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• W2022385500 startingPage "60" @default.
• W2022385500 abstract "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 calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes. This allows us to use multigrid iterations with a simple point relaxation strategy. We have combined this with an adaptive mesh refinement (AMR) procedure. We provide evidence that the algorithm is second-order accurate on various exact solutions and compare the adaptive and nonadaptive calculations." @default.
• W2022385500 created "2016-06-24" @default.
• W2022385500 creator A5029775474 @default.
• W2022385500 creator A5082013692 @default.
• W2022385500 date "1998-11-01" @default.
• W2022385500 modified "2023-10-12" @default.
• W2022385500 title "A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains" @default.
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• W2022385500 doi "https://doi.org/10.1006/jcph.1998.5965" @default.
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