THE IMMERSED INTERFACE METHOD FOR ELLIPTIC-EQUATIONS WITH DISCONTINUOUS COEFFICIENTS AND SINGULAR SOURCES
THE IMMERSED INTERFACE METHOD FOR ELLIPTIC-EQUATIONS WITH DISCONTINUOUS COEFFICIENTS AND SINGULAR SOURCES
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DOI：
10.1137/0731054
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发表时间：
1994-08-01
影响因子：
2.9
通讯作者：
LI, ZL
中科院分区：
文献类型：
--
作者：
LEVEQUE, RJ;LI, ZL
本文发展了求解椭圆型方程的有限差分方法。（beta（x）delu（x））+ kappa（x）u（x）= f（x）。假设Ω是简单区域（例如，矩形）并且使用均匀的矩形网格。的情况进行了研究，其中有一个不规则的表面伽玛的余维1包含在欧米茄的β，κ，和f可能是不连续的，和沿着的源f可能有一个δ函数奇异性。结果。解u的导数在Gamma上可能是不连续的。允许指定u本身在Gamma上的跳跃不连续。它表明，它是可以修改的标准中心差分近似，以保持二阶精度的均匀网格，即使当伽马不与网格对齐。这种方法也比较了离散δ函数的方法来处理奇异源，用于佩斯金的浸没边界法。
The authors develop finite difference methods for elliptic equations of the form del . (beta(x)delu(x)) + kappa(x)u(x) = f(x) in a region OMEGA in one or two space dimensions. It is assumed that OMEGA 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 GAMMA of codimension 1 contained in OMEGA across which beta, kappa, 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 GAMMA. The specification of a jump discontinuity in u itself across GAMMA 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 GAMMA 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.