An Adaptive Domain Partitioning Technique for Meshfree-Type Methods

• Main Author: Kamal Shanazari
• Format: Article
• Language: English
• Published: Hindawi Limited 2012-01-01
• Series: Journal of Applied Mathematics
• Online Access: http://dx.doi.org/10.1155/2012/817026

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.