Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 373, Issue -, Pages 722-735Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2018.07.015
Keywords
Radial basis function; High-order method; Manifolds
Funding
- Army Research Laboratory [W911NF-12-2-0023]
- NSF [DMS-1521748, CISE AF-1714844, DMS-1160432, DMS-1720416]
- AFOSR [FA9550-15-1-0467]
Ask authors/readers for more resources
We present a new method for the solution of PDEs on manifolds M subset of R(d )of co-dimension one using stable scale-free radial basis function (RBF) interpolation. Our method involves augmenting polyharmonic spline (PHS) RBFs with polynomials to generate RBF-finite difference (RBF-FD) formulas. These polynomial basis elements are obtained using the recently-developed least orthogonal interpolation technique (LOI) on each RBF-FD stencil to obtain local restrictions of polynomials in R-3 to stencils on M. The resulting RBF-LOI method uses Cartesian coordinates, does not require any intrinsic coordinate systems or projections of points onto tangent planes, and our tests illustrate robustness to stagnation errors. We show that our method produces high orders of convergence for PDEs on the sphere and torus, and present some applications to reaction-diffusion PDEs motivated by biology. (C) 2018 Elsevier Inc. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available