A shape optimization algorithm for interface identification allowing topological changes

TL;DR

This paper presents a computationally efficient shape optimization algorithm that combines PDE-constrained methods with a rounding strategy to identify interfaces and allow topological changes in groundwater flow models.

Contribution

It introduces a novel approach that integrates shape optimization with topology changes, improving interface detection in PDE-constrained problems.

Findings

The algorithm effectively identifies radioactive regions in groundwater flow.

It can modify topology of initial guesses without large deformations.

The method is computationally efficient on coarse and fine grids.

Abstract

In this work we investigate a combination of classical PDE constrained optimization methods and a rounding strategy based on shape optimization for the identification of interfaces. The goal is to identify radioactive regions in a groundwater flow represented by a control that is either active or inactive. We use a relaxation of the binary problem on a coarse grid as initial guess for the shape optimization with higher resolution. The result is a computationally cheap method that does not have to perform large shape deformations. We demonstrate that our algorithm is moreover able to change the topology of the initial guess.