Geodesic
Parallel implementation of stability analysis of difference schemes with MATHEMATICA
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part IV, Tome 258 (1999), pp. 231-255 
V. G. Ganzha; E. V. Vorozhtsov. Parallel implementation of stability analysis of difference schemes with MATHEMATICA. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part IV, Tome 258 (1999), pp. 231-255. http://geodesic.mathdoc.fr/item/ZNSL_1999_258_a11/
@article{ZNSL_1999_258_a11,
     author = {V. G. Ganzha and E. V. Vorozhtsov},
     title = {Parallel implementation of stability analysis of difference schemes with {MATHEMATICA}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {231--255},
     year = {1999},
     volume = {258},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_258_a11/}
}
TY  - JOUR
AU  - V. G. Ganzha
AU  - E. V. Vorozhtsov
TI  - Parallel implementation of stability analysis of difference schemes with MATHEMATICA
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1999
SP  - 231
EP  - 255
VL  - 258
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1999_258_a11/
LA  - en
ID  - ZNSL_1999_258_a11
ER  - 
%0 Journal Article
%A V. G. Ganzha
%A E. V. Vorozhtsov
%T Parallel implementation of stability analysis of difference schemes with MATHEMATICA
%J Zapiski Nauchnykh Seminarov POMI
%D 1999
%P 231-255
%V 258
%U http://geodesic.mathdoc.fr/item/ZNSL_1999_258_a11/
%G en
%F ZNSL_1999_258_a11

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.