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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.

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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.

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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.

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