Meshing Strategies for Shape Optimization in Electromechanics based on the Virtual Element Method

The Virtual Element Method (VEM) is a recent and successful method for the numerical solution of partial differential equations. The methodological background of the VEM is presented and its application in magnetic field analysis is shown; accordingly, the numerical solution of non-linear magnetostatic problems is worked out in two-dimensional domains. In this paper, we are interested in the analysis and synthesis of an internal permanent magnet motor. In this framework, the VEM is particularly suitable thanks to its flexibility in handling generally shaped polygons, specifically the possibility of treating in a smart way both hanging nodes and mesh gluing.