On the Fundamental Solutions for the Difference Helmholtz Operator

In this paper we construct the difference approximation of the Helmholtz operator on a square grid and we analyze asymptotic properties of the difference operator fundamental solutions. We show that for a Sommerfeld-type asymptotic condition there exists a fundamental solution that is determined in...

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Bibliographic Details
Published in:	SIAM journal on numerical analysis Vol. 32; no. 2; pp. 560 - 570
Main Author:	Zemla, Adam
Format:	Journal Article
Language:	English
Published:	Philadelphia, PA Society for Industrial and Applied Mathematics 01-04-1995
Subjects:	Approximation Asymptotic properties Coefficients Critical points Difference and functional equations, recurrence relations Exact sciences and technology Helmholtz equations Infinity Mathematical functions Mathematical intervals Mathematical lattices Mathematics Numerical analysis Numerical analysis. Scientific computation Partial differential equations, boundary value problems Sciences and techniques of general use Sine function Uniqueness Grid pattern Numerical solution Asymptotic behavior Helmholtz equation Partial differential equation Finite difference method Stationary phase
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Summary:	In this paper we construct the difference approximation of the Helmholtz operator on a square grid and we analyze asymptotic properties of the difference operator fundamental solutions. We show that for a Sommerfeld-type asymptotic condition there exists a fundamental solution that is determined in a unique way.
ISSN:	0036-1429 1095-7170
DOI:	10.1137/0732024