| Full text | |
| Author(s): |
Birgin, Ernesto G.
;
Laurain, Antoine
;
Souza, Danilo R.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS; v. 30, p. 37-pg., 2024-11-08. |
| Abstract | |
In this paper we propose and analyze a numerical method for the recovery of a piecewise constant parameter with multiple phases in the inverse potential problem. The potential is assumed to be constant in each phase, and the phases are modeled by a Voronoi diagram generated by a set of sites, which are used as control parameters. We first reformulate the inverse problem as an optimization problem with respect to the position of the sites. Combining techniques of non-smooth shape calculus and sensitivity of Voronoi diagrams, we are able to compute the gradient of the cost function, under standard non-degeneracy conditions of the diagram. We provide two different formulas for the gradient, a volumetric and an interface one, which are compared in numerical experiments. We provide several numerical experiments to investigate the dependence of the reconstruction on the problem parameters, such as noise, number of sites and initialization. (AU) | |
| FAPESP's process: | 22/05803-3 - Cutting, packing, lot-sizing, scheduling, routing and location problems and their integration in industrial and logistics settings |
| Grantee: | Reinaldo Morabito Neto |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 22/16733-6 - Reconstruction of Voronoi diagrams in electrical impedance tomography |
| Grantee: | Danilo Rodrigues de Souza |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | Francisco Louzada Neto |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |
| FAPESP's process: | 23/08706-1 - Numerical optimization |
| Grantee: | Ernesto Julián Goldberg Birgin |
| Support Opportunities: | Research Projects - Thematic Grants |