A fourthorder Cartesian grid embeddedboundary method for Poisson’s equation
In this paper, we present a fourthorder 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 secondorder algorithm. We also discuss in depth strategies for retaining higherorder accuracy in the presence of nonsmooth geometries.
 Authors:

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 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Publication Date:
 Grant/Contract Number:
 AC0205CH11231
 Type:
 Accepted Manuscript
 Journal Name:
 Communications in Applied Mathematics and Computational Science
 Additional Journal Information:
 Journal Volume: 12; Journal Issue: 1; Journal ID: ISSN 15593940
 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) (SC21)
 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 fourthorder 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 fourthorder 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 fourthorder 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 fourthorder 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 fourthorder 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 secondorder algorithm. We also discuss in depth strategies for retaining higherorder 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
journal, August 1994
 LeVeque, Randall J.; Li, Zhilin
 SIAM Journal on Numerical Analysis, Vol. 31, Issue 4, p. 10191044