Domain Decomposition for Radial Basis Meshless Methods

Both overlapping and nonoverlapping domain decomposition methods (DDM) on matching and nonmatching grid have been developed to couple with the meshless radial basis function (RBF) method. Example shows that overlapping DDM with RBF can achieve much better accuracy with less nodal points compared to FDM and FEM. Numerical results also show that nonmatching grid DDM can achieve almost the same accuracy within almost the same iteration steps as the matching grid case; hence our method is very attractive, because it is much easier to generate nonmatching grid just by putting blocks of grids together (for both overlapping and nonoverlapping), where each block grid can be generated independently. Also our methods are showed to be able to handle discontinuous coefficient. © 2004 Wiley Periodicals, Inc.