Finite Element Method (FEM)

FEM mesh for PM motor

Finite elements solve by breaking up a problem into small regions and solutions are found for each region taking into account only the regions that are right next to the one being solved. In the case of magnetic fields where FEM is often used, the vector potential is what is solved for in these regions.

Magnetic field solutions are derived from the vector potential through differentiating the solution. This can cause problems in smoothness of field solutions. Theoretically, any partial differential equation class of problem can be solved using FEM (although some types will do better than others.)

The Finite Element Method (FEM) is a numerical technique for solving models in differential form. For a given design, the FEM requires the entire design, including the surrounding region, to be modeled with finite elements. A system of linear equations is generated to calculate the potential (scalar or vector) at the nodes of each element. Therefore, the basic difference between these two techniques is the fact that BEM only needs to solve the unknowns on the boundaries, whereas FEM solves for a chosen region of space and requires a boundary condition bounding that region.

While BEM can solve nonlinear problems, the nonlinear contribution requires a volume mesh. Putting a volume mesh in begins to diminish the benefits of BEM listed above. In fact, for a saturating nonlinear magnetic problem, the saturatation characteristic is best solved with FEM.

BEM and FEM: A Comparison