Nyström discretization of parabolic boundary integral equations
type: Item
instance of: scholarly article
title: Nyström discretization of parabolic boundary integral equations
zbMATH Open document ID: 1176.65103
author: Johannes Tausch
published in: Applied Numerical Mathematics
publication date: 2009-09-28T00:00:00Z
review text: A Nystrom method for the discretization of thermal layer potentials is proposed and analyzed. The method is based on considering the potentials as generalised Abel integral operators in time, where the kernel is a time dependent surface integral operator. The time discretization is the trapezoidal rule with a corrected weight at the end point to compensate for singularities of the integrand. The spatial discretization is a standard quadrature rule for surface integral of smooth functions. The explicit method developed by this discretization is used to solve the Neumann problem for the heat equation in the exterior of the unit sphere. The numerical results are in good agreement with the theoretical estimates.
Mathematics Subject Classification ID: 65M38
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 5608062
zbMATH Keywords: heat equation
zbMATH Keywords: boundary element method
zbMATH Keywords: Nyström discretization
zbMATH Keywords: Abel integral equation
zbMATH Keywords: trapezoidal rule
zbMATH Keywords: quadrature rule
zbMATH Keywords: Neumann problem
zbMATH Keywords: numerical results
MaRDI profile type: Publication
full work available at URL: j.apnum.2008.12.032
OpenAlex ID: W2024654176
cites work: Q3826070
cites work: The Numerical Solution of Fredholm integral Equations of the Second Kind
cites work: Boundary integral operators for the heat equation
cites work: Spectral approximation of the free-space heat kernel
cites work: Boundary integral solution of the two-dimensional heat equation
cites work: Linear integral equations
cites work: Time discretization of parabolic boundary integral equations
cites work: Numerical Quadrature and Asymptotic Expansions
cites work: Q5511546
cites work: Application of `operational quadrature methods' in time domain boundary element methods
cites work: A generalization of discrete Gronwall inequality and its application to weakly singular Volterra integral equation of the second kind
cites work: A fast method for solving the heat equation by layer potentials
DOI: 10.1016/J.APNUM.2008.12.032
Recommended article: Fast Nyström Methods for Parabolic Boundary Integral Equations
Recommended article: A Nyström method for boundary integral equations on domains with a piecewise smooth boundary
Recommended article: Q4207544
Recommended article: Discretization of parabolic problems
Recommended article: A boundary integral method for parabolic equations in non‐smooth domains
Recommended article: Nitsche mortaring for parabolic initial-boundary value problems
Recommended article: Fully discrete approximations of parabolic boundary-value problems with nonsmooth boundary data
Recommended article: Time discretization of parabolic boundary integral equations
Recommended article: Numerical Solution of Parabolic Problems with Nonlocal Boundary Conditions
Recommended article: Q4015055
description: scientific article; zbMATH DE number 5608062