Nonsingular kernel boundary integral and finite element coupling method (Q1728331)

To couple finite elements with the boundary element method, the Stekhlov-Poincaré mapping is used at the coupling boundary. Specifically, the unknown Neumann data can be written down in terms of the unknown Dirichlet data on that boundary. This can be done by either a convolution integral or by a Fourier series which is denoted here as the conventional methods. The main focus of this article is the construction of an alternative method. The new method represents the unknown Dirichlet data by an unknown solution value on an interior curve in 2D or an interior surface in 3D. Precisely, a Dirichlet-to-Dirichlet map is used instead of a Dirichlet-to-Neumann map. The authors show that the convergence of the new method is of optimal order. Finally, numerical examples are given both in 2D and 3D to show the accuracy of the new method in comparison with the two conventional methods.