Stable model reduction for linear variational inequalities with parameter-dependent constraints

IF 1.9 3区 数学 Q2 Mathematics
Idrissa Niakh, G. Drouet, V. Ehrlacher, A. Ern
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引用次数: 1

Abstract

We consider model reduction for linear variational inequalities with parameter-dependent constraints. We study the stability of the reduced problem in the context of a dualized formulation of the constraints using Lagrange multipliers. Our main result is an algorithm that guarantees inf-sup stability of the reduced problem. The algorithm is computationally effective since it can be performed in the offline phase even for parameter-dependent constraints. Moreover, we also propose a modification of the Cone Projected Greedy algorithm so as to avoid ill-conditioning issues when manipulating the reduced dual basis. Our results are illustrated numerically on the frictionless Hertz contact problem between two half-spheres with parameter-dependent radius and on the membrane obstacle problem with parameter-dependent obstacle geometry.
具有参数相关约束的线性变分不等式的稳定模型约简
研究了具有参数依赖约束的线性变分不等式的模型约简。在使用拉格朗日乘子的约束对偶形式下,研究了约简问题的稳定性。我们的主要成果是一个保证简化问题的中支持稳定性的算法。该算法具有计算效率高的特点,即使在参数相关的约束条件下也能在离线阶段进行。此外,我们还提出了一种改进的锥投影贪心算法,以避免在处理约简对偶基时出现病态问题。我们的结果用数值方法说明了具有参数依赖半径的两个半球之间的无摩擦赫兹接触问题和具有参数依赖障碍物几何的膜障碍问题。
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来源期刊
CiteScore
2.70
自引率
5.30%
发文量
27
审稿时长
6-12 weeks
期刊介绍: M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.
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