Tearing and interconnecting algorithms are well established domain decomposition methods which are suitable for parallelization, jumping coefficients, coupling of different discretization techniques etc. While the standard approach is based on the use of the classical Dirichlet and Neumann transmission conditions, for non-elliptic operators it is not possible to use the equivalent minimization formulation with constraints. Moreover, the localized problems may fail to be uniquely solvable. Hence we discuss alternative interface boundary conditions to ensure unique solvability of the local subproblems, and we give an appropriate tearing and interconnecting formulation. First numerical results for Helmholtz problems are given.
This is joint work with Olaf Steinbach.