A reconstruction algorithm based on topological gradient for an inverse problem related to a semilinear elliptic boundary value problem

Elena Beretta, Andrea Manzoni, Luca Ratti

Research output: Contribution to journalArticle

Abstract

In this paper we develop a reconstruction algorithm for the solution of an inverse boundary value problem dealing with a semilinear elliptic partial differential equation of interest in cardiac electrophysiology. The goal is the detection of small inhomogeneities located inside a domain ω, where the coefficients of the equation are altered, starting from observations of the solution of the equation on the boundary ∂ω. Exploiting theoretical results recently achieved in [13], we implement a reconstruction procedure based on the computation of the topological gradient of a suitable cost functional. Numerical results obtained for several test cases finally assess the feasibility and the accuracy of the proposed technique.

Original languageEnglish (US)
Article number035010
JournalInverse Problems
Volume33
Issue number3
DOIs
StatePublished - Feb 15 2017

Fingerprint

Semilinear Elliptic Boundary Value Problem
Reconstruction Algorithm
Inverse problems
Boundary value problems
Partial differential equations
Inverse Problem
Cardiac Electrophysiology
Gradient
Inverse Boundary Value Problem
Elliptic Partial Differential Equations
Inhomogeneity
Semilinear
Numerical Results
Costs
Coefficient
Observation

Keywords

  • inverse problem
  • nonlinear elliptic equation
  • reconstruction algorithm

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

Cite this

A reconstruction algorithm based on topological gradient for an inverse problem related to a semilinear elliptic boundary value problem. / Beretta, Elena; Manzoni, Andrea; Ratti, Luca.

In: Inverse Problems, Vol. 33, No. 3, 035010, 15.02.2017.

Research output: Contribution to journalArticle

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