*(English)*Zbl 1037.65130

Summary: This paper presents several interface relaxation algorithms for boundary element–boundary element coupling (BEM-BEM) and for finite element–boundary element coupling (FEM-BEM). The domain of the original problem is sub-divided into sub-domains, which are modeled by the finite element or boundary element methods. The multi-domain system is coupled using smoothing operators on the inter-domain boundaries.

Separate computations for the BEM and FEM sub-domains and successive update of the boundary conditions at the interfaces are performed until convergence is achieved. The interface relaxation coupling algorithms preserve the nature of the FEM and BEM. Further, they do not require any access to the matrices generated by the FEM or BEM and make it easier to utilize different software in different sub-domains.

##### MSC:

65N55 | Multigrid methods; domain decomposition (BVP of PDE) |

35J05 | Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation |

65N30 | Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE) |

65N38 | Boundary element methods (BVP of PDE) |

65N12 | Stability and convergence of numerical methods (BVP of PDE) |