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Title: A fourth-order Cartesian grid embeddedboundary method for Poisson’s equation

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.
Authors:
 [1] ;  [1] ;  [1] ;  [1]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Grant/Contract Number:
AC02-05CH11231
Type:
Accepted Manuscript
Journal Name:
Communications in Applied Mathematics and Computational Science
Additional Journal Information:
Journal Volume: 12; Journal Issue: 1; Journal ID: ISSN 1559-3940
Publisher:
Mathematical Sciences Publishers
Research Org:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Poisson equation; finite volume methods; high order; embedded boundary
OSTI Identifier:
1379639

Devendran, Dharshi, Graves, Daniel, Johansen, Hans, and Ligocki, Terry. A fourth-order Cartesian grid embeddedboundary method for Poisson’s equation. United States: N. p., Web. doi:10.2140/camcos.2017.12.51.
Devendran, Dharshi, Graves, Daniel, Johansen, Hans, & Ligocki, Terry. A fourth-order Cartesian grid embeddedboundary method for Poisson’s equation. United States. doi:10.2140/camcos.2017.12.51.
Devendran, Dharshi, Graves, Daniel, Johansen, Hans, and Ligocki, Terry. 2017. "A fourth-order Cartesian grid embeddedboundary method for Poisson’s equation". United States. doi:10.2140/camcos.2017.12.51. https://www.osti.gov/servlets/purl/1379639.
@article{osti_1379639,
title = {A fourth-order Cartesian grid embeddedboundary method for Poisson’s equation},
author = {Devendran, Dharshi and Graves, Daniel and Johansen, Hans and Ligocki, Terry},
abstractNote = {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.},
doi = {10.2140/camcos.2017.12.51},
journal = {Communications in Applied Mathematics and Computational Science},
number = 1,
volume = 12,
place = {United States},
year = {2017},
month = {5}
}

Works referenced in this record:

The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
journal, August 1994
  • LeVeque, Randall J.; Li, Zhilin
  • SIAM Journal on Numerical Analysis, Vol. 31, Issue 4, p. 1019-1044
  • DOI: 10.1137/0731054