New optimized domain decomposition order 4 method(OO4) applied to reaction advection diffusion equation

Abstract

The purpose of this work is the study of a new approach of domain decomposition method, the optimized order 4 method(OO4), to solve a reaction advection diusion equation. This method is a Schwarz waveform relaxation approach extending the known OO2 idea. The OO4 method is a reformulation of the Schwarz algorithm with specific conditions at the interface. This condition are a dierential equation of order 1 in the normal direction and of order 4 in the tangential direction to the interface resulting of artificial boundary conditions. The obtained scheme is solved by a Krylov type algorithm. The main result in this paper is that the proposed OO4 algorithm is more robust and faster than the classical OO2 method. To confirm the performance of our method , we give several numerical test-cases.