Parallel implementation of stability analysis of difference schemes with MATHEMATICA

We consider a parallel algorithm for stability investigation of the schemes of the finite difference method or the finite volume method approximating the two-dimensional Euler equations of compressible fluids on curvilinear grids. The algorithm is implemented with the computer algebra system Mathematica 3.0. We apply a two-level parallelization process. At the first level, the parallelization of the symbolic computation of the amplification matrix is performed by a parallel computation of the matrix rows on different processors. At the second parallelization level, we compute numerically the values of the coordinates of points of the stability region boundary. For the communication between the workstations we use a special program LaunchSlave, which uses the MathLink communication protocol. The examples of the application of the proposed parallel symbolic/numeric algorithm are presented.