| 耦合有限单元法扩边的直流电阻率勘探无单元Galerkin法正演 |
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| 引用本文： | 麻昌英,柳建新,郭荣文,孙娅,崔益安,刘嵘,刘海飞.耦合有限单元法扩边的直流电阻率勘探无单元Galerkin法正演[J].地球物理学报,2018,61(6):2578-2588. |
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| 作者姓名： | 麻昌英 柳建新 郭荣文 孙娅 崔益安 刘嵘 刘海飞 |
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| 作者单位： | 1. 中南大学 地球科学与信息物理学院, 长沙 410083;2. 有色资源与地质灾害探查湖南省重点实验室, 长沙 410083 |
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| 基金项目： | 中南大学博士研究生自主探索创新项目（2016zzts088）和国家自然科学基金项目（41674080，41674079，41574123）联合资助. |
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| 摘 要： | 本文分析了目前直流电阻率正演模拟中的无单元Galerkin法（EFGM）和有限单元法（FEM）的优缺点，针对采用第一类边界条件需要足够大的计算域时EFGM计算成本高的问题，在计算域外围区域采用FEM扩边，提出了直流电阻率的无单元Galerkin-有限单元耦合法（EFG-FE）.采用具有Kronecker delta函数性质的径向基点插值法（RPIM）构造EFGM形函数，在外围区域将EFGM与FEM直接耦合，无需其他处理手段，消除了传统EFGM与FEM耦合中存在的界面耦合困难.EFG-FE将模型计算域分割为EFGM区域和FEM区域，模型核心区域采用EFGM计算，发挥EFGM灵活性、适应性强和高精度的优点，使得模型建立简单方便，对任意复杂地电模型适应性强，同时获得高精度模拟结果.在模型计算域外围采用快速扩展的FEM单元网格进行剖分，利用其数值稳定性和高效性，使用少量FEM节点和单元网格将计算域大范围扩大满足第一类边界条件，同时不大幅增加计算成本，进而提高计算效率.最后，通过不同正演方法的模型算例的模拟结果对比，验证了本文提出的EFG-FE有效可行，其模拟结果具有很高的模拟精度，且相比于采用第三类边界条件的EFGM提高了计算效率，具有更好的模拟性能.
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| 关 键 词： | 无单元Galerkin-有限单元耦合法 RPIM形函数 无单元Galerkin法 有限单元法 直流电阻率 |
| 收稿时间： | 2017-08-11 |
Element-free Galerkin forward modeling of DC resistivity using a coupled finite element method with extended the boundaries |
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| MA ChangYing,LIU JianXin,GUO RongWen,SUN Ya,CUI YiAn,LIU Rong,LIU HaiFei.Element-free Galerkin forward modeling of DC resistivity using a coupled finite element method with extended the boundaries[J].Chinese Journal of Geophysics,2018,61(6):2578-2588. |
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| Authors: | MA ChangYing LIU JianXin GUO RongWen SUN Ya CUI YiAn LIU Rong LIU HaiFei |
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| Institution: | 1. School of Geosciences and Info-Physics, Central South University, Changsha 410083, China;2. Non-ferrous Resources and Geologic Disasters Prospecting Emphases Laboratory of Hunan, Changsha 410083, China |
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| Abstract: | In this paper, we analyze the advantages and disadvantages of the Element-Free Galerkin Method (EFGM) and Finite Element Method (FEM) in forward simulation of Direct Current (DC) resistivity. A large enough computational domain is required when the first class boundary condition is used, which will significantly increase the computational cost of EFGM. To solve this problem, we propose a Element-Free Galerkin-Finite Element (EFG-FE) coupling method for forward modeling of DC resistivity. The FEM is used in the peripheral region of the calculation domain in the EFG-FE. In order to eliminate the difficulties in the traditional EFGM and FEM coupling method on the interface, the Radial Point Interpolation Method (RPIM) is used to construct the element-free shape function. Due to the RPIM shape function has the Kronecker delta function property, EFGM and FEM can be coupled directly without any other processing technology. EFG-FE divides the model calculation domain into a EFGM region and FEM region. In order to exert the flexibility, adaptability and high precision of EFGM, the core area of the model is calculated using EFGM, which results in the simplicity and convenience of model establishment, the adaptability of any complex geoelectric model and high precision of simulation results. In order to reduce the calculation time and expand the computational domain so that the natural boundary conditions are satisfied, a rapidly expanding FEM grid is used in the periphery of the EFGM region, which results in a small number of nodes and FEM grid cells. Finally, the simulation results of different forward modeling methods are compared. The results show that the proposed EFG-FE is feasible. And compared to the EFGM with the third kind of boundary conditions, the proposed EFG-FE method can improve the computational efficiency. In conclusion, the proposed EFG-FE has a better simulation performance. |
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| Keywords: | Element-free Galerkin-finite element coupling method RPIM shape function Element-free Galerkin method Finite element method Direct current resistivity |
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