2019/01/01 by Peter Gangl, Gangl, Peter, Kevin Sturm +1
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1908.10775
openalex publication_date 2019/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the asymptotic behaviour of the quasilinear\ncurl-curl equation of 3D magnetostatics with respect to a singular\nperturbation of the differential operator and prove the existence of the\ntopological derivative using a Lagrangian approach. We follow the strategy\nproposed in our recent previous work (arXiv:1907.13420) where a systematic and\nconcise way for the derivation of topological derivatives for quasi-linear\nelliptic problems in H1 is introduced. In order to prove the asymptotics for\nthe state equation we make use of an appropriate Helmholtz decomposition. The\nevaluation of the topological derivative at any spatial point requires the\nsolution of a nonlinear transmission problem. We discuss an efficient way for\nthe numerical evaluation of the topological derivative in the whole design\ndomain using precomputation in an offline stage. This allows us to use the\ntopological derivative for the design optimization of an electrical machine.\n