三层同心圆模型的有限元网格模型

Finite element mesh models of three-layer concentric circular model

目的改变网格数量和单元阶次,探讨二维三层同心圆模型电阻抗断层成像正问题数值解的精度。方法通过数值模拟实验,以二维同心圆模型的解析解为参考,比较不同网格数量和单元阶次的数值解,分析特定网格模型的数值精度。结果增加网格数量对于高阶单元结果精度的提高作用有限;应用更高阶单元如三阶、四阶单元提高计算精度的作用不大。结论二维场域用有限元求解EIT正问题采用中等网格数目的二阶三角形单元既可以达到满意的计算精度,又可以节省计算时耗、提高成像效率。

Objective We investigate the numerical precision of FEM solutions in three-layer concentric circular model by changing the number of meshes and element order.Methods Through numerical simulation experiments and taking analytic solutions of three-layer concentric circular model as the reference,we compare the numerical solutions in different number of meshes and element order,and analyze the numerical precision with certain mesh model.Results The increased number of meshes played a limited role in improving the calculation accuracy for a certain element of high order.Furthermore,the improvement of the higher order such as the third or fourth order elements is poor.Conclusions We choose the forward model with second order triangular element with medium number on two-dimensional field.This model can ensure calculating precision and save calculation consumption to improve the image reconstruction efficiency.