Robust block diagonal preconditioners for poroelastic problems with strongly heterogeneous material

IF 1.8 3区数学 Q1 MATHEMATICS

Numerical Linear Algebra with Applications Pub Date : 2023-12-26 DOI:10.1002/nla.2546

Tomáš Luber, Stanislav Sysala

引用次数: 0

Abstract

This paper focuses on the analysis and the solution of the saddle-point problem arising from a three-field formulation of Biot's model of poroelasticity, discretized in time by the implicit Euler method. A block diagonal-preconditioner, based on the Schur complement, is analyzed on a functional level and compared with two other block-diagonal preconditioners having a similar structure. The problem is discretized in space using mixed finite elements and solved with appropriate iterative solvers, incorporating the investigated preconditioners. The solvers are tested on numerical examples inspired by geotechnical practice, with particular attention devoted to the solvers' robustness concerning strong heterogeneity in permeability.

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强异质材料孔弹性问题的稳健分块对角线预处理器

本文重点分析和解决了用隐式欧拉法进行时间离散的 Biot 孔弹性模型的三场公式所产生的鞍点问题。基于舒尔补码的块对角线预处理在函数层面上进行了分析，并与其他两个具有类似结构的块对角线预处理进行了比较。使用混合有限元对问题进行空间离散化，并使用适当的迭代求解器结合所研究的预处理器进行求解。这些求解器在受岩土工程实践启发的数值示例中进行了测试，并特别关注了求解器对渗透性强异质性的鲁棒性。

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

Numerical Linear Algebra with Applications 数学-数学

CiteScore

3.40

自引率

2.30%

发文量

审稿时长

12 months

期刊介绍： Manuscripts submitted to Numerical Linear Algebra with Applications should include large-scale broad-interest applications in which challenging computational results are integral to the approach investigated and analysed. Manuscripts that, in the Editor’s view, do not satisfy these conditions will not be accepted for review. Numerical Linear Algebra with Applications receives submissions in areas that address developing, analysing and applying linear algebra algorithms for solving problems arising in multilinear (tensor) algebra, in statistics, such as Markov Chains, as well as in deterministic and stochastic modelling of large-scale networks, algorithm development, performance analysis or related computational aspects. Topics covered include: Standard and Generalized Conjugate Gradients, Multigrid and Other Iterative Methods; Preconditioning Methods; Direct Solution Methods; Numerical Methods for Eigenproblems; Newton-like Methods for Nonlinear Equations; Parallel and Vectorizable Algorithms in Numerical Linear Algebra; Application of Methods of Numerical Linear Algebra in Science, Engineering and Economics.