Domain decomposition for parallelization of finite difference schemes for parabolic equations in wave propagation

Abstract

Tropospheric wave propagation can be described by a parabolic differential equation which may be solved using implicit finite differences. The large grid systems which can be required in such solutions make parallelization expedient. This can be accomplished by decomposing the computational domain into several subdomains over which the solution is calculated in parallel at each step in a marching procedure. A Schwarz‐type algorithm, which has become popular in computational fluid dynamics applications, is investigated for accomplishing this domain decomposition. It is found to be unconditionally unstable for the wave propagation parabolic equation when the subdomains overlap, while for nonoverlapping subdomains, its accuracy depends strongly on the method for establishing the boundary conditions on the pseudoboundaries of the subdomains.