Preconditioned minimum residual iteration for the \(h\)--\(p\) version of the coupled FEM/BEM with quasi-uniform meshes (Q2760364)

The paper is concerned with an \(h\)-\(p\) version of the coupled finite element/boundary element method (FEM/BEM) applied on quasiuniform meshes to the numerical solution of an interface problem. Special attention is paid to the construction of efficient preconditioners for the minimum residual method for the solution of indefinite, symmetric systems arising from the coupled \(h\)-\(p\) finite element -- boundary element discretization of the problem. Two- and three-block preconditioners corresponding to Neumann and Dirichlet problems are studied. The following cases are treated: exact inversion of the blocks for the two-block Jacobi solver, three-block Jacobi solver, the influence of various preconditioners based on decomposing the trial functions into nodal, edge and interior functions. Numerical results supporting the theory are presented.