基于局部加密非结构化网格的三维电阻率法有限元数值模拟

总结了目前常用的结构化网格及其局限性，分析了非结构化网格对复杂地质体边界的适应性和Delaunay三角化算法及其网格加密策略，提出了一种新的局部节点加密方法，实现了对复杂模型的完全非结构化四面体全自动剖分，给出了三维直流电阻率模拟中四面体网格的质量评价标准和最优指标.计算和分析表明，数值解在点电流源及附近的奇异区精度最低，网格加密策略可以有效地减少其影响，极大地提高数值解的精度.本文提出的局部节点加密策略计算量最小，对精度的改善也优于经典方法.在精度要求苛刻或模型十分复杂时，局部体积加密策略和二次单元是高精度模拟的可靠保证.

Finite element modeling of 3-D DC resistivity using locally refined unstructured meshes

This paper briefly reviewed the disadvantages of commonly used structured meshes in geophysical fields. We introduced a new unstructured mesh based on Delaunay refinement algorithm to efficiently approximate the geometrically complex model boundaries. Additionally, we proposed a new local nodal refinement method. Based on our new algorithm, we have implemented the automatic mesh generation on complex geological models by unstructured mesh and also offered the highly accurate numerical solutions in 3D DC resistivity problem. The final numerical solutions show that the singularity effects of current source point can be efficiently avoided and the new local nodal refinements approach can efficiently upgrade the accuracy of numerical solutions. Therefore, we can conclude that the new local refinement is nearly optimal and its combination with second order mesh can give us very accurate numerical solutions.