Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 326, Issue -, Pages 596-611Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2016.08.045
Keywords
Compact moving least squares; CMLS; Optimization; Compact finite difference; Meshless method
Funding
- U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program, Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4) [DE-SC0009247]
- U.S. Department of Energy (DOE) [DE-SC0009247] Funding Source: U.S. Department of Energy (DOE)
Ask authors/readers for more resources
A generalization of the optimization framework typically used in moving least squares is presented that provides high-order approximation while maintaining compact stencils and a consistent treatment of boundaries. The approach, which we refer to as compact moving least squares, resembles the capabilities of compact finite differences but requires no structure in the underlying set of nodes. An efficient collocation scheme is used to demonstrate the capabilities of the method to solve elliptic boundary value problems in strong form stably without the need for an expensive weak form. The flexibility of the approach is demonstrated by using the same framework to both solve a variety of elliptic problems and to generate implicit approximations to derivatives. Finally, an efficient preconditioner is presented for the steady Stokes equations, and the approach's efficiency and high order of accuracy is demonstrated for domains with curvi-linear boundaries. (C) 2016 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