The Truncated Region Eigenfunction Expansion Method for the Solution of Boundary Value Problems in Eddy Current Nondestructive Evaluation

Abstract

A number of complex problems in eddy current nondestructive evaluation have been solved recently using the truncated region eigenfunction expansion method. The solution of a boundary value problem is commonly obtained by separation of variables. In a particular unbounded coordinate, the solution is usually expressed as an integral form such as a Fourier or Bessel integral. However, by truncating the domain of the problem, a modified solution is obtained in the form of a series expansion instead of an integral. Although one achieves a gain in computation efficiency in this way, the most significant advantage of the approach is the ability to match interface conditions across several boundaries simultaneously and thus obtain analytical solutions to complex problems. We illustrate the approach by solving the axisymmetric, time harmonic boundary value problem of a coil above a coaxial hole in a plate.