Summary: Multidomain Local Fourier Method for PDEs in
Complex Geometries \Lambda
appeared in J. Computational and Applied Mathematics, Vol. 66, pp. 5435 55, 1996
L. Vozovoi y , M. Israeli y , A. Averbuch z
y Faculty of Computer Science, Technion, Haifa 32000, Israel
z School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
A low communication parallel algorithm is developed for the solution of time
dependent nonlinear PDEs. The parallelization is achieved by domain decomposition.
The discretization in time is performed via a third order semiimplicit stiffly stable
scheme. The elemental solutions in the subdomains are constructed using a highorder
method with the Local Fourier Basis (LFB).
The continuity of the global solution is accomplished by a pointwise matching of
the local subsolutions on the interfaces. The matching relations are derived in terms of
the jumps on the interfaces. The LFB method enables splitting a 2D problem with a
global coupling of the interface unknowns into a set of uncoupled 1D differential equa
tions. Localization properties of an elliptic operator, resulting from the discretization
in time of a timedependent problem, are utilized in order to simplify the matching
relations. In effect, only local (neighbortoneighbor) communication between the pro
cessors becomes necessary.