一种快速计算二维缺陷漏磁场的有限元建模和求解方法

漏磁检测的速度快，灵敏度高，检测过程操作简单，是一种常用的铁磁材料无损检测方法，其中有限元模型被广泛用于漏磁检测中。有限元模型的求解精度高但是计算时间较长，因此，本文提出了一种快速计算二维缺陷漏磁场的有限元建模和求解方法，在保证精度的同时缩短计算时间。通过对有限元数值计算的理论推导，建立了漏磁场的有限元模型，首先采用六节点三角形单元划分网格，其次使用稀疏矩阵的形式求解方程组，再利用边界条件矩阵零空间的正交基求解出磁势。与COMSOL仿真软件的计算结果进行比较，表明本文所建模型是正确可行的。经过实测数据验证，该模型相比于传统有限元模型有明显的性能提升，精度上最大提高83.49%,计算时间能减少95.43%,为研究不规则缺陷的漏磁重构提供了快速有效的正演模型。

Fast finite element modeling and solving method for 2D defect magnetic leakage field

The magnetic flux leakage detection is a common nondestructive detection method for ferromagnetic materials with high speed, high sensitivity and simple operation. The finite element model is widely used in magnetic flux leakage detection. The solution accuracy of the finite element model is high. But, the calculation time is long. Therefore, this article proposes a finite element modeling and solution method for fast calculation of 2D defect magnetic leakage field, which can reduce the calculation time while ensuring the accuracy. Through the theoretical derivation of finite element numerical calculation, the finite element model of magnetic leakage field is established. First, the six-node triangular element is used to divide the grid. Then, the sparse matrix is used to solve the equations, and the orthogonal basis of the zero space of the boundary condition matrix is used to solve the magnetic potential. The comparison with the calculation results of COMSOL simulation software shows that the formulated model is correct and feasible. Through the verification of actual testing data, this model has significantly improved performance compared with the traditional finite element model. The maximum accuracy is increased by 83. 49% , and the calculation time can be reduced by 95. 43% . A fast and effective forward model is provided for studying the magnetic flux leakage reconstruction of irregular defects.