Structured inverse modeling in parabolic diffusion processess

TL;DR

This paper introduces efficient shape calculus-based methods for identifying structured diffusivity in parabolic diffusion processes, utilizing a novel shape gradient and quasi-Newton acceleration, supported by numerical validation.

Contribution

The paper develops a new shape gradient for parabolic processes and combines it with quasi-Newton methods to improve inverse modeling of structured diffusivity.

Findings

The new shape gradient effectively guides inverse modeling.

Quasi-Newton techniques accelerate convergence.

Numerical results validate the theoretical approach.

Abstract

Often, the unknown diffusivity in diffusive processes is structured by piecewise constant patches. This paper is devoted to efficient methods for the determination of such structured diffusion parameters by exploiting shape calculus. A novel shape gradient is derived in parabolic processes. Furthermore quasi-Newton techniques are used in order to accelerate shape gradient based iterations in shape space. Numerical investigations support the theoretical results.