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# The finite element technique is also quite flexible

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The finite element technique is also quite flexible in terms of the discretization process. Being a discrete technique, it requires discretization of the solution region but no restrictions are imposed on the shape, size and number of finite elements. 143 The solution process as well as the formulation is not affected by the size and shape of the elements used. Furthermore, although the finite difference technique assumes linear relations between the unknowns, the finite element technique can handle higher order relations as well. 143,157 Problems with convergence have no meaning in the context of finite elements. These factors are of particular importance for the simulation of electromagnetic test techniques and the technique has received considerable attention. Numerical models based on the G j R A I [ ] + [ ] [ ] { } = { } 101 Modeling of Electromagnetic Testing

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finite element technique have been developed for two-dimensional 158,159 and three-dimensional 160,161 eddy current applications. When compared to finite difference techniques, problems solved by the finite element technique generally require larger computer resources, especially for nonlinear and time dependent problems. The technique does not lend itself well to the solution of transient problems because it cannot efficiently handle time discretization. The two techniques are complementary, each being suited to the solution of different situations. Time integration in finite element computer codes is usually handled by various forms of finite difference schemes. 162 In the following discussions, the finite element formulation of the electromagnetic field equations is outlined with reference to a particular element shape. The technique of formulation is completely general, however, and any other element shape can be used with relatively minor changes in the formulation. Finite Element Formulation for Two-Dimensional and Axisymmetric Geometries The finite element technique does not provide a direct solution to electromagnetic field equations. Rather, the solution is obtained by first formulating these equations into a suitable form for finite element solution and then solving the resulting set of simultaneous algebraic equations for the magnetic vector potential at discrete points in the solution region. The formulation of the two-dimensional and axisymmetric field equations is presented here using the magnetic vector potential and an energy functional equivalent to the original equations. The following assumptions are made throughout this derivation. 1. The source current density J s and the magnetic vector potential A vary sinusoidally with time. Harmonics in both the source and induced fields are absent. 2. The source medium is assumed to be infinitely conducting, thus effectively neglecting eddy currents in the source.
• Fall '19
• Wind, The Land, Magnetic Field, Dodd, Modeling of Electromagnetic Testing

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