预条件共轭梯度法求解三维地电场有限元方程的网格分析

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英文篇名：The mesh analysis in solving 3D geoelectric FE equation with pre-conditioned conjugate gradient method 作者：王威 ; 李景富 ; 刘洁 英文作者：WANG Wei;LI Jingfu;LIU Jie;School of Earth Sciences and Engineering,Sun Yat-sen University∥Guangdong Provincial Key Laboratory of Mineral Resources & Geological Processes;Guangdong Nonferrous Geological Environment Center; 关键词：网格分析 ; 预条件共轭梯度 ; 有限元 ; 三维地电场 英文关键词：mesh analysis;;pre-conditioned conjugate gradient;;finite element;;3D geoelectrics 中文刊名：ZSDZ 英文刊名：Acta Scientiarum Naturalium Universitatis Sunyatseni 机构：中山大学地球科学与工程学院∥广东省地质过程与矿产资源探查重点实验室;广东省有色地质环境中心; 出版日期：2018-05-15 出版单位：中山大学学报(自然科学版) 年：2018 期：v.57;No.257 基金：国家自然科学基金(41704074,41574087);; 中国石油天然气总公司973项目(2014CB239004) 语种：中文; 页：ZSDZ201803001 页数：6 CN：03 ISSN：44-1241/N 分类号：7-12

摘要

为了优化预条件共轭梯度法求解三维地电场有限元方程的效率,通过系统的网格分析,提出在常规六面体网格基础上二次剖分得到四面体网格的方案。模型分析结果表明,对于均匀网格,不完全Cholesky共轭梯度法(ICCG)和超松弛预条件共轭梯度法(SORCG)均可成功求解;对于非均匀网格,六面体剖分会导致ICCG的预条件因子不符合条件而求解失败,但采用新的四面体剖分ICCG不仅成功求解而且相对六面体网格可以节省约50%的内存需求。
        Mesh division scheme affects the efficiency of 3D geoelectric finite element(FE) modelling when using pre-conditioned conjugate gradient method. The tetrahedral mesh,which is derived from regular hexahedral mesh,is recommended after mesh analysis. Results from model computations reveal that the incomplete Cholesky conjugate gradient method(ICCG) and successive over-relaxation conjugate gradient method(SORCG) could succeed when employing uniform meshes. However,the non-uniform hexahedral meshes might lead to unsuccessful pre-condition matrix and ICCG might fail. In contrast,the presented tetrahedral meshes overcome this drawback and make ICCG a stable solver. Besides,the new mesh scheme could save 50% computer memories compared to traditional hexahedral mesh.

引文

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