Integral equation fast solver with truncated and degenerated kernel for computing flaw signals in eddy current non-destructive testing

Abstract

In this article, the kernel independent H-matrix method is applied as the mathematical framework. The dense matrix generated by the selected integral equation, without low frequency breakdown problem for solving 3D arbitrary shaped eddy current nondestructive evaluation (NDE) forward problems, is compressed by the truncated and degenerated (TD) kernel function method. It results in a significant reduction in computational burden with nearly linear complexity. The kernel functions (Green's function) are degenerated by Lagrange polynomials which leads to two advantages: firstly, the double integrals are separated in two single integrals, and secondly, they are represented in a factorized form with good accuracy control. Meanwhile, due to the nature of the kernel function with exponential decay in the lossy medium, it is truncated to improve the overall performance. The TD kernel function-based boundary element method (BEM) fits well for solving eddy current NDE problems over the adaptive cross approximation based BEM, especially for detections of flaws or slots in planar objects. Several numerical predictions calculated by the proposed method are compared with those achieved by others such as the experiment, analytical and semi-analytical methods from benchmarks. The robustness and efficiency are demonstrated with excellent agreements and reduced complexity.