Summary: Parallel Implementation of NonLinear Evolution Problems using
Parabolic Domain Decomposition \Lambda
appeared in Parallel Computing, Vol. 21, No. 7, pp. 11511183, 1995
School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
M. Israeli L. Vozovoi
Faculty of Computer Science, Technion, Haifa 32000, Israel
We present implementation of parallel algorithms for the numerical solution of nonlinear
timedependent partial differential equations of parabolic type arising from complex large scale
problems. The parallelization is achieved by using domain decomposition (DD) techniques.
The essential feature of this algorithm is that the spatial discretization in each subdomain is
performed by using spectral method with the Local Fourier Basis (LFB). Our solutions are
based on a special projection technique that employed to localize functions in a smooth way on
the extended subdomain.
The current paper continue the flow of our previous results [1, 4, 12, 13] on spectral mul
tidomain algorithm. The application of the Parabolic Domain Decomposition (PDD) approach
along with the LFB is shown to be very efficient when applied to a 2dimensional domain splitted
into strips and rectangular cells. In this case, all matching relations become completely uncou
pled (at the price of some overlapping of subdomains required by the LFB implementation).