Journal of Applied Mathematics
Volume 2012 (2012), Article ID 817026, 13 pages
Research Article

An Adaptive Domain Partitioning Technique for Meshfree-Type Methods

Department of Mathematics, University of Kurdistan, Sanandaj, Iran

Received 7 July 2011; Accepted 7 December 2011

Academic Editor: Mehmet Sezer

Copyright © 2012 Kamal Shanazari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An overlapping domain partitioning based on adapting nodes is presented for the meshless-type methods. The decomposition of the domain is carried out based on the distribution of the nodes produced rather than the geometry of the problem. A set of adaptive nodes is first generated using the dimension reduction and equidistributing along the coordinate directions with respect to arc-length monitor. The domain is then partitioned in such a way that the same number of nodes are allocated to the subdomains. A radial basis function collocation method is applied to each subdomain followed by assembling the global solution from the subproblem's solutions. A generalized thin plate spline with sufficient smoothness is used as a basis function in the collocation method. Some numerical results will be presented to show the performance of the proposed method.