Algebraic multigrid methods for uncertainty quantification of source-type flows through randomly heterogeneous porous media

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-07-03 DOI:10.1016/j.apnum.2025.06.015

Vincenzo Schiano Di Cola , Salvatore Cuomo , Gerardo Severino , Marco Berardi

{"title":"Algebraic multigrid methods for uncertainty quantification of source-type flows through randomly heterogeneous porous media","authors":"Vincenzo Schiano Di Cola , Salvatore Cuomo , Gerardo Severino , Marco Berardi","doi":"10.1016/j.apnum.2025.06.015","DOIUrl":null,"url":null,"abstract":"<div><div>We consider steady flow generated by a source through a porous medium where, due to its erratic variations in the space, the conductivity <em>K</em> is regarded as a random field. As a consequence, flow variables become stochastic, and we aim at quantifying their uncertainty. To this purpose, we use Monte Carlo simulations, where for each realization the governing flow equation is solved by a finite volume method. This yields a deterministic linear system solved by algebraic multigrid (AMG) techniques. By leveraging analytical solutions valid for homogeneous (constant <em>K</em>) formations, we first compare different AMG solvers, that are subsequently used as trial in order to extend our approach to heterogeneous porous media. Results demonstrate that AMG methods enable achieving, especially at higher iteration counts, an <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-error lower than other, Gaussian-type, approximations.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"218 ","pages":"Pages 58-72"},"PeriodicalIF":2.4000,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Numerical Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168927425001321","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

We consider steady flow generated by a source through a porous medium where, due to its erratic variations in the space, the conductivity K is regarded as a random field. As a consequence, flow variables become stochastic, and we aim at quantifying their uncertainty. To this purpose, we use Monte Carlo simulations, where for each realization the governing flow equation is solved by a finite volume method. This yields a deterministic linear system solved by algebraic multigrid (AMG) techniques. By leveraging analytical solutions valid for homogeneous (constant K) formations, we first compare different AMG solvers, that are subsequently used as trial in order to extend our approach to heterogeneous porous media. Results demonstrate that AMG methods enable achieving, especially at higher iteration counts, an

L_{2}

-error lower than other, Gaussian-type, approximations.

查看原文本刊更多论文

随机非均质多孔介质中源型流动不确定性量化的代数多重网格方法

我们考虑由源通过多孔介质产生的稳定流，其中，由于其在空间中的不规则变化，电导率K被视为随机场。因此，流量变量是随机的，我们的目标是量化它们的不确定性。为此，我们使用蒙特卡罗模拟，其中每个实现的控制流方程都是用有限体积法求解的。这产生了一个由代数多重网格（AMG）技术求解的确定性线性系统。通过利用对均质（恒定K）地层有效的解析解，我们首先比较了不同的AMG求解器，随后将其用作试验，以便将我们的方法扩展到非均质多孔介质。结果表明，AMG方法能够实现比其他高斯型近似更低的l2误差，特别是在更高的迭代次数下。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.