Benchmark problems for optimal shape design for 2D eddy currents

Two new benchmark inverse problems for eddy currents are proposed. The first originates in the optimal design of the tubular inductive heater. The authors’ goal is to offer a simple problem which will check whether new software is able to minimize a multimodal objective function. The second benchmark is a simplified model of a hardening device. The purpose of this problem is to test the ability of the software to deal with different design parameters. This benchmark can be easily extended for more complicated, coupled fields problems. For both benchmarks reference standard solutions are presented. They were obtained using a finite element package for electromagnetics, developed by the authors.