基于非结构化网格的2.5-D直流电阻率自适应有限元数值模拟

2.5-D直流电阻率有限元数值模拟中，模型的剖分及加密主要通过手动实现.另外，采用的单元类型比较规则如矩形单元等，不易实现复杂模型的模拟.为解决上述问题，文中提出了一种自适应有限元算法.算法中采用稳健的后验误差估计来自动预测下一次网格的单元尺寸，直到设定的迭代条件满足为止.另外，采用非结构化三角形单元实现了任意复杂模型的灵活剖分.基于此，利用垂直接触面模型分析和对比了不同自适应策略的效率.通过对比发现，点源附近的单元得到了加密以消除源的奇异性.另外，对于任意一种策略，有限元结果均能最终收敛到精确解.最后，模拟了两个模型：2-D单个异常体模型和2-D地形模型.

2.5-D DC RESISTIVITY MODELING BY ADAPTIVE FINITE-ELEMENT METHOD WITH UNSTRUCTURED TRIANGULATION

In 2.5-D DC resistivity modeling with the finite-element method, models are often subdivided and refined according to user's experiences. Moreover, the regular elements like rectangle are usually adopted. Due to these, it will need more efforts to simulate complicated models. To deal with these problems, we present an adaptive finite-element technique for 2.5-D DC resistivity modeling. A robust posteriori error estimator is incorporated to automatically predicate the new element size for the next mesh until the specified target condition is satisfied. Moreover, unstructured triangulation is employed for the discretizaiton of arbitrary complex models. Base on these, we use a vertical contact model to discuss the efficiencies of different adaptive schemes. The comparison shows that, the elements near the source points are highly refined to eliminate the singularity during the adaptive process. Furthermore, the numerical results for different schemes all can converge to the analytical solution in the final generated mesh. Finally, two additional models: a 2-D inhomogeneity buried in the homogenous half space and a 2-D valley model are tested to show the distinctive performance of our adaptive finite-element algorithm.