A Perturbation Method for Computing Field Distortions due to Conductive Regions with H-Conform Magnetodynamic Finite Element Formulations

Abstract

A method for solving eddy current problems in two separate steps is developed for global-local analyses with hconform finite element formulations. An unperturbed problem is first solved in a global mesh excluding additional conductive regions. Its solution gives the sources for a sequence of other problems, perturbed by adding conductive regions. Each problem only requires a new adapted mesh of a local region. The way the local problems and their sources are defined leads to a significant speed-up of parameterized analyses, e.g. in optimization and sensitivity analyses.

Subproblem approach for modeling multiply connected thin regions with an h-conformal magnetodynamic finite element formulation

“…where h i is the magnetic field, b i is the magnetic flux density, e i is the electric field, j i is the electric current density, µ i is the magnetic permeability, i is the electric conductivity and n is the unit normal exterior to ⌦ [13]. This is the case when some field traces in SP p are forced to be discontinuous, whereas their continuity must be recovered via a SP k, which is done via a SS in SP k fixing the opposite of the trace discontinuity solution of SP p. The TS model for the h i -formulation requires an unknown discontinuity h d,i through the TS t,i of the tan-…”

“…3 Finite element weak formulations 3.1 h-formulation with source and reaction magnetic fields The weak h ii formulation is obtained from the weak form of Faraday's law (1c) [13]. The magnetic field h i is split into two parts, i.e.…”

A Perturbation Method for the 3D Finite Element Modeling of Electrostatically Driven MEMS

“…An unperturbed problem is first defined in Ω without considering the properties of a so-called perturbing region Ω c,p which will further lead to field distortions [8][9] [10]. At the discrete level, this region is not described in the mesh of Ω.…”

“…An unperturbed problem is first solved in a large mesh taking advantage of any symmetry and excluding additional regions and thus avoiding their mesh. Its solution is applied as a source to the further computations of the perturbed problems when conductive regions are added [8][9] [10]. It benefits from the use of different subproblem-adapted meshes, this way the computational efficiency increases as the size of each sub-problem diminishes [9].…”

An Iterative Finite Element Perturbation Method for Computing Electrostatic Field Distortions

“…Its solution is applied as a source to the further computations of the perturbed problems when some regions are added. The method benefits from the use of different subproblem-adapted meshes, what increases the computational efficiency when the size of each subproblem diminishes [2]. For some positions where the coupling between regions is significant, an iterative procedure is required to obtain an accurate solution.…”