Shape optimization approach based on the extended finite element method

Abstract

Purpose

This paper proposes to extend the combination of Extended Finite Element Method (XFEM) and Level Set Method (LSM) from structural mechanics to electromagnetics. Based on this approach, the actual stage of the research work, dedicated to the investigation, development, implementation and validation of a shape optimization methodology, particularly tailored for 2D electric structures is described.

Design/methodology/approach

The proposed numerical approach is based on the efficiency of the XFEM and the flexibility of the LSM, to handle moving material interfaces without remeshing the whole studied domain at each optimization step.

Findings

This approach eliminates the conventional use of discrete finite elements and provides efficient, stable, accurate and faster computation schemes in comparison with other methods.

Research limitations/implications

This research is limited to shape optimization of two‐dimensional electric structures, however, the work can be extended to 3D ones too.

Practical implications

The implementation of the proposed numerical approach for the shape optimization of a planar resistor is hereby described.

Originality/value

The main value of the proposed approach is a powerful and robust numerical shape optimization algorithm that demonstrates outstanding suppleness of handling topological changes, fidelity of boundary representation and a high degree of automation in comparison with other methods.

Citation

Topa, V., Purcar, M., Munteanu, C., Grindei, L., Pacurar, C. and Garvasiuc, O. (2012), "Shape optimization approach based on the extended finite element method", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 31 No. 2, pp. 477-497. https://doi.org/10.1108/03321641211200545