北京生物醫(yī)學(xué)工程

三層同心圓模型的有限元網(wǎng)格模型

Finite element mesh models of three-layer concentric circular model

作者：吳克堅趙清波劉爍徐清華梁銳華楊繼慶董秀珍

單位：                      第四軍醫(yī)大學(xué)生物醫(yī)學(xué)工程學(xué)院數(shù)理教研室(西安710032)        

關(guān)鍵詞：電阻抗斷層成像；有限元網(wǎng)格；計算精度

分類號：

出版年·卷·期（頁碼）：2014·33·5（441-445）

摘要：

目的改變網(wǎng)格數(shù)量和單元階次，探討二維三層同心圓模型電阻抗斷層成像正問題數(shù)值解的精度。方法通過數(shù)值模擬實驗，以二維同心圓模型的解析解為參考，比較不同網(wǎng)格數(shù)量和單元階次的數(shù)值解，分析特定網(wǎng)格模型的數(shù)值精度。結(jié)果增加網(wǎng)格數(shù)量對于高階單元結(jié)果精度的提高作用有限；應(yīng)用更高階單元如三階、四階單元提高計算精度的作用不大。結(jié)論二維場域用有限元求解EIT正問題采用中等網(wǎng)格數(shù)目的二階三角形單元既可以達到滿意的計算精度，又可以節(jié)省計算時耗、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.

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