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# Numerical modeling numerical modeling in

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Numerical Modeling. Numerical modeling in nondestructive testing is an outgrowth of the failure of analytical models reliably to predict the necessary field interactions with any degree of generality. A numerical model uses a digital computer to solve the governing equations directly, with few simplifying assumptions. This in itself is enough to explain the value of such models. Numerical modeling allows the solution of very complex problems and, at the same time, does not require the user to know the intricacies of electromagnetic theory or differential calculus. All that the user is required to do is input the problem variables and, if necessary, verify the results experimentally. General Overview of Analytical and Numerical Modeling The existence of models for eddy current testing phenomena depends entirely on the ability to solve Maxwell’s equations with or without approximations. The value of such models in solving the inversion problem satisfactorily is beyond dispute. Solution of this important problem is possible only with the development of good theoretical models, capable of predicting the complex interactions of a multitude of factors in the test object. A good, reliable theoretical model for nondestructive testing should be able to satisfy the following conditions. 1. The model should describe the physics of interaction between the applied alternating current field, induced currents and discontinuities in the test object. 2. The model should serve as a theoretical test bed for situations difficult or impossible to replicate experimentally. 3. The model should generate eddy current output signals for a wide variety of discontinuities and specimen shapes, avoiding costly sample preparation and helping to determine discontinuity characterization parameters. 4. The model should provide training data for automated discontinuity characterization systems and equipment. 5. The model should aid in the design of eddy current probes for specific applications. For the purpose of deriving such a model, two main avenues are available: the analytical approach and the numerical approach. Analytical Modeling Analytical models are derived from basic field and circuit theory considerations. In effect, an attempt is made to solve Maxwell’s equations directly. These equations are generally three-dimensional, nonlinear, partial differential equations within complex boundaries and discontinuity shapes. In addition, for moving probe problems, the solution is both time and position dependent. It is therefore not surprising to find that such solutions are only possible for the most elementary of test geometries, with simplifying assumptions in terms of geometry, dimensionality, discontinuity shapes and sources. This oversimplification accounts for the fact that analytical models are limited in scope, applicable only to selected problems and not easily extended to other geometries. On the other hand, the solution to problems for which an analytical model applies is relatively

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• Fall '19
• Wind, The Land, Magnetic Field, Dodd, Modeling of Electromagnetic Testing

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