Domain Decomposition Algorithm for Coupling of Finite Element and Boundary Element Methods

In several engineering problems, especially the ones associated with the unbounded domains, the coupling of the finite element method (FEM) and the boundary element method (BEM) improves the efficiency of the numerical analysis. Due to the complexity of direct coupling techniques, iterative domain decomposition method became a popular approach. However, in the conventional domain decomposition algorithms, the boundary conditions at the interface boundary must be of one type, i.e., Neumann/Dirichlet. In this paper a new algorithm is presented for the iterative coupling of the FEM and the BEM. Both Dirichlet and Neumann boundary conditions are assumed simultaneously in different parts of the interface boundary and an iterative procedure is conducted by two relaxation parameters to solve the coupled problem. To demonstrate the accuracy of the proposed method, some numerical examples are investigated at the end of the paper.