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An Adaptive Domain Partitioning Technique for Meshfree-Type Methods

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  • Kamal Shanazari

Abstract

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.

Suggested Citation

  • Kamal Shanazari, 2012. "An Adaptive Domain Partitioning Technique for Meshfree-Type Methods," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, April.
    • Handle: RePEc:hin:jnljam:817026
    DOI: 10.1155/2012/817026
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