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A Reduced Radial Basis Function Method for Partial Differential Equations on Irregular Domains

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Abstract

We propose and test the first Reduced Radial Basis Function Method for solving parametric partial differential equations on irregular domains. The two major ingredients are a stable Radial Basis Function (RBF) solver that has an optimized set of centers chosen through a reduced-basis-type greedy algorithm, and a collocation-based model reduction approach that systematically generates a reduced-order approximation whose dimension is orders of magnitude smaller than the total number of RBF centers. The resulting algorithm is efficient and accurate as demonstrated through two- and three-dimensional test problems.

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Authors and Affiliations

  1. Department of Mathematics, University of Massachusetts Dartmouth, 285 Old Westport Road, North Dartmouth, MA, 02747, USA

    Yanlai Chen, Sigal Gottlieb, Alfa Heryudono & Akil Narayan

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  1. Yanlai Chen
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  2. Sigal Gottlieb
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  3. Alfa Heryudono
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  4. Akil Narayan
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Correspondence to Yanlai Chen.

Additional information

Y. Chen: The research of this author was partially supported by National Science Foundation Grant DMS-1216928.

S. Gottlieb, A. Heryudono: The research of this author was partially supported by AFOSR Grant FA9550-09-1-0208.

A. Heryudono, A. Narayan: The research of this author was partially supported by National Science Foundation Grant DMS-1318427.

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Chen, Y., Gottlieb, S., Heryudono, A. et al. A Reduced Radial Basis Function Method for Partial Differential Equations on Irregular Domains. J Sci Comput 66, 67–90 (2016). https://doi.org/10.1007/s10915-015-0013-8

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