A Multiscale Hybrid Method

IF 3 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Scientific Computing Pub Date : 2024-05-13 DOI:10.1137/22m1542556

Gabriel R. Barrenechea, Antonio Tadeu A. Gomes, Diego Paredes

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引用次数: 0

Abstract

SIAM Journal on Scientific Computing, Volume 46, Issue 3, Page A1628-A1657, June 2024.
Abstract. In this work we propose, analyze, and test a new multiscale finite element method called Multiscale Hybrid (MH) method. The method is built as a close relative to the Multiscale Hybrid Mixed (MHM) method, but with the fundamental difference that a novel definition of the Lagrange multiplier is introduced. The practical implication of this is that both the local problems to compute the basis functions, as well as the global problem, are elliptic, as opposed to the MHM method (and also other previous methods) where a mixed global problem is solved and constrained local problems are solved to compute the local basis functions. The error analysis of the method is based on a hybrid formulation, and a static condensation process is done at the discrete level, so the final global system only involves the Lagrange multipliers. We tested the performance of the method by means of numerical experiments for problems with multiscale coefficients, and we carried out comparisons with the MHM method in terms of performance, accuracy, and memory requirements.

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多尺度混合方法

SIAM 科学计算期刊》，第 46 卷第 3 期，第 A1628-A1657 页，2024 年 6 月。摘要在这项工作中，我们提出、分析并测试了一种新的多尺度有限元方法，称为多尺度混合（MH）方法。该方法与多尺度混合（MHM）方法近似，但有一个根本区别，即引入了拉格朗日乘数的新定义。其实际意义在于，计算基函数的局部问题和全局问题都是椭圆问题，而 MHM 方法（以及之前的其他方法）则是解决混合全局问题，并解决受约束局部问题以计算局部基函数。该方法的误差分析基于混合表述，并在离散级完成了静态压缩过程，因此最终的全局系统只涉及拉格朗日乘数。我们通过多尺度系数问题的数值实验测试了该方法的性能，并在性能、精度和内存要求方面与 MHM 方法进行了比较。

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

SIAM Journal on Scientific Computing 数学-应用数学

CiteScore

5.50

自引率

3.20%

发文量

209

审稿时长

1 months

期刊介绍： The purpose of SIAM Journal on Scientific Computing (SISC) is to advance computational methods for solving scientific and engineering problems. SISC papers are classified into three categories: 1. Methods and Algorithms for Scientific Computing: Papers in this category may include theoretical analysis, provided that the relevance to applications in science and engineering is demonstrated. They should contain meaningful computational results and theoretical results or strong heuristics supporting the performance of new algorithms. 2. Computational Methods in Science and Engineering: Papers in this section will typically describe novel methodologies for solving a specific problem in computational science or engineering. They should contain enough information about the application to orient other computational scientists but should omit details of interest mainly to the applications specialist. 3. Software and High-Performance Computing: Papers in this category should concern the novel design and development of computational methods and high-quality software, parallel algorithms, high-performance computing issues, new architectures, data analysis, or visualization. The primary focus should be on computational methods that have potentially large impact for an important class of scientific or engineering problems.