The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
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چکیده
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.
منابع مشابه
A Comparison of the Extended Finite Element Method with the Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
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تاریخ انتشار 1994