# A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains

@article{Johansen1998ACG, title={A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains}, author={Hans Johansen and Phillip Colella}, journal={Journal of Computational Physics}, year={1998}, volume={147}, pages={60-85} }

We present a numerical method for solving Poisson's equation, with variable coefficients and Dirichlet boundary conditions, on two-dimensional regions. The approach uses a finite-volume discretization, which embeds the domain in a regular Cartesian grid. We treat the solution as a cell-centered quantity, even when those centers are outside the domain. Cells that contain a portion of the domain boundary use conservative differencing of second-order accurate fluxes on each cell volume. The…

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