastodynamic problems in the frequency domain. The curved quadratic elements are employed to achieve high accuracy in BEM analysis. By using the Nyström discretization, the boundary integral equation is transformed into a summation, and thus the fast BEM algorithms can be applied conveniently. A newly developed kernel-independent fast multipole method (KIFMM) is used for BEM acceleration. This method is of nearly optimal computational complexity; more importantly, the numerical implementation of the method does not rely on the expression of the fundamental solutions and the accuracy is controllable and can be higher with only slight increase of the computational cost. By taking advantage of the cheap matrix assembly of Nyström discretization, the memory cost of the KIFMM accelerated BEM can be further reduced by several times. The performance of the present method in terms of accuracy and computational cost are demonstrated by numerical examples with up to 2.3 million degrees of freedom and by comparisons with existing methods.