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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