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A Minimal Distance Constrained Adaptive Mesh Algorithm with Application to the Dual Reciprocity Method

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Abstract

We present a new technique for generating error equi-distributing meshes that satisfy both local quasi-uniformity and a preset minimal mesh spacing. This is first done in the one-dimensional case by extending the Kautsky and Nichols method and then in the two-dimensional case by generalizing the tensor product methods to alternating curved line equi-distributions. With the new meshing approach, we have achieved better accuracy in approximation using interpolatory radial basis functions. Furthermore, improved accuracy in numerical results has been obtained when the interpolatory strategy is applied to the dual reciprocity boundary element method for solving a class of linear and nonhomogeneous partial differential equations.

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Authors and Affiliations

  1. Department of Mathematical Sciences, The University of Liverpool, Liverpool, L69 7ZL, UK

    Kamal Shanazari & Ke Chen

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  1. Kamal Shanazari
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  2. Ke Chen
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Correspondence to Ke Chen.

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Shanazari, K., Chen, K. A Minimal Distance Constrained Adaptive Mesh Algorithm with Application to the Dual Reciprocity Method. Numerical Algorithms 32, 275–286 (2003). https://doi.org/10.1023/A:1024027723984

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