摘要
为了解决传统有限元截断边界所引起的问题,提出一种新的2.5D直流电阻率有限元-无限元耦合数值模拟方法。首先推导无限元2.5D单元映射函数,然后提出一种无限元形函数,将其与传统有限元相结合,取代传统的混合边界,使得电位在无限域内连续并在无限远处衰减为0 V,最终形成的刚度矩阵稀疏对称并与场源位置无关。研究结果表明:在相同的网格剖分下,有限元无限元耦合方法比传统有限元法能够在边界测点处得到更高的计算精度,能够在较小的计算范围内得到更优的计算结果,从而有利于减少节点数,提高计算速度;由于系数矩阵不随场源位置改变,有利于加速反演计算。
To solve the problems caused by artificial boundary conditions in conventional finite element modeling, a new 2.5D DC resistivity finite-infinite coupling method was proposed. Firstly, the 2.5D mapping functions of infinite elements were derived. Then, a new type of shape functions was proposed. Infinite element method was integrated into conventional finite element method to replace the mixed boundary conditions, which made the electrical potential distribute continuously in half space and decay to 0 at infinity. Meanwhile, the global system matrix was independent of the locations of source points but still sparse and symmetric. The results show that the finite-infinite coupling method can obtain a more accurate solution than traditional FEM method in the same meshing area, and reasonable numerical solutions can be obtained in a relatively small meshing area. Due to the reduction of the discretization domain and node, it can improve the calculation speed. A more superior property is the invariability of the global system matrix with variant source positions which makes this new method alleviate the computational burden and speed up inversions.
出处
《中南大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2014年第8期2691-2700,共10页
Journal of Central South University:Science and Technology
基金
国家公益性行业基金资助项目(SinoProbe-03)
国家自然科学基金资助项目(41174105,41104071,41204082)
中南大学研究生学位论文创新基金资助项目(2011ssxt063)
