We treat the inverse problem of determining material losses, such as cavities, in a conducting body, by performing electrostatic measurements at the boundary. We develop a numerical approach, based on variational methods, to reconstruct the unknown material loss by a single boundary measurement of current and voltage type. The method is based on the use of phase-field functions to model the material losses and on a perimeter-like penalization to regularize the otherwise ill-posed problem. We justify the proposed approach by a convergence result, as the error on the measurement goes to zero.
|Titolo:||Reconstruction of material losses by perimeter penalization and phase-field methods|
RONDI, LUCA (Corresponding)
|Parole Chiave:||inverse problems; cavities; phase-field functions; perimeter penalization|
|Settore Scientifico Disciplinare:||Settore MAT/05 - Analisi Matematica|
|Data di pubblicazione:||2011|
|Digital Object Identifier (DOI):||10.1016/j.jde.2011.03.014|
|Appare nelle tipologie:||01 - Articolo su periodico|