Third Order Accuracy of the 4-Point Hexagonal Net Grid
Finite Difference Scheme for Solving the 2D Helmholtz Equation

Eric S. Carlson and Haiwei Sun
Department of Chemical Engineering
University of Alabama
P. O. Box 870203
Tuscaloosa, AL 35487-0203, USA

and
Duane H. Smith
United States Department of Energy
National Energy Technology Laboratory
Morgantown, WV 26507, USA

and
Jun Zhang
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506-0046, USA

Abstract

In this paper, we present a 4-point compact finite difference scheme for solution of the Helmholtz equation that gives $O(h^3)$ accuracy. These finite difference solutions using the hexagonal net grid exhibit global $O(h^3)$ accuracy despite a local truncation error that is $O(h)$. We present a proof for why this happens, and provide the resul ts of a number of computational tests to verify the third order behavior.


Key words: Helmholtz equation, hexagonal net grid, triangular net grid, hexagonal grid, triangular grid, second order scheme, finite difference

Mathematics Subject Classification: 65F10, 65N06, 65N22, 65N5 5, 76D07


Download the compressed postscript file hexgrid3.ps.gz, or the PDF file hexgrid3.pdf.
Technical Report No. 379-03, Department of Computer Science, University of Kentucky, Lexington, KY, 2003.