Efficient methods for solving boundary integral equation in diffusive scalar problem and eddy current nondestructive evaluation

Analysis of electromagnetic non-destructive evaluation modelling using Stratton-Chu formulation-based fast algorithm

“…In the frequency range of ECT, because the displacement currents in the metal test pieces are negligible compared with conducting currents. Equations (2.4) and (2.5) can be written as [22]…”

“…Auld's formula is used to calculate the impedance change corresponding to the isolated probe coil in the presence of the conductor (flawed or unflawed) and the impedance variation of unflawed and flawed cases [25]. If only the equivalent surface currents J S and M S exist on the surface, Auld's formula for the impedance change in the surface integral form reads [22] Figure 2. Cross-section for a single turn coil above a conducting sphere [26].…”

“…In the frequency range of ECT, because the displacement currents in the metal test pieces are negligible compared with conducting currents. Equations (2.4) and (2.5) can be written as [22] right left right left right left right left right left right left3pt0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278emH1(r)≈Hnormalinc(r)−(1/μ1)∮Snormal∇G1false(boldr,r′false)boldnfalse^⋅boldBfalse(r′false) normaldS′+∮Snormal∇G1false(boldr,r′false)×false[n^×H(boldrnormal′)false] normaldS′ …”

“…Then the Galerkin's method is applied, (2.24) (2.25) are tested with boldΛmfalse(boldrfalse) and (2.16) is tested with bmfalse(boldrfalse). The discretized impedance matrix of the Stratton-Chu formulations reads [22] [center center center4pt1em12boldT−K1×0R1×jμ2μ1L2×12boldT+K2×0μ2μ1K2n−jk22L2n12boldD−R2n][4pt1emacnormal′d…”

“…Then the Galerkin's method is applied, (2.24) (2.25) are tested with Λ m (r) and (2.16) is tested with b m (r). The discretized impedance matrix of the Stratton-Chu formulations reads[22] …”