有限元法
计算机科学
计算科学
四面体
自适应网格优化
解算器
计算
离散化
区域分解方法
算法
反演(地质)
网格生成
电磁场
几何学
数学
地质学
数学分析
物理
构造盆地
热力学
古生物学
量子力学
程序设计语言
作者
Zhengguang Liu,Zhengyong Ren,Hongbo Yao,Jingtian Tang,Xushan Lu,Colin G. Farquharson
摘要
SUMMARY To effectively and efficiently interpret or invert controlled-source electromagnetic (CSEM) data which are recorded in areas with the kind of complex geological environments and arbitrary topography that are typical, 3-D CSEM forward modelling software that can quickly solve large-scale problems, provide accurate electromagnetic responses for complex geo-electrical models and can be easily incorporated into inversion algorithms are required. We have developed a parallel goal-oriented adaptive mesh refinement finite-element approach for frequency-domain 3-D CSEM forward modelling with hierarchical tetrahedral grids that can offer accurate electromagnetic responses for large-scale complex models and that can efficiently serve for inversion. The approach uses the goal-oriented adaptive vector finite element method to solve the total electric field vector equation. The geo-electrical model is discretized by unstructured tetrahedral grids which can deal with complex underground geological models with arbitrary surface topography. Different from previous adaptive finite element software working on unstructured tetrahedral grids, we have utilized a novel mesh refinement technique named the longest edge bisection method to generate hierarchically refined grids. As the refined grids are nested into the coarse grids, the refinement technique can precisely map the electrical parameters of inversion grids onto the forward modelling grids so that the extra numerical errors generated by the inconsistency of electrical parameters between inversion grids and forward modelling grids are eliminated. In addition, we use the parallel domain-decomposition technique to further accelerate the computations, and the flexible generalized minimum residual solver (FGMRES) with an auxiliary Maxwell solver pre-conditioner to solve the final large-scale system of linear equations. In the end, we validate the performance of the proposed scheme using two synthetic models and one realistic model. We demonstrate that accurate electromagnetic fields can be obtained by comparison with the analytic solutions and that the code is highly scalable for large-scale problems with millions or even hundreds of millions of unknowns. For the synthetic 3-D model and the realistic model with complex geometry, our solutions match well with the results calculated by an existing 3-D CSEM forward modelling code. Both synthetic and realistic examples demonstrate that our newly developed code is an effective, efficient forward modelling engine for interpreting CSEM field data acquired in areas of complex geology and topography.
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