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The Finite Element Method (FEM)

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Historically, much of the formal development of the finite element method (FEM) occurred in the mechanical engineering community. While electrostatics problems typically have fairly simple boundary conditions, they can have very complex structures, so the applicability and popularity of the FEM is well deserved. This chapter shows solving of Laplace's equation by minimizing the stored energy. It demonstrates a very simple finite element approximation. The next step in the process of improving the approximate solution to the concentric circle problem is to break the region down into a large number of line segments. One attribute of the FEM equation organization is the ease with which mixed dielectric regions are handled. Improved voltage approximation can be found by defining a function that itself has one or more adjustable parameters. The chapter also discusses a simple two-dimensional FEM program.