Numerical Modeling for Electromagnetic Non-Destructive Evaluation

This book describes numerical modelling of non-destructive testing phenomena. Electromagnetic methods of NDT are presented and their numerical formulation and solution outlined. The purpose is to allow students to model and represent fields that would be non-solvable by any other means, for the purpose of modelling and understanding the various aspects of non-destructive testing of materials. The intention is to create a book suitable for both higher level undergraduate and graduate study. This book should be of interest to senior/graduate students taking an NDE option on all engineering courses; course text for post-experience courses; researchers/NDE practitioners in industry.

Table of Contents:
1 Elliptic, parabolic and hyperbolic processes.- 2 General approaches to solution of field problems.- 3 The analytic approach.- 4 The numerical approach in NDT.- 5 Numerical methods.- 1. The electromagnetic field equations.- 1.1 Introduction.- 1.2 Maxwell’s equations in differential form.- 1.3 Maxwell’s equations in integral form.- 1.4 Constitutive relations.- 1.5 Electromagnetic interface conditions.- 1.6 Material properties.- 1.7 Hysteresis.- 1.8 Magnetization.- 1.9 Permanent magnets.- 1.10 The Poynting theorem.- 1.11 Potential functions.- 1.12 Gage condition.- 1.13 Field equations in terms of potential functions.- 1.14 Derivation in terms of scalar potentials.- 1.15 Time-harmonic fields.- 1.16 Nonlinear fields.- 1.17 Plane waves and scattering.- 1.18 Propagation of waves: plane waves.- 1.19 Propagation of plane waves in lossy media.- 1.20 Microwaves, waveguides and resonant cavities.- 1.21 Skin depth.- 1.22 Classification of field equations.- 1.23 Problems.- 1.24 Bibliography.- 2. Analytic methods of solution.- 2.1 Introduction.- 2.2 Analytic methods.- 2.3 Separation of variables: solution to Laplace’s equation.- 2.4 Example: skin effect.- 2.5 Example: TM modes in a rectangular waveguide.- 2.6 Green’s function method.- 2.7 Conformal mapping.- 2.8 Other methods.- 2.9 Problems.- 2.10 Bibliography.- 3. The finite difference method.- 3.1 Introduction.- 3.2 The finite difference approximation.- 3.3 The finite difference grid.- 3.4 Explicit and implicit finite difference methods.- 3.5 Finite difference approximation for time dependent equations.- 3.6 Inclusion of material properties.- 3.7 Problems.- 3.8 Bibliography.- 4. The finite element method.- 4.1 Introduction.- 4.2 The finite element approximation.- 4.3 The finite element method.- 4.4 The finite element.- 4.5Finite element formulation.- 4.6 The finite element mesh.- 4.7 Two-dimensional mesh generation.- 4.8 Pre-processing software.- 4.9 Problems.- 4.10 Bibliography.- 5. Elliptic partial differential equations.- 5.1 Introduction.- 5.2 The general elliptic partial differential equation.- 5.3 Classes of problems.- 5.4 Applications to NDT.- 5.5 2-D, axisymmetric, and 3-D applications: differences and similarities.- 5.6 Bibliography.- 6. Finite difference solution of elliptic processes.- 6.1 Introduction.- 6.2 Elliptic processes: applications in 2-D and 3-D electrostatics.- 6.3 Magnetostatic applications.- 6.4 Eddy Current applications.- 6.5 Time-harmonic wave propagation.- 6.6 Nonlinear applications.- 6.7 Problems.- 6.8 Bibliography.- 7. Finite element formulation.- 7.1 Introduction.- 7.2 Choice of formulations and finite elements (2-D and 3-D).- 7.3 Formulation using an energy functional: variational approach.- 7.4 Formulation using Galerkin’s method.- 7.5 Examples: static applications.- 7.6 Examples: eddy current applications.- 7.7 Examples: axisymmetric applications.- 7.8 Examples: three-dimensional applications.- 7.9 Extensions and modifications.- 7.10 Problems.- 7.11 Bibliography.- 8. Boundary integral, volume integral and combined formulations.- 8.1 Introduction.- 8.2 Boundary integral methods.- 8.3 The method of moments: an intuitive approach.- 8.4 Integral equations.- 8.5 Finite element implementation.- 8.6 Integral equations for static fields.- 8.7 Problems.- 8.8 Bibliography.- 9. Parabolic partial differential equations.- 9.1 Introduction.- 9.2 The general parabolic partial differential equation.- 9.3 Transient finite element formulation.- 9.4 Transient finite difference formulation.- 9.5 Three-dimensional solutions.- 9.6 Finite difference time domain methods.- 9.7Examples.- 9.8 Problems.- 9.9 Bibliography.- 10. Hyperbolic partial differential equations.- 10.1 Introduction.- 10.2 The general hyperbolic partial differential equation.- 10.3 The finite difference time domain method.- 10.4 Examples.- 10.5 Problems.- 10.5 Bibliography.- 11. Miscellaneous numerical methods.- 11.1 Introduction.- 11.2 Numerical integration.- 11.3 Numerical differentiation.- 11.4 Solution of linear systems of equations.- 11.5 Solution of nonlinear systems of equations.- 11.6 Methods of solution for eigenvalues and eigenvectors.- 11.7 Insertion of Dirichlet boundary conditions.- 11.8 Bibliography.