3D numerical simulation for the transient electromagnetic field excited by the central loop based on the vector finite-element method
3D numerical simulation for the transient electromagnetic field excited by the central loop based on the vector finite-element method
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DOI：
10.1088/1742-2132/8/4/008
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发表时间：
2011-12
影响因子：
1.4
通讯作者：
Jianhui Li;Zi-qiang Zhu;Shuaijie Liu;S. Zeng
中科院分区：
文献类型：
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作者：
Jianhui Li;Zi-qiang Zhu;Shuaijie Liu;S. Zeng
根据反常场算法的基本原理，推导了电磁场的亥姆霍兹方程。以电场亥姆霍兹方程为控制方程，采用伽辽金法推导了相应的矢量有限元方程组。为了用矢量有限元法求解控制方程，我们将计算区域划分为齐次块单元，并采用Whitney型矢量基函数。利用矢量有限元法在拉普拉斯域得到电场的异常场后，利用Gaver-Stehfest算法将电场的异常场变换到时域，并利用电磁感应法拉第定律得到磁场异常场的脉冲响应。通过比较准H型地电模型的一维解析解，验证了矢量有限元法的精度。对于低电阻率砖体地电模型，矢量有限元法计算的电动势图形与积分方程法和时域有限差分法计算的电动势图形一致。
Based on the principle of abnormal field algorithms, Helmholtz equations for electromagnetic field have been deduced. We made the electric field Helmholtz equation the governing equation, and derived the corresponding system of vector finite element method equations using the Galerkin method. For solving the governing equation using the vector finite element method, we divided the computing domain into homogenous brick elements, and used Whitney-type vector basis functions. After obtaining the electric field's anomaly field in the Laplace domain using the vector finite element method, we used the Gaver–Stehfest algorithm to transform the electric field's anomaly field to the time domain, and obtained the impulse response of magnetic field's anomaly field through the Faraday law of electromagnetic induction. By comparing 1D analytic solutions of quasi-H-type geoelectric models, the accuracy of the vector finite element method is tested. For the low resistivity brick geoelectric model, the plot shape of electromotive force computed using the vector finite element method coincides with that of the integral equation method and finite difference in time domain solutions.