You can use two fundamentally different approaches to solve magnetic field problems. Both involve solving Maxwell's equations, but you can choose to solve them in either integral or differential form. The most common methods for solving problems in differential form are the finite difference (FD) method and the finite element method (FEM). Because of fundamental limitations of the FD approach, FEM is usually the preferred technique. The second approach is to solve Maxwell's equations in integral form using either a boundary element method (BEM) or a volume integral method. We'll restrict the discussion to the BEM approach, as this is more typically used. Both FEM and BEM have advantages and disadvantages, depending on the geometry and material properties involved, as well as the required accuracy. As a result, it's generally advantageous to combine differential and integral equation solvers to take advantage of their strengths to solve a given field problem. We'll use some real-world problems to show the advantages of each method and why a hybrid of the two is a better solution for some classes of problems.
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