Robust Boundary Element Domain Decomposition Solvers in Acoustics

Tearing and interconnecting domain decomposition methods [ 2, 3] are well established for an efficient and parallel solution of various elliptic partial differential equations by using finite and boundary element methods. But in the case of the Helmholtz equation, additional difficulties may appear. Although the global boundary value problem admits a unique solution, local subdomain solvers as used in the tearing and interconnecting approach may fail due to spurious modes. In a recent paper [7] we have introduced a boundary element tearing and interconnecting domain decomposition approach which is robust for all local wave numbers. The aim of the present paper is the discussion of some efficient preconditioners which are needed in the iterative solution of the resulting linear system. In particular we will use preconditioners of the opposite order [6] for the solution of the local boundary value problems, while the construction of the global preconditioner is based on the use of planar waves following the FETI–H method as introduced in [ 1]. Numerical results confirm the efficiency and the robustness of the proposed solution strategies.