多源条件下直流电阻率法有限元三维数值模拟中一种近似边界条件

发布时间：2018-06-09 12:07

本文选题：直流电阻率法 + 有限单元法　；参考：《地球物理学报》2016年09期

【摘要】：在多源直流电阻率法有限元三维数值模拟中,传统混合边界条件由于刚度矩阵与源点位置相关,无法实现线性方程组的快速回代求解,目前常用齐次边界条件或无限元边界进行替代,虽然实现了快速回代求解,但同时也降低了数值模拟的精度.为了实现快速回代求解,并确保数值模拟的计算精度,本文提出了一种近似边界条件方法.其核心思想是将与场源位置相关的边界系数矩阵从刚度矩阵中分离出来,使得分离后的刚度矩阵与场源位置无关.并将边界系数矩阵与边界处一次电场向量的乘积移到线性方程组右端源项中,当场源位置发生改变时,只需要重新计算右端源项就可以实现快速回代求解.理论模型数值计算表明,在水平地形条件下,本文边界条件数值精度优于混合边界条件;在起伏地形条件下,与齐次边界条件相比,本文边界条件数值结果与混合边界条件吻合度更高.
[Abstract]:In the finite element numerical simulation of multi-source DC resistivity method, the traditional mixed boundary condition can not be solved quickly because the stiffness matrix is related to the location of the source point. At present, homogeneous boundary conditions or infinite element boundaries are commonly used to replace them. Although the fast iterative solution is realized, the accuracy of numerical simulation is also reduced. An approximate boundary condition method is proposed in this paper in order to solve the problem quickly and to ensure the accuracy of numerical simulation. The core idea is to separate the boundary coefficient matrix related to the position of the field source from the stiffness matrix so that the separated stiffness matrix is independent of the position of the field source. The product of the boundary coefficient matrix and the primary electric field vector at the boundary is moved to the source term of the right end of the linear equation system. When the source position changes on the spot, only the right end source term can be recalculated to realize the quick solution. The numerical calculation of the theoretical model shows that the numerical accuracy of the boundary condition is better than that of the mixed boundary condition under the horizontal terrain condition, and the numerical accuracy of the boundary condition is better than that of the homogeneous boundary condition under the undulating terrain condition. The numerical results of the boundary conditions in this paper are more consistent with the mixed boundary conditions.
【作者单位】：中南大学有色金属成矿预测与地质环境监测教育部重点实验室;中南大学地球科学与信息物理学院;桂林理工大学地球科学学院;
【基金】：国家重大科研仪器设备研制专项资助项目(41227803) 国家自然科学基金项目(41574127,41174104,41674075)联合资助
【分类号】：P631.322

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