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

被引：12

作者：

Chen, Yanlai ^{[1
]}

Gottlieb, Sigal ^{[1
]}

Heryudono, Alfa ^{[1
]}

Narayan, Akil ^{[1
]}

机构：

[1] Univ Massachusetts Dartmouth, Dept Math, N Dartmouth, MA 02747 USA

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2016年 / 66卷 / 01期

基金：

美国国家科学基金会;

关键词：

Reduced basis method; Radial basis function method; Pseudospectral method; Model reduction; COMPUTATIONAL FLUID-DYNAMICS; DATA APPROXIMATION SCHEME; SCATTERED DATA; STABLE COMPUTATION; ANALYTIC-FUNCTIONS; ERROR; INTERPOLATION; BOUNDS; MULTIQUADRICS; PARAMETER;

D O I：

10.1007/s10915-015-0013-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：67 / 90

页数：24

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