Nonuniform spatial mesh adaptation using a posteriori error estimates: Applications to forward and inverse problems
type: Item
instance of: scholarly article
title: Nonuniform spatial mesh adaptation using a posteriori error estimates: Applications to forward and inverse problems
zbMATH Open document ID: 0803.92014
DOI: 10.1016/0168-9274(94)90031-0
author: Christopher Johnson
author: Robert S. MacLeod
published in: Applied Numerical Mathematics
publication date: 1995-01-03T00:00:00Z
review text: The following tasks occurring in biomedicine are considered: Direct problem: Given a subset of potentials of the surface of the heart, or a description of the primary current sources within the heart. Find the electric and potential fields everywhere within the body and the voltages on the surface of the torso. Inverse problem I: Given a subset of voltages on the surface of the thorax. Find either the voltages on a closed surface bounding the heart or the primary currents within the volume of the heart. Inverse problem II: Given known currents or voltages which are applied from external sources. Find the distribution of applied current throughout the heart. Both of the inverse problems are ill-posed. The mathematical formulation of these problems leads to an elliptic equation of second order in a three-dimensional inhomogeneous, anisotropic domain with boundary conditions, respectively. For its solution the authors develop an adaptive meshing scheme based upon a posteriori error estimates from the finite element approximation. Furthermore, a brief description of its implementation and some results using these techniques are given.
Mathematics Subject Classification ID: 92C50
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 78A70
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 65N15
zbMATH DE Number: 609624
zbMATH Keywords: inverse problem
zbMATH Keywords: primary current sources
zbMATH Keywords: electric and potential fields
zbMATH Keywords: voltages
zbMATH Keywords: elliptic equation of second order
zbMATH Keywords: three-dimensional inhomogeneous, anisotropic domain
zbMATH Keywords: a posteriori error estimates
zbMATH Keywords: finite element approximation
reviewed by: S. Handrock-Meyer
MaRDI profile type: Publication
full work available at URL: 0168-9274(94)90031-0
OpenAlex ID: W1972819716
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description: scientific article; zbMATH DE number 609624