Phani P. Chinchapatnam*, K. Djidjeli, Prasanth B. Nair
Computational Engineering and Design Group, University of Southampton, Southampton SO17 1BJ, UK
ABSTRACT
In this paper, we present a radial basis function based meshless method that employs Schwarz domain decomposition techniques and Newton iteration for solving nonlinear elliptic partial differential equations (PDEs). Numerical results are presented for a model nonlinear Poisson problem. We find that the domain decomposition algorithms give accurate results at a much lower cost. In addition, these algorithms are straightforward to parallelize.
Keywords:
Nonlinear PDEs; Schwarz domain decomposition; Radial basis functions; Newton iteration