Comparison of two techniques for the solution of the 3-D nonlinear transient eddy current problem

Transient Eddy Current Response Due to a Subsurface Crack in a Conductive Plate

“…By assigning f (3) (z) = csc 4 (z)− 2 3 csc 2 (z), the offending term cancels and the three stages of integration yield − 1 6 (cot(z) + z). Discarding the analytical term, −z/6, we put f (z) = − 1 6 cot(z), and use the same poles and residues as before to give 4 (1.53) and…”

“…4 shows the discrepancy of the results in comparison with calculations using a fast Fourier transform (FFT) with 2 17 sample points. Note that in order to represent…”

Transient eddy current response due to a subsurface crack in a conductive plate

“…These matrix equations are, then, solved using appropriate solvers, such as conjugate gradient method, at each time step. A large number of models [3] - [4] fall into this category.…”

“…Using the same poles and residues as before for this function to give cos(z) csc 3 3 (1.51) and (3) (z) = csc 4 (z)− 2 3 csc 2 (z), the offending term cancels and the three stages of integration yield − 1 6 (cot(z) + z). Discarding the analytical term, −z/6, we put f (z) = − 1 6 cot(z), and use the same poles and residues as before to give 4 (1.53) and…”

“…4 shows that the peak amplitude of the magnetic field decreases Variation of ∆H z at coil axis due to eddy currents in a conducting plate excited by an exponential driver coil current with time constant, τ 0 = 250µs.…”