Translator Disclaimer
2017 A fourth-order Cartesian grid embedded boundary method for Poisson's equation
Dharshi Devendran, Daniel Graves, Hans Johansen, Terry Ligocki
Commun. Appl. Math. Comput. Sci. 12(1): 51-79 (2017). DOI: 10.2140/camcos.2017.12.51

Abstract

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.

Citation

Download Citation

Dharshi Devendran. Daniel Graves. Hans Johansen. Terry Ligocki. "A fourth-order Cartesian grid embedded boundary method for Poisson's equation." Commun. Appl. Math. Comput. Sci. 12 (1) 51 - 79, 2017. https://doi.org/10.2140/camcos.2017.12.51

Information

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

MathSciNet: MR3652440
Digital Object Identifier: 10.2140/camcos.2017.12.51

Subjects:
Primary: 65M08, 65M50

Rights: Copyright © 2017 Mathematical Sciences Publishers

JOURNAL ARTICLE
29 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.12 • No. 1 • 2017
MSP
Back to Top