### 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 |

### Fingerprint

### 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

*Inverse Problems*,

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

**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.

Research output: Contribution to journal › Article

*Inverse Problems*, vol. 33, no. 3, 035010. https://doi.org/10.1088/1361-6420/aa5c0a

}

TY - JOUR

T1 - A reconstruction algorithm based on topological gradient for an inverse problem related to a semilinear elliptic boundary value problem

AU - Beretta, Elena

AU - Manzoni, Andrea

AU - Ratti, Luca

PY - 2017/2/15

Y1 - 2017/2/15

N2 - 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.

AB - 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.

KW - inverse problem

KW - nonlinear elliptic equation

KW - reconstruction algorithm

UR - http://www.scopus.com/inward/record.url?scp=85014661290&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85014661290&partnerID=8YFLogxK

U2 - 10.1088/1361-6420/aa5c0a

DO - 10.1088/1361-6420/aa5c0a

M3 - Article

AN - SCOPUS:85014661290

VL - 33

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 3

M1 - 035010

ER -