Reconstruction of material losses by perimeter penalization and phase-field methods

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:251

Article

Rondi, Luca

关键词: Inverse problems;    Cavities;    Phase-field functions;    Perimeter penalization;   

DOI  :  10.1016/j.jde.2011.03.014

来源: Elsevier

【 摘 要 】

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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free