Symmetric Formulation for Non-Conforming Meshes in Magnetostatic Problems

In this paper, we present a method to solve 2D magnetostatic problems for non-conforming meshes using the penalty method, where the interface conditions are imposed at the integration points. In the case of non-conforming meshes, there are two interfaces at the artificial contact of the two bodies, so in order to impose the interface conditions, which connect the two bodies involved, the interface conditions must be expressed with respect to one interface, in this case we call slave, the body containing this interface and the other the master one. The best choice of the slave body, in order to obtain the most accurate solution, is investigated in this paper. Furthermore, this paper introduces a novel formulation known as the symmetric formulation, where each body is taken simultaneously as slave and as master, so there is no need to make the best choice of the slave body which in some situations is difficult to do. Additionally, this formulation leads to more accurate solutions. The penalty method in this paper can be viewed as a tool to demonstrate the importance of the symmetric formulation, allowing for the exploration of alternative techniques beyond the penalty method.