An efficient domain-decomposition pseudo-spectral method for solving elliptic differential equations

Abstract

In this paper, a new numerical scheme based on non-overlapping domain decompositions and integrated Chebyshev approximations for solving elliptic differential equations is presented. The distinguishing feature of the present scheme is that it achieves a Cp continuous solution across the interfaces (p is the order of the differential equation). Several test problems are employed to verify the method. The obtained results indicate that the achievement of higher-order smoothness leads to a significant improvement in accuracy.