skip to main content

DOE PAGESDOE PAGES

This content will become publicly available on February 1, 2017

Title: A radial basis function Galerkin method for inhomogeneous nonlocal diffusion

We introduce a discretization for a nonlocal diffusion problem using a localized basis of radial basis functions. The stiffness matrix entries are assembled by a special quadrature routine unique to the localized basis. Combining the quadrature method with the localized basis produces a well-conditioned, sparse, symmetric positive definite stiffness matrix. We demonstrate that both the continuum and discrete problems are well-posed and present numerical results for the convergence behavior of the radial basis function method. As a result, we explore approximating the solution to anisotropic differential equations by solving anisotropic nonlocal integral equations using the radial basis function method.
Authors:
 [1] ;  [2]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Texas A & M Univ., College Station, TX (United States)
Publication Date:
OSTI Identifier:
1237367
Report Number(s):
SAND--2015-0511J
Journal ID: ISSN 0045-7825; 562414
Grant/Contract Number:
AC04-94AL85000
Type:
Accepted Manuscript
Journal Name:
Computer Methods in Applied Mechanics and Engineering
Additional Journal Information:
Journal Volume: 299; Journal ID: ISSN 0045-7825
Publisher:
Elsevier
Research Org:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING nonlocal diffusion; radial basis functions; nonlocal vector calculus; Lagrange functions