### 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 language | English (US) |
---|---|

Article number | 035010 |

Journal | Inverse Problems |

Volume | 33 |

Issue number | 3 |

DOIs | |

State | Published - Feb 15 2017 |

### Keywords

- inverse problem
- nonlinear elliptic equation
- reconstruction algorithm

### ASJC Scopus subject areas

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

## Fingerprint Dive into the research topics of 'A reconstruction algorithm based on topological gradient for an inverse problem related to a semilinear elliptic boundary value problem'. Together they form a unique fingerprint.

## Cite this

*Inverse Problems*,

*33*(3), [035010]. https://doi.org/10.1088/1361-6420/aa5c0a