This paper presents a numerical investigation of rectangular 2D waveguide problems. Thereby, the resulting Helmholtz equation is approximated by different finite elements techniques. Both homogeneous and heterogeneous material parameters are considered.
This paper deals with the numerical solution of a two-dimensional (2-D) magnetostatic field problem. Thereby, a finite element method (FEM) with the magnetic vector potential as field variable and a discretization with edge elements is used. For the efficient solution of the obtained matrix equation system, a geometric multigrid solver (MG) is presented which reduces the number of iterations considerably.
A geometric multigrid method for the efficient solution of time-harmonic 3-D eddy-current problems is presented. A finite element method with a scalar potential and a vector potential is used to describe the problem. Numerical examples show that using the right smoother in the multigrid, a good convergence of solutions, which does not deteriorate for bad quality meshes can be obtained. The computation time for solving the eddy-current problem of the multigrid method is much faster than that of the conjugate gradient method with incomplete Cholesky factorization as preconditioner.