Shape optimization for interface identification in nonlocal models

TL;DR

This paper develops shape optimization techniques for identifying interfaces in nonlocal models governed by PDEs, deriving a new shape derivative and applying numerical methods for solution.

Contribution

It introduces a novel shape derivative for nonlocal systems with interface-dependent kernels, advancing interface identification in nonlocal PDE models.

Findings

Derived a new shape derivative for nonlocal models

Successfully applied numerical methods to solve the optimization problem

Enhanced interface detection in nonlocal PDEs

Abstract

Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization problems constrained by nonlocal equations which involve interface-dependent kernels. We derive a novel shape derivative associated to the nonlocal system model and solve the problem by established numerical techniques.