What type of solvers should be used for my particular application?

For the electromagnetic portion of the solution, you can use either the Boundary Element Method (BEM) or the Finite Element Method (FEM) if you are performing a time harmonic (phasor) simulation.  If you are performing an electromagnetic transient, the Finite Element Method must be used.  For thermal analysis (static or transient), only the Finite Element Method can be used.

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