Optimal actuator design based on shape calculus

TL;DR

This paper introduces a shape calculus-based method for designing optimal actuators in linear diffusion systems, utilizing shape and topology optimization, sensitivities, and a level-set numerical algorithm, with numerical validation.

Contribution

It presents a novel approach combining shape calculus and topology optimization for actuator design in linear diffusion equations, including sensitivity analysis and a level-set based numerical method.

Findings

Numerical results validate the effectiveness of the proposed methodology.

Optimal actuators depend on initial conditions and specified norms.

The approach successfully computes actuators for different scenarios.

Abstract

An approach to optimal actuator design based on shape and topology optimisation techniques is presented. For linear diffusion equations, two scenarios are considered. For the first one, best actuators are determined depending on a given initial condition. In the second scenario, optimal actuators are determined based on all initial conditions not exceeding a chosen norm. Shape and topological sensitivities of these cost functionals are determined. A numerical algorithm for optimal actuator design based on the sensitivities and a level-set method is presented. Numerical results support the proposed methodology.