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A boundary condition capturing method for Poisson’s equation on irregular domains. (English) Zbl 0958.65105
Interface problems have a variety of boundary conditions (or jump conditions) that needs to be enforced. The ghost fluid method (GFM) was developed to capture the boundary conditions at a contact discontinuity in the inviscid Euler equations and has been extended to treat more general discontinuities such as shocks, detonations, and deflagrations and compressible viscous flows. In this paper, a similar boundary condition capturing approach is used to develop a new numerical method for the variable coefficient Poisson equation in the presence of interfaces where both the variable coefficients and the solution itself may be discontinuous. This new method is robust and easy to implement even in three spatial dimensions. Futhermore, the coefficient matrix of the associated linear system is the standard symmetric matrix for the variable coefficient Poisson equation in the absence of interfaces allowing for straightforward application of standard ”black box” solvers.

MSC:
65N06Finite difference methods (BVP of PDE)
35R05PDEs with discontinuous coefficients or data
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
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References:
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