Toward Fast Topological-Shape Optimization With Boundary Elements

TL;DR

This paper enhances boundary element methods for topological-shape optimization by addressing computational efficiency issues, validated through numerical examples, to facilitate faster engineering design processes.

Contribution

It proposes methods to overcome computational drawbacks of boundary element approaches in topological-shape optimization, improving efficiency.

Findings

Improved boundary element method reduces optimization time.

Validated approach with numerical example demonstrating efficiency gains.

Enhanced tools enable faster topological-shape optimization in engineering design.

Abstract

Wide variety of engineering design tasks can be formulated as constrained optimization problems where the shape and topology of the domain are optimized to reduce costs while satisfying certain constraints. Several mathematical approaches were developed to address the problem of finding optimal design of an engineered structure. Recent works have demonstrated the feasibility of boundary element method as a tool for topological-shape optimization. However, it was noted that the approach has certain drawbacks, and in particular high computational cost of the iterative optimization process. In this short note we suggest ways to address critical limitations of boundary element method as a tool for topological-shape optimization. We validate our approaches by supplementing the existing complex variables boundary element code for elastostatic problems with robust tools for fast topological-shape optimization. The efficiency of the approach is illustrated with a numerical example.