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The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources (1994)
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| Venue: | SIAM J. Num. Anal |
| Citations: | 273 - 31 self |
BibTeX
@ARTICLE{Leveque94theimmersed,
author = {Randall J. Leveque and Zhilin Li},
title = {The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources},
journal = {SIAM J. Num. Anal},
year = {1994},
pages = {1019--1044}
}
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Abstract
Abstract. The authors develop finite difference methods for elliptic equations of the form V. ((x)Vu(x)) + (x)u(x) f(x) in a region in one or two space dimensions. It is assumed that gt is a simple region (e.g., a rectangle) and that a uniform rectangular grid is used. The situation is studied in which there is an irregular surface F of codimension contained in fl across which, a, and f may be discontinuous, and along which the source f may have a delta function singularity. As a result, derivatives of the solution u may be discontinuous across F. The specification of a jump discontinuity in u itself across F is allowed. It is shown that it is possible to modify the standard centered difference approximation to maintain second order accuracy on the uniform grid even when F is not aligned with the grid. This approach is also compared with a discrete delta function approach to handling singular sources, as used in Peskin’s immersed boundary method. Key words, elliptic equation, finite difference methods, irregular domain, interface, discontinuous coefficients, singular source term, delta functions AMS subject classifications. 65N06, 65N50 1. Introduction. Consider
Keyphrases
elliptic equation discontinuous coefficient singular source immersed interface method finite difference method simple region subject classification singular source term boundary method delta function second order accuracy key word jump discontinuity uniform grid uniform rectangular grid irregular surface space dimension discrete delta function approach difference approximation delta function singularity irregular domain
