Data structures and program techniques of finite element methods for analysis and optimization of electric devices

Abstract

State-of-the-art programming techniques of finite element methods (FEM) for electromagnetic field computation are presented. It covers program structure, data structure and algebraic matrix equation solver. The advantages of the proposed program structure are that multi-developers are empowered to work on different solvers and share common algorithms. The beauty of the proposed data structure are that two dimensional (2-D) FEM, multi-slice FEM and three-dimensional (3-D) FEM can share the same data structure. It allows quick access to all data and is efficient for organizing FEM programs and convenient for mesh generation. It can also deal with motion problems readily. The merits of the matrix equation solver are that it can automatically deal with Dirichlet boundary conditions, master-salve boundary conditions and all other constraints in sparse matrix equations. The sub-matrix operation technique allows the electric circuit equations to be coupled easily with electromagnetic field equations. To couple the FEM with optimization method, a parameterized mesh technique is proposed to avoid mesh regeneration in the optimization progress.