Rapid Electromagnetic Modeling and Simulation of Eddy Current NDE by MLKD-ACA Algorithm with Integral Kernel Truncations

Abstract

In this article, a novel hybrid method of multilevel kernel degeneration and adaptive cross approximation (MLKD-ACA) algorithm with integral kernel truncations is proposed to accelerate solving integral equations using method of moments (MoM), and to simulate the 3D eddy current nondestructive evaluation (NDE) problems efficiently. The MLKD-ACA algorithm with an integral kernel-truncations-based fast solver is symmetrical in the sense that: (1) the impedance matrix, which is generated by the MoM representing the interactions among the field and source basis functions, is symmetrical; (2) the factorized form of the integral kernel (Green’s function) resulted from degenerating it by the Lagrange polynomial interpolation is symmetrical; (3) the structure of the truncated integral kernel for the interactions among the blocks, which ignores the trivial ones of the far block pairs, is symmetrical using the integral kernel truncations technique. The impedance variations predicted by the proposed symmetrical eddy current NDE solver are compared with other methods in benchmarks to show the remarkable accuracy and efficiency.