Derivation, application, and evaluation of the method of moments to solve two-dimensional magnetostatic problems
The method of moments (MoM) is a numerical technique used to solve integral equations. The MoM has been commonly applied to solve three-dimensional electromagnetic field problems, where for example one is interested in determining the time-varying electric current distribution on an antenna or the static charge distribution on capacitor plates. In this research, the MoM is formulated to solve general two-dimensional problems of the form: Find the magnetization and magnetic field within a universe that consists solely of magnetic materials and current sources. Within the formulation, a linear system of equations is first established that can be used to represent general discretized problems. A formulation is also derived to handle the inclusion of non-linear magnetic materials. Next, the coefficient matrix is expressed based upon analytical derivations of the mappings between 1) element magnetization and equivalent element edge current and 2) sheet current and magnetic field along elements. Finally, techniques to determine the forces and inductance from the resulting MoM solution have been derived. Validation of the proposed methods is presented based upon the comparison of results with those obtained using traditional methods (magnetic equivalent circuit analysis and finite element analysis). Close agreement has been found in all cases including those with minimal element counts (two elements per side of geometrical structures). The proposed 2D magnetostatic MoM enhances the potential application of fields based models in optimization of electromagnetic devices. Specifically, mesh requirements are greatly reduced leading to relatively fast solutions.
Pekarek, Purdue University.
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