土壤水流中溶质输运的CN有限元解系数向量的降维方法

侯晓丽; 罗振东; 符辉

doi:10.21656/1000-0887.450226

土壤水流中溶质输运的CN有限元解系数向量的降维方法

doi: 10.21656/1000-0887.450226

侯晓丽^1,2,
罗振东^1, ,,
符辉²

1. 湖南三一工学院院士专家工作站, 长沙 410128;
2. 湖南农业大学环境与生态学院, 长沙 410128

基金项目:

国家自然科学基金(11671106)

详细信息

作者简介:
侯晓丽(1990—), 女, 讲师, 博士生(E-mail: 50901655@ncepu.edu.cn);罗振东(1958—), 男, 教授, 博士, 博士生导师(通讯作者. E-mail: zhdluo@ncepu.edu.cn).

通讯作者:
罗振东(1958—), 男, 教授, 博士, 博士生导师(通讯作者. E-mail: zhdluo@ncepu.edu.cn).

中图分类号: O242.21
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- 文章访问数: 14
- HTML全文浏览量: 2
- PDF下载量: 3
- 被引次数: 0
出版历程
- 收稿日期: 2024-08-06
- 修回日期: 2024-08-06
- 网络出版日期: 2025-12-05

A Reduced-Dimension Method of CN Finite Element Solution Coefficient Vectors for Solute Transport in Soil Flow

HOU Xiaoli^1,2,
LUO Zhendong^{1
, ,},
FU Hui²

1. Academician Expert Workstation, Hunan Sany Polytechnic College, Changsha 410128, P.R.China;
2. College of Environment and Ecology, Hunan Agricultural University, Changsha 410128, P.R.China

Funds:

The National Science Foundation of China(11671106)

摘要

摘要: 利用特征投影分解(proper orthogonal decomposition,POD)方法建立土壤水流中溶质输运的一种很少未知量和精度足够高的CrankNicolson(CN)有限元解系数向量的降维外推仿真模型, 并分析这种降维外推仿真模型解的存在性和稳定性及误差.用数值实验检验该模型的有效性和理论结果的正确性.
- 特征投影分解 /
- 土壤水流中溶质输运 /
- 降维外推仿真模型 /
- 存在性、稳定性和误差估计
Abstract: The proper orthogonal decomposition (POD) method was used to establish a dimensionally reduced extrapolation simulation model of the Crank-Nicolson (CN) finite element solution coefficient vectors with few degrees of freedom and sufficiently high accuracy for solute transport in soil flow. The existence, stability, and errors of the solutions to the reduced-dimension extrapolation simulation model were analyzed. Some numerical tests were used to verify the validity of the reduced-dimension extrapolation model and the correctness of the theoretical results.

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参考文献(15)

[2]李焕荣, 罗振东. 非粘性土壤中溶质运移问题的守恒混合有限元法及其数值模拟[J]. 计算数学, 2010,32(2): 183-194.(LI Huanrong, LUO Zhendong. Conservation mixed finite element methods and simulations for the solute moving problems in the nonstick soil water[J]. Mathematica Numerica Sinica,2010,32(2): 183-194. (in Chinese))

雷志栋. 土壤水动力学[M]. 北京: 清华大学出版社, 1988.(LEI Zhidong. Soil Hydrodynamics[M]. Beijing: Tsinghua University Press, 1988. (in Chinese))

[3]LUO Z D, LI H, ZHOU Y J, et al. A reduced finite element formulation based on POD method for two-dimensional solute transport problems[J]. Journal of Mathematical Analysis and Applications,2012,385(1): 371-383.

[4]LUO Z D. Finite Element and Reduced Dimension Methods for Partial Differential Equations[M]. Beijing: Springer and Science Press of China, 2024.

[5]TENG F, LUO Z D. A natural boundary element reduced-dimension model for uniform high-voltage transmission line problem in an unbounded outer domain[J]. Computational and Applied Mathematics,2024,43(3): 106.

[6]LI H, SONG Z. A reduced-order energy-stability-preserving finite difference iterative scheme based on POD for the Allen-Cahn equation[J]. Journal of Mathematical Analysis and Applications,2020,491(1): 124245.

[7]LI K, HUANG T Z, LI L, et al. A reduced-order discontinuous Galerkin method based on POD for electromagnetic simulation[J]. IEEE Transactions on Antennas and Propagation,2018,66(1): 242-254.

[8]SELTEN F M. Baroclinic empirical orthogonal functions as basis functions in an atmospheric model[J]. Journal of the Atmospheric Sciences,1997,54(16): 2099-2114.

[9]LI K, HUANG T Z, LI L, et al. A reduced-order discontinuous Galerkin method based on a Krylov subspace technique in nanophotonics[J]. Applied Mathematics and Computation,2019,358: 128-145.

[10]LUO Z D, CHEN G. Proper Orthogonal Decomposition Methods for Partial Differential Equations[M]. London: Academic Press of Elsevier, 2019.

[11]LUO Z D, LI H, SHANG Y, et al. A reduced-order LSMFE formulation based on POD method and implementation of algorithm for parabolic equations [J]. Finite Elements in Analysis and Design,2012,60: 1-12.

[12]LUO Z D, DU J, XIE Z, et al. A reduced stabilized mixed finite element formulation based on proper orthogonal decomposition for the non-stationary Navier-Stokes equations[J]. International Journal for Numerical Methods in Engineering, 2011,88(1): 31-46.

[13]LUO Z D, ZHOU Y, YANG X. A reduced finite element formulation based on proper orthogonal decomposition for Burgers equation[J]. Applied Numerical Mathematics,2009,59(8): 1933-1946.

[14]张恭庆, 林源渠. 泛函分析讲义[M]. 北京: 北京大学出版社, 2011.(ZHANG Gongqing, LIN Yuanqu. Notes on Functional Analysis[M]. Beijing: Peking University Press, 2011. (in Chinese))

[15]CIARLET P G. The Finite Element Method for Elliptic Problems[M]. Philadelphia: Society for Industrial and Applied Mathematic, 2002.

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土壤水流中溶质输运的CN有限元解系数向量的降维方法

doi: 10.21656/1000-0887.450226

作者简介:
侯晓丽(1990—), 女, 讲师, 博士生(E-mail: 50901655@ncepu.edu.cn);罗振东(1958—), 男, 教授, 博士, 博士生导师(通讯作者. E-mail: zhdluo@ncepu.edu.cn).

通讯作者:
罗振东(1958—), 男, 教授, 博士, 博士生导师(通讯作者. E-mail: zhdluo@ncepu.edu.cn).

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A Reduced-Dimension Method of CN Finite Element Solution Coefficient Vectors for Solute Transport in Soil Flow

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留言板

土壤水流中溶质输运的CN有限元解系数向量的降维方法

doi: 10.21656/1000-0887.450226

作者简介: 侯晓丽(1990—), 女, 讲师, 博士生(E-mail: 50901655@ncepu.edu.cn);罗振东(1958—), 男, 教授, 博士, 博士生导师(通讯作者. E-mail: zhdluo@ncepu.edu.cn).

通讯作者: 罗振东(1958—), 男, 教授, 博士, 博士生导师(通讯作者. E-mail: zhdluo@ncepu.edu.cn).

计量

出版历程

A Reduced-Dimension Method of CN Finite Element Solution Coefficient Vectors for Solute Transport in Soil Flow

计量

出版历程

目录

作者简介:
侯晓丽(1990—), 女, 讲师, 博士生(E-mail: 50901655@ncepu.edu.cn);罗振东(1958—), 男, 教授, 博士, 博士生导师(通讯作者. E-mail: zhdluo@ncepu.edu.cn).

通讯作者:
罗振东(1958—), 男, 教授, 博士, 博士生导师(通讯作者. E-mail: zhdluo@ncepu.edu.cn).