A spectral multi-domain method for the solution of 1-D-Helmholtz and Stokes-type equations (Q1100019)

We present a spectral multi-domain method using the influence matrix technique to enforce boundary conditions as well as the continuity conditions at the interfaces. The method is applied to the solution of the Helmholtz equation with general boundary conditions and of a Stokes- type problem in a 1-D case. For each of these problems, the technique leads to the solution of the Helmholtz equations with Dirichlet conditions. These equations are solved by a Tau-Chebyshev method. The influence matrix method allows treatment of the case of mixed conditions on each boundary, while preserving the separation of the odd and even Chebyshev modes. This absence of coupling leads to the inversion of quasi-tridiagonal matrix which can efficiently be carried out by means of a factorization algorithm.