Modification of the weak form to enforce electromagnetic field interface conditions in element-free Galerkin method

Abstract

The disposal of interface conditions is a key problem for the application of meshless method in numerical computation of engineering electromagnetic field. Due to the meshless methods employing moving least square approximation scheme can not verify the Kronecker-δ property, the interface conditions can not be enforced automatically as done in FEM. This paper applies methods based on the modification of the weak form, such as Lagrange multiplier method and penalty method, to impose electromagnetic field interface conditions. Using above methods, the general models of electromagnetic field interface conditions expressed by A-φ-A approach are implemented by using the element-free Galerkin method. Then, a rectangular cross section solenoid with analytical solution is employed to validate the effect of the imposition of electromagnetic field interface conditions, and discuss the potential problems when using above two methods in different cases.