A fast topology optimisation for material- and geometry-independent cloaking devices with the BEM and the ${\mathcal H}$-matrix method

TL;DR

This paper introduces a topology optimization method for designing cloaking devices that are effective regardless of the target object's shape or material, utilizing boundary element and ${ m H}$-matrix methods for efficiency.

Contribution

The study develops a novel topology optimization approach for shape- and material-independent cloaking devices, with an efficient sensitivity analysis technique.

Findings

Successfully designed cloaking devices effective for arbitrary objects

Achieved low computational cost in optimization process

Validated the method's effectiveness through numerical examples

Abstract

We show a design method of cloaking devices which work for target objects with arbitrary shape and material by a topology optimisation with an accurate and efficient sensitivity analysis. Most of past researches on topology optimisation of cloaking devices intend to hide a circle-shaped perfect electric conductor. In this case, the cloaking effect is highly dependent on the shape and material of a target object. In this study, we consider to design a cloaking device which work regardless of the property of target objects by modifying the definition of the objective function. Also, we developed an efficient and accurate sensitivity analysis with the boundary element method and the ${\mathcal H}$-matrix method. We show that the proposed method can successfully obtain desired cloaking devices with low computational cost.