Overlapping domain decomposition method by radial basis functions Original Research Article

In this paper, overlapping domain decomposition with both multiplicative and additive Schwarz iterative techniques are incorporated into the radial basis functions for solving partial differential equations. These decomposition techniques circumvent the ill-conditioning problem resulted from using the radial basis functions as a global interpolant. Both the multiplicative and additive Schwarz iterative techniques achieve high performances even without the Krylov subspace accelerators. The effectiveness of the algorithms are demonstrated by performing numerical experiments for both a regular elliptic problem and a singularly perturbed elliptic problem respectively.