Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

Meshless domain decomposition schemes for nonlinear elliptic PDEs

Phani P. Chinchapatnam*, K. Djidjeli, Prasanth B. Nair
Computational Engineering and Design Group, University of Southampton, Southampton SO17 1BJ, UK

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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

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