A novel dimensionality reduction iterative method for the unknown coefficient vectors in TGFECN solutions of unsaturated soil water flow problem

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-10-05 DOI:10.1016/j.jmaa.2024.128930

Xiaoli Hou , Yuejie Li , Qiuxiang Deng , Zhendong Luo

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引用次数: 0

Abstract

The main purpose of this paper is to reduce the dimensionality of unknown coefficient vectors in finite element (FE) solutions of two-grid FE Crank-Nicolson (CN) (TGFECN) format for the unsaturated soil water flow (USWF) problem with two strong nonlinear terms by using proper orthogonal decomposition (POD). For this purpose, our first step involves designing a time semi-discrete CN (TSDCN) scheme for the USWF problem and demonstrate the existence, boundedness, and error estimations of TSDCN solutions. Thereafter, we discretize the TSDCN scheme using the two-grid FE method to create a new TGFECN format and prove the existence, boundedness, and error estimations of TGFECN solutions. The primary focus should be on reducing the dimension of unknown coefficient vectors of TGFECN solutions through the utilization of the POD technique in creating a novel format, referred to as dimension reduction iterative TGFECN (DRITGFECN) format, while establishing the existence, boundedness, and error estimations for DRITGFECN solutions. Lastly, we use two sets of numerical tests to exhibit the advantage of the DRITGFECN format. Due to the presence of two highly nonlinear terms in the unsaturated soil flow problem, the development and analysis of DRITGFECN format pose greater challenges and necessitates more advanced technical skills compared to previous studies. However, the significance and broad applications of this research make it a valuable subject for investigation.

查看原文本刊更多论文

非饱和土壤水流问题 TGFECN 解中未知系数向量的新型降维迭代法

本文的主要目的是通过使用适当的正交分解（POD），降低具有两个强非线性项的非饱和土壤水流（USWF）问题的双网格 FE Crank-Nicolson（CN）（TGFECN）格式有限元（FE）解中未知系数向量的维数。为此，我们首先为 USWF 问题设计了一种时间半离散 CN（TSDCN）方案，并证明了 TSDCN 解的存在性、有界性和误差估计。之后，我们使用双网格 FE 方法对 TSDCN 方案进行离散化，创建新的 TGFECN 格式，并证明 TGFECN 解的存在性、有界性和误差估计。在建立 DRITGFECN 解的存在性、有界性和误差估计的同时，主要重点应放在利用 POD 技术减少 TGFECN 解的未知系数向量维数上，并创建一种新格式，称为降维迭代 TGFECN（DRITGFECN）格式。最后，我们使用两组数值测试来展示 DRITGFECN 格式的优势。由于非饱和土流问题中存在两个高度非线性项，DRITGFECN 格式的开发和分析与以往的研究相比面临更大的挑战，需要更先进的技术技能。然而，这项研究的重要意义和广泛应用使其成为一个有价值的研究课题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.