Journal
APPLIED NUMERICAL MATHEMATICS
Volume 93, Issue -, Pages 87-106Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.apnum.2014.08.002
Keywords
Difference potentials; Boundary projections; Cauchy's type integral; Parabolic problems; Variable coefficients; Heterogeneous media; High-order finite difference schemes; Difference Potentials Method; Immersed Interface Method; Interface/composite domain problems; Non-matching interface conditions; Non-matching grids; Parallel algorithms
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Funding
- National Science Foundation Grant [DMS-1112984]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1112984] Funding Source: National Science Foundation
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Highly-accurate numerical methods that can efficiently handle problems with interfaces and/or problems in domains with complex geometry are crucial for the resolution of different temporal and spatial scales in many problems from physics and biology. In this paper we continue the work started in [8], and we use modest one-dimensional parabolic problems as the initial step towards the development of high-order accurate methods based on the Difference Potentials approach. The designed methods are well-suited for variable coefficient parabolic models in heterogeneous media and/or models with non-matching interfaces and with non-matching grids. Numerical experiments are provided to illustrate high-order accuracy and efficiency of the developed schemes. While the method and analysis are simpler in the one-dimensional settings, they illustrate and test several important ideas and capabilities of the developed approach. (C) 2014 Published by Elsevier B.V. on behalf of IMACS.
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