Communications in Applied Mathematics and Computational Science

A fourth-order Cartesian grid embedded boundary method for Poisson's equation

Dharshi Devendran, Daniel Graves, Hans Johansen, and Terry Ligocki

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In this paper, we present a fourth-order algorithm to solve Poisson’s equation in two and three dimensions. We use a Cartesian grid, embedded boundary method to resolve complex boundaries. We use a weighted least squares algorithm to solve for our stencils. We use convergence tests to demonstrate accuracy and we show the eigenvalues of the operator to demonstrate stability. We compare accuracy and performance with an established second-order algorithm. We also discuss in depth strategies for retaining higher-order accuracy in the presence of nonsmooth geometries.

Article information

Commun. Appl. Math. Comput. Sci., Volume 12, Number 1 (2017), 51-79.

Received: 25 March 2016
Revised: 19 December 2016
Accepted: 30 January 2017
First available in Project Euclid: 19 October 2017

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Mathematical Reviews number (MathSciNet)

Primary: 65M08: Finite volume methods 65M50: Mesh generation and refinement

Poisson equation finite volume methods high order embedded boundary


Devendran, Dharshi; Graves, Daniel; Johansen, Hans; Ligocki, Terry. A fourth-order Cartesian grid embedded boundary method for Poisson's equation. Commun. Appl. Math. Comput. Sci. 12 (2017), no. 1, 51--79. doi:10.2140/camcos.2017.12.51.

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