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

Journal Article · · Communications in Applied Mathematics and Computational Science
 [1];  [1];  [1];  [1]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
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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.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1379639
Journal Information:
Communications in Applied Mathematics and Computational Science, Vol. 12, Issue 1; ISSN 1559-3940
Publisher:
Mathematical Sciences PublishersCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 9 works
Citation information provided by
Web of Science

References (24)

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Related Subjects

97 MATHEMATICS AND COMPUTING
Poisson equation
finite volume methods
high order
embedded boundary