Nonsingular kernel boundary integral and finite element coupling method

Abstract

In the finite element and boundary element coupling method, the Stekhlov–Poincaré mapping is often adopted at the coupling boundary, i.e., the unknown Neumann data are represented by the unknown Dirichlet data on the same boundary. This coupling method (either by a convolution integral, or by a Fourier series) is referred as the conventional method. We propose an alternative method, where the unknown Dirichlet data at the boundary are represented by the unknown solution value on an interior curve or surface, i.e., a Dirichlet-to-Dirichlet (D-to-D) mapping is employed instead of a Dirichlet-to-Neumann (D-to-N) mapping. The convergence of the method is shown to be of optimal order. 2D and 3D numerical experiments are performed to demonstrate the accuracy of the proposed method, comparing to the two conventional D-to-N coupling methods.