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In numerical computation, the finite-element method associated with external electric circuits is often used to evaluate electromagnetic devices with voltage sources. To study the solution of the steady state, the computation time can be prohibitive due to a large transient state compared with the time step used to discretize the time domain. In this paper, a method based on the waveform relaxation method is developed in order to impose the steady state of the solution in the case of a nonlinear magnetostatic problem coupled with electric circuit equations. [ABSTRACT FROM AUTHOR]

The numerical solution of partial differential equations onto random domains can be done by using a mapping transforming this random domain into a deterministic domain. The issue is then to determine this one to one random mapping. In this paper, we present two methods—one based on the resolution of the Laplace equations, one based on a geometric transformation—to determine the random mapping. A stochastic magnetostatic example is treated to compare these methods. [ABSTRACT FROM PUBLISHER]

An approach based on the double Lagrange multipliers is developed using the finite element method in order to impose complex periodic or anti-periodic boundary conditions. The magnetostatic equations are solved using the vector or scalar potential formulations. In order to show the possibilities of the proposed approach, an example of application is studied and the results are discussed. [ABSTRACT FROM AUTHOR]