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A fourth-order
Cartesian grid embedded boundary method for Poisson's
equation
Dharshi Devendran, Daniel T. Graves, Hans Johansen and Terry Ligocki |
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Vol. 12 (2017), No. 1, 51–79
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Abstract |
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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. |
Keywords
Poisson equation, finite volume methods, high order,
embedded boundary
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Mathematical Subject Classification 2010
Primary: 65M08, 65M50
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Milestones
Received: 25 March 2016
Revised: 19 December 2016
Accepted: 30 January 2017
Published: 8 May 2017
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Authors |
| Dharshi Devendran | |
| Applied Numerical Algorithms Group
(ANAG) Lawrence Berkeley National Laboratory 1 Cyclotron Road Berkeley, CA 94720 United States |
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| Daniel T. Graves | |
| Computational Research
Division Lawrence Berkeley National Laboratory 1 Cyclotron Road Berkeley, CA 94720 United States |
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| Hans Johansen | |
| Applied Numerical Algorithms Group
(ANAG) Computational Research Division Lawrence Berkeley National Laboratory MS 50A1148 One Cyclotron Road Berkeley, CA 94720 United States |
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| Terry Ligocki | |
| Applied Numerical Algorithms Group
(ANAG) Lawrence Berkeley National Laboratory 1 Cyclotron Road Berkeley, CA 94720 United States |
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