Spectral Stochastic Simulation of a Ferromagnetic Cylinder Rotating at High Speed

Abstract

This paper addresses the influence of uncertainty on ferromagnetic material properties on the torque yielded by ferromagnetic cylinders rotating at high speeds. To that end, two state-of-the-art high-order stochastic solution approaches, the stochastic collocation and stochastic Galerkin method, are applied to a nonlinear convection-diffusion problem with random coefficients and their performance is compared.

Approximation Methods to Solve Stochastic Problems in Computational Electromagnetics

“…Besides, dedicated solvers can be employed to solve the equation (19) by taking advantage the expression (21) based on Kronecker products. Accounting for non-linearities in the Galerkin approach is more tricky than in the non-intrusive case but remains possible [28]. The Galerkin method, for given approximation spaces W (D) and P K P , minimizes the error of approximation in the L2 sense which is not the case with other approximation methods based on the evaluations of the deterministic model (non intrusive methods like projection method, collocation method, regression method).…”

“…The methods have been evaluated on academic examples [26,28] but one can notice a trend towards more and more realistic applications which shows that the stochastic approach is getting more and more mature in the community of computational electromagnetics. In [19], the projection method has been applied uncertainties in the EEG source analysis.…”

Comparison of two approaches to compute magnetic field in problems with random domains

“…However, for the elements of e and h it requires several integral calculations. One can notice that these integral calculations can be done numerically by (9) but in some cases it requires some additional numerical treatments because of the irregularity (discontinuity) of the integrand. In [11], one technique that consists in using a recursive method and dividing the integral domain into several "boxes" is proposed.…”

“…In computational electromagnetics, there are generally three kinds of uncertainties: those on the source terms, those on the material behavior and those on the dimensions of the apparatus under study. In [3,4,5,6,7,8,9], some methods using polynomial chaos expansions were proposed to quantify the effect of uncertainties on the behavior laws on the outputs of the model. For problems with random domains (the dimensions are uncertain), discontinuities can appear on the field distribution in the "random dimension"…”

An analysis of electromagnetic processes in a turbogenerator with a real rotor and a stator tooth structure in the no-load mode

“…Thus, in the world scientific and technical literature, much attention has been paid to the development of theoretical and metho do lo gi cal approaches to solving the problems arising when de veloping mathematical models of elec tric objects. In these approaches, efforts are made to take the construction of objects into account to as great an extent as possible and apply real physical laws of electromagnetic phe nomena occurring in the device media [1][2][3][4][5][6][7][8][9][10][11][12]. One of the more advanced strategies for successfully tackling this problem is to develop mathematical models of electric objects exclusively based on the theory of electromagnetic fields.…”