R Mertens

Solution strategies for transient, field-circuit coupled systems

Transient simulation time for field-circuit coupled models of realistic electromagnetic devices becomes unacceptably high. A magnetodynamic formulation is coupled to an electric circuit analysis, yielding a sparse, symmetric and indefinite matrix. The unknown circuit currents correspond to negative eigenvalues in the matrix spectrum. The Quasi-Minimal Residual method performs better than the Minimal Residual approach that is restricted to positive definite preconditioners. The positive definite variant is solved by the Conjugate Gradient method without explicitly building the dense coupled matrix. As an example, both approaches are applied to an induction motor.

A parametric finite element environment tuned for numerical optimization

Nowadays, numerical optimization in combination with finite element (FE) analysis plays an important role in the design of electromagnetic devices. To apply any kind of optimization algorithm, a parametric description of the FE problem is required and the optimization task must be formulated. Most optimization tasks described in the literature, feature either specially developed algorithms for a specific optimization task, or extensions to standard finite element packages. Here, a 2D parametric FE environment is presented, which is designed to be best suited for numerical optimization while maintaining its general applicability. Particular attention is paid to the symbolic description of the model, minimized computation time and the user friendly definition of the optimization task.

An algebraic multigrid method for solving very large electromagnetic systems

Although most finite element programs have quite effective iterative solvers such as an incomplete Cholesky (IC) or symmetric successive overrelaxation (SSOR) preconditioned conjugate gradient (CG) method, the solution time may still become unacceptably long for very large systems. Convergence and thus total solution time can be shortened by using better preconditioners such as geometric multigrid methods. Algebraic multigrid methods have the supplementary advantage that no geometric information is needed and can thus be used as black box equation solvers. In the case of a finite element solution of a non-linear magnetostatic problem, the algebraic multigrid method reduces the overall computation time by a factor of 6 compared to a SSOR-CG solver.

Combined time-harmonic-transient approach to calculate the steady-state behaviour of induction machines

Due to less computational expenses, a time-harmonic approach is often preferred over a transient approach to calculate the steady-state behaviour of induction machines. However the computation time of the transient approach with a one-step time-stepping scheme is significantly reduced by using a combined time-harmonic transient approach and by varying the parameter which determines the difference scheme with time.

Selected projection methods to improve the convergence of non‐linear problems

Short computation times required for the design and numerical optimisation of electromagnetic devices with the finite element method are obtained using an adaptive mesh refinement algorithm. Less time is spent on the initial mesh generation, while the time needed for refinement is negligible when special data structures are used. But an even more significant reduction in total computation time is achieved with the initialisation of the solution on the generated mesh. Fewer Newton steps are required to solve non‐linear problems compared to a zero initial solution, while the time needed for the projection of the solution is far less than the time needed for a Newton step.

Calculation of the Electric and the Magnetic Field Generated by Busbar Systems

More and more people ask questions on eventual influence of electric and magnetic fields. Therefore, accurate numerical prediction methods for geometrically difficult configurations are important to compare with measured values. In this way standards can be checked during design. For magnetic fields the International Radiation Protection Association (IRPA) proposes the limiting values as shown in table 1.