期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 229, 期 3, 页码 875-889出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2009.10.017
关键词
Level set method; Robin boundary condition; Stefan; Poisson; Diffusion; Irregular domains
资金
- Sloan Research Fellowship in Mathematics
- National Science Foundation [DMS 0713858]
- U.S. Army Research Office [W911NF-09-D-0001]
- Department of Energy [DE-FG02-08ER15991]
- Direct For Mathematical & Physical Scien [1027797] Funding Source: National Science Foundation
- Division Of Chemistry [1027797] Funding Source: National Science Foundation
We present a novel and efficient method for solving the Poisson equation, the heat equation, and Stefan-type problems with Robin boundary conditions over potentially moving, arbitrarily-shaped domains. The method utilizes a level set framework, thus it has all of the benefits of a sharp, implicitly-represented interface such as the ease of handling complex topological changes. This method is straightforward to implement and leads to a linear system that is symmetric and positive definite, which can be inverted efficiently with standard iterative methods. This approach is second-order accurate for both the Poisson and heat equations, and first-order accurate for the Stefan problem. We demonstrate the accuracy in the L-1 and L-infinity norms. (C) 2009 Elsevier Inc. All rights reserved.
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