A Reduced Radial Basis Function Method for Partial Differential Equations on irregular domains
Numerical Analysis
2014-10-09 v1
Abstract
We propose and test the first Reduced Radial Basis Function Method (RBFM) 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.
Cite
@article{arxiv.1410.1890,
title = {A Reduced Radial Basis Function Method for Partial Differential Equations on irregular domains},
author = {Yanlai Chen and Sigal Gottlieb and Alfa Heryudono and Akil Narayan},
journal= {arXiv preprint arXiv:1410.1890},
year = {2014}
}