Parallel implementation of stability analysis of difference schemes with MATHEMATICA. (English) Zbl 1168.65300

Ganzha, V. G.; Vorozhtsov, E. V.

J. Math. Sci., New York 108, No. 6, 1070-1088 (2002) and Zap. Nauchn. Semin. POMI 258, 231-255 (1999).

Summary: We consider a parallel algorithm for investigating the stability of the schemes of the finite-difference and finite-volume methods that approximate the two-dimensional Euler equations of compressible fluid on a curvilinear grid. The algorithm is implemented with the aid of the computer algebra system Mathematica 3.0. We apply a two-level parallelization process. At the first level, the symbolic computation of the amplification matrix is parallelized by a parallel computation of the matrix rows on different processors. At the second level, the values of the coordinates of points of the stability-region boundary are computed numerically. For the communication between the workstations, we apply a special program, LaunchSlave, which uses the MathLink communication protocol. Examples of application of the proposed parallel symbolic/numerical algorithm are presented.

MSC:

65-04	Software, source code, etc. for problems pertaining to numerical analysis
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65Y05	Parallel numerical computation
76M10	Finite element methods applied to problems in fluid mechanics
76M20	Finite difference methods applied to problems in fluid mechanics

Software:

MathLink; LaunchSlave; Mathematica