Fast multipole method for poroelastodynamics

摘要

Wave propagation phenomena occur in reality often in semi-infinite two-phase (porous) regions. It is well known that such problems can be handled well with the poroelastodynamic Boundary Element Method (BEM). But, it is also well known that the BEM with its dense matrices becomes prohibitive with respect to storage and computing time. This is especially true for poroelastodynamics, where in the best case four degrees of freedom per node are required. As well, the fundamental solution of poroelastodynamics is computationally expensive.Here, a fast multipole BEM is proposed to circumvent those points. The Chebyshev interpolation-based FMM significantly reduces the memory consumption of the system matrix and thus allows for larger problem sizes to be treated. As well, it requires fewer evaluations of the fundamental solution. To employ an iterative solver, the use of a transformation of the material data is mandatory. Numerical tests show the expected almost linear complexity of the proposed method.