On the definition of surface potentials for finite-difference operators
type: Item
instance of: scholarly article
title: On the definition of surface potentials for finite-difference operators
zbMATH Open document ID: 1041.65079
DOI: 10.1023/A:1021111713715
published in: Journal of Scientific Computing
publication date: 2003-08-20T00:00:00Z
review text: The author introduces a concept of single- and double-layer potentials for linear constant-coefficient finite difference operators of second order on rectangular mesh in 2-D. Although similar to the conventional potentials for differential operators, the discrete potentials are introduced and studied completely independently. The resulting discrete ``surface'' potentials appear to be solutions to systems of linear difference equations with special source terms. The possible application of such new mathematical objects is active shielding and control of sound of domain of interest.
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 1968060
zbMATH Keywords: fundamental solution
zbMATH Keywords: difference potential
zbMATH Keywords: surface potential
zbMATH Keywords: discontinuous solution
zbMATH Keywords: single- and double-layer potentials
zbMATH Keywords: multi-layer grid boundary
zbMATH Keywords: discontinuous grid function
zbMATH Keywords: Calderon's potential
author: S. V. Tsynkov
reviewed by: Raytcho D. Lazarov
MaRDI profile type: Publication
full work available at URL: a:1021111713715
OpenAlex ID: W4231203926
description: scientific article; zbMATH DE number 1968060