Non-conforming finite element method with tetrahedral elements

Abstract

This paper presents a non-conforming finite element (FE) method with tetrahedral elements, which is applied to 3-D shape optimization. In the present method, continuity of magnetic flux is directly enforced on the interfaces of different domains in which FE meshes are independently generated. The slave unknowns in one side which are linearly dependent on the unknowns in the other side are eliminated. It is shown that the present method yields accurate solutions to 3-D nonlinear magnetostatic problems. Moreover, evolutional shape optimization of an inductor is shown to be successfully carried out using the present method.