Second kind boundary integral equation for multi-subdomain diffusion problems
type: Item
instance of: scholarly article
title: Second kind boundary integral equation for multi-subdomain diffusion problems
zbMATH Open document ID: 1381.65094
author: Xavier Claeys
author: Ralf Hiptmair
author: Elke Spindler
published in: Advances in Computational Mathematics
publication date: 2017-12-06T00:00:00Z
review text: The authors are concerned with the linear second-order diffusion problem for a given excitation field at infinity, harmonic on all of real 3D space. They restrict to piecewise constant real-valued diffusion coefficients. Then, they precisely describe the geometry and the boundary value problem, review basic definitions and results related to Sobolev spaces, introduce a functional framework well adapted to dealing with trace functions in a multi-subdomain context and establish the well-posedness of a variational formulation for the original problem. The corresponding trial functions are sought in single-trace spaces, and the test functions are chosen in some complementary subspace. Subsequently they rewrite this formulation in order to simplify the functional framework and carry out two numerical experiments. The Galerkin boundary element method applied to their new integral equations provides competitive results compared to the more classical first kind approach.
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 6816265
zbMATH Keywords: second-order transmission problem
zbMATH Keywords: piecewise constant diffusion coefficient
zbMATH Keywords: 3D free space
zbMATH Keywords: boundary integral equation
zbMATH Keywords: second kind single integral equation
zbMATH Keywords: regularized singular integral
zbMATH Keywords: numerical quadrature
zbMATH Keywords: Galerkin boundary element
zbMATH Keywords: linear second-order diffusion problem
zbMATH Keywords: numerical experiment
reviewed by: Calin Ioan Gheorghiu
describes a project that uses: Gmsh
describes a project that uses: BETL
MaRDI profile type: Publication
full work available at URL: s10444-017-9517-0
OpenAlex ID: W2594371642
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DOI: 10.1007/S10444-017-9517-0
description: scientific article; zbMATH DE number 6816265