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Journal of Scientific Computing

, Volume 66, Issue 1, pp 67–90 | Cite as

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

  • Yanlai ChenEmail author
  • Sigal Gottlieb
  • Alfa Heryudono
  • Akil Narayan
Article

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.

Keywords

Reduced basis method Radial basis function method Pseudospectral method Model reduction 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Yanlai Chen
    • 1
    Email author
  • Sigal Gottlieb
    • 1
  • Alfa Heryudono
    • 1
  • Akil Narayan
    • 1
  1. 1.Department of MathematicsUniversity of Massachusetts DartmouthNorth DartmouthUSA

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