Immersed Interface Methods for Neumann and Related Problems in Two and Three Dimensions

Authors:
Aaron L. Fogelson;James P. Keener
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2000

Citing 0
Cited 19

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Abstract

We develop and apply a finite-difference method to discretize the Laplacian operator with Neumann boundary conditions on an irregular domain using a regular Cartesian grid. The method is an extension of the immersed interface method developed by LeVeque and Li [SIAM J. Numer. Anal., 31 (1994) 1019--1044]. With careful selection of stencils, the method is second order accurate and produces a matrix that is stable (diagonally semidominant). The method is illustrated on several two-dimensional problems and one three-dimensional problem.