An Adaptive Domain Partitioning Technique for Meshfree‐Type Methods

Kamal Shanazari

Journal of Applied Mathematics, 2012, vol. 2012, issue 1

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.

Date: 2012
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https://doi.org/10.1155/2012/817026

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2012:y:2012:i:1:n:817026

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