基于非结构化网格的三维大地电磁自适应矢量有限元模拟

来源期刊:中南大学学报(自然科学版)2010年第5期

论文作者:刘长生 汤井田 任政勇 冯德山

文章页码:1855 - 1859

关键词:MT三维正演;非结构化网格;矢量有限元;残差型后验误差;h-型自适应有限元

Key words:magnetotelluric three-dimensional modeling; unstructured mesh; vector finite element method; residual based error estimation; h-adaptive finite element method

摘    要:基于能够模拟复杂模型的非结构化网格,提出基于矢量单元的三维自适应有限元大地电磁模拟算法。其过程是:利用残差型的后验误差算子初步估算粗网格上的单元误差,通过加密误差超过限定的单元,生成新的网格;对新的网格重复上一步过程,从而得到更加精确的数值结果;重复迭代过程直到计算结果的精度达到预定要求为止,从而生成最优化的有限元网格;基于COMMEMI 3D-1 MT模型的数值模拟,验证本文算法的正确性。研究结果表明:通过自适应的网格加密和迭代求解过程,本文算法可以产生迭代收敛的数值结果,计算结果具有较高的精度。

Abstract: Based on unstructured grid which can simulate complex geoelectric models, the vector edge-based finite-elements were proposed. An adaptive finite element three-dimensional magnetotelluric modeling algorithm was introduced. The procedures are as follows: Element errors was estimated by a residual-based posteriori error on the coarse grid, and then elements with high error indicators were refined to generate a new grid. A new finite-element numerical processes were repeated on this new mesh to obtain more accurate and reliable numerical results. The iterative process was terminated until the accuracy of results on the final mesh became a required one. The COMMEMI 3D-1 model was tested to verify the correctness of the algorithm. The results show that for a complex three-dimensional electromagnetic model of the earth, using the adaptive mesh refinement and iterative solution procedure, the algorithm can generate iterative numerical results with high reliability.

基金信息:国家自然科学基金资助项目
湖南省自然科学基金重点资助项目

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