A fast boundary node method for transient scalar waves in domains with localized inhomogeneities

In this paper, we propose an efficient method suitable for 1D/2D/3D plus time wave propagation in homogeneous domains containing localized inhomogeneities. It is well-understood that the numerical solution of such problems, using finite difference and finite element methods, for instance, needs fine discretization depending on the size of the region of the inhomogeneity, making the solution cumbersome. In this study, a time-domain boundary node method, initially devised for homogeneous mediums, is extended to incorporate the inhomogeneities. In addition to the boundary nodes, the so-called sampling points are added to the formulation. The salient feature is that such sampling points are only required in the non-homogeneous regions, making the method efficient and most suitable for scattering problems. Starting from assuming homogeneity, the proposed method considers the effects of the inhomogeneities in an iterative procedure with just a few steps. The efficiency and performance of the method are assessed and compared with the finite element method through some numerical 1D, 2D, and 3D examples.