Summary: Application of the Multidomain Local Fourier Method
for CFD in Complex Geometries \Lambda
A. Averbuch y M. Israeli z L. Vozovoi z
y School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
z Faculty of Computer Science, Technion, Haifa 32000, Israel
Abstract
A low communication parallel algorithm is presented for the solution of nonlinear
time­dependent PDEs. Our particular interest lies in the application of this algorithm
to fluid dynamics problems in complex geometries. The parallelization is achieved by
domain decomposition. A high­order method with the Local Fourier Basis (LFB) is
employed to construct the elemental solutions in the subdomains. The discretization
in time is performed via a third order semi­implicit stiffly stable scheme.
The continuity of the global solution is accomplished by using 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 transformation enables to split a 2­D problem
with global coupling of the interface unknowns, into a set of uncoupled 1­D differential
equations with local matching relations. Localization properties of an elliptic operator,
resulting from the discretization in time of time­dependent problem, are utilized in
order to simplify the matching relations. In effect, only local (neighbor­to­neighbor)
communication between the processors is necessary.

Source: Averbuch, Amir - School of Computer Science, Tel Aviv University

Collections: Computer Technologies and Information Sciences