3-D transient eddy-current simulations using FI/sup 2/TD schemes with variable time-step selection

Abstract

A variable step size time integration method is used for transient eddy-current problems within the framework of finite integration implicit time-domain (FI 2 TD) formulations. The time-step selection is based on embedded Runge-Kutta methods, which provide an error with the difference of the two solutions of different order. This error allows a prediction of the next time step, for which different types of controller strategies are compared. The accuracy and efficiency of the method is investigated with various numerical examples.

Time-Domain Geometric Eddy-Current $A$ Formulation for Hexahedral Grids

“…In this way, an formulation for eddy-current problems in the time domain is derived by the DGA, for unstructered and nonorthogonal dual grids, in which the primal grid is hexaedral. As far as the authors know, this is a major achievement with respect to previous results reported in literature [8], [9], in which eddy-current problems were discretized by DGA only over structured hexahedral grids. As shown by the proposed numerical analysis, the novel constitutive relations can lead to very accurate results at reduced computational costs, since they avoid the geometric discretization inaccuracy deriving from the use of orthogonal hexahedral grids [8], such as staircase effects, or from the use of structured hexahedral grids for modeling complex geometries [9].…”

“…TIME INTEGRATION METHOD FOR DAE PROBLEM Systems (7) and (8) can be recast into the general form (14) where array denotes one of the unknown arrays or , and and are square matrices of dimension , being the number of primal edges in . Their definition can be easily evinced from (7) and (8). In our eddy-current problem, matrix is time invariant and independent of , the magnetic medium being linear.…”

“…With this aim, we express the array as , where contains the contribution produced by the source currents in and due to the eddy currents in . Equation (7) can then be rewritten as (8) where…”

Linear-implicit time integration schemes for error-controlled transient nonlinear magnetic field simulations

“…Its use was refined in [4] and [5], the latter reference specifically adding results to increase the robustness of the scheme in practical simulations. In this method, however, an additional error-control scheme is required for the nonlinear algebraic systems of equations for each internal stage.…”

“…While already tested for linear magnetic problems in [5], these methods were originally designed to directly include the nonlinear Newton process, thus allowing to completely avoid additional nonlinear iterations within the error-controlled time marching process [2], [6].…”