Multilevel adaptive cross approximation for efficient modeling of 3D arbitrary shaped eddy current NDE problems

In this article, the multilevel adaptive cross approximation (MLACA) algorithm is presented to accelerate the boundary element method (BEM) for eddy current nondestructive evaluation (NDE) 3D problems involving arbitrary shapes. The Stratton-Chu formula, which does not have the low frequency breakdown issue, has been selected for modeling. The equivalent electric and magnetic surface currents are expanded with Rao-Wilton-Glisson (RWG) vector basis functions while the normal component of the magnetic field is expanded with pulse basis functions. The MLACA compresses the rank deficient matrices with the ACA and the butterfly algorithm. We improve the efficiency of MLACA by truncating the integral kernels after a certain distance and applying the multi-stage (level) algorithm adaptively based on the criteria for different operators to further decrease the memory and CPU time requirements while keeping almost the same accuracy comparing with the traditional MLACA. The proposed method is especially helpful to deal with the large solution domain issue of the BEM for eddy current problems. Numerical predictions are compared with the analytical, the semi-analytical predictions and the experimental results for 3D eddy current NDE problems of practical interest to demonstrate the robustness and efficiency of the proposed method.

在本文中，提出了多级自适应交叉近似（MLACA）算法，用于加速边界元法（BEM）来解决涉及任意形状的涡流无损检测（NDE）三维问题。选择了不存在低频失效问题的斯特拉顿 - 朱（Stratton - Chu）公式进行建模。等效的电和磁表面电流用拉奥 - 威尔顿 - 格利森（Rao - Wilton - Glisson，RWG）矢量基函数展开，而磁场的法向分量用脉冲基函数展开。MLACA利用自适应交叉近似（ACA）和蝶形算法对秩亏矩阵进行压缩。我们通过在一定距离后截断积分核，并根据不同算子的标准自适应地应用多级（层）算法，提高了MLACA的效率，在与传统MLACA保持几乎相同精度的同时，进一步降低了内存和CPU时间需求。所提出的方法对于处理涡流问题边界元法的大求解域问题特别有帮助。通过将数值预测与实际感兴趣的三维涡流NDE问题的解析解、半解析解预测以及实验结果进行比较，证明了所提方法的稳健性和高效性。