Method of Moments Toolbox (MoMT), Version 1.1

The Method of Moments (MoM) is a numerical method that can be used to solve fields-based integral equations. In contrast to methods used to solve differential equations, such as Finite Element Analysis (FEA), MoM has an advantage that only the active material is meshed. As a result, the number of unknowns can be greatly reduced compared to FEA. Additional advantages include that any combination of polygons can be used to establish the mesh, and the nodes are not required to be coincident. Furthermore, only a surface mesh is required when the materials are magnetically linear. There are disadvantages to the MoM compared to FEA. Chief among these is that the system matrix is full. Thus, establishing the matrix can require significant effort compared to that of the sparse stiffness matrix of FEA.

Over the past several years, researchers at Purdue University have been considering an MoM formulation for the analysis and design of electric machinery [1]-[4]. An initial culmination of these efforts is a MATLAB-based MoM toolbox that has been configured for the analysis and design of surface-mount permanent magnet synchronous machines (PMSM) and their associated drives. The MoM toolbox includes functions to perform the MoM calculations. It also relies on several supporting functions to calculate, for example, stator, rotor, and permanent magnet material properties, as well as perform multi-objective optimization. These supporting functions have been written, documented, and provided to the community by S.D. Sudhoff and his students independent of the MoM effort. Many of these supporting functions, or at least the key calculations performed within them, are described in [5] and [6]. Indeed, to ease the documentation burden, the data structures used to describe the PMSM geometry, materials, winding functions, etc. utilized in [5] are applied in the MoM toolbox.

It is acknowledged that research continues on the application of MoM to electric machinery. One goal in providing this tool is to support those interested in pursuing such research. Indeed, the underlying calculations are often tedious, and having to start from scratch could be a strong deterrent. In this initial public version of the MoM, the calculations for the analysis and design of PMSMs is constrained to linear materials. A nonlinear MoM has been established and is being used in design within the Purdue graduate student group. The nonlinear updates to the toolbox will be incorporated into the public release once publications of the nonlinear MoM are in print.

1. R. Howard, A. Brovont and S. Pekarek, "Analytical Evaluation of 2-D Flux Integral for Magnetostatic Galerkin Method of Moments," in IEEE Transactions on Magnetics, vol. 52, no. 4, pp. 1-8, April 2016.

2. R. Howard and S. Pekarek, "Two-Dimensional Galerkin Magnetostatic Method of Moments," in IEEE Transactions on Magnetics, vol. 53, no. 12, pp. 1-6, Dec. 2017.

3. D. C. Horvath, S. D. Pekarek and R. A. Howard, "Analysis and Design of Electric Machines Using 2D Method of Moments," 2019 IEEE International Electric Machines & Drives Conference (IEMDC), San Diego, CA, USA, 2019, pp. 476-483.

4. D. Horvath, R. Howard and S. Pekarek, "Lorentz Force/Torque Calculation in 2-D Method of Moments," in IEEE Transactions on Magnetics, vol. 56, no. 8, pp. 1-8, Aug. 2020.