Summary: Spectral Multidomain Technique with Local
Fourier Basis II: Decomposition into Cells \Lambda
appeared in Journal of Scientific Computing, Vol. 9, No. 3, pp. 311326, 1994
A. Averbuch z ,L. Vozovoi y , M. Israeli y
y Faculty of Computer Science, Technion, Haifa 32000, Israel
z School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
The spectral multidomain method for the solution of 2D elliptic and parabolic
PDE's is developed. The computational region is decomposed into rectangular cells.
A Local Fourier Basis technique is implemented for the discretization in space. Such a
technique enables the global (typically ¸ 10 4 \Gamma 10 5 ) matching relations for the interface
unknowns to be decoupled into a set of relations for only few interface points at a time.
Domain decomposition methods for solving differential equations were intensively devel
oped during the last several years because they are suitable for parallel computers of the
MIMD (messagepassing or sharedmemory) type. The basic technique consists of splitting
the computational region into smaller subdomains, distributed to different processors. The
computations are carried out concurrently by all the processors, after which the particular
solutions in the subdomains are ``patched'' to ensure the smoothness of the global solution.
In  a spectral domain decomposition method was developed with the Local Fourier