Comptes Rendus. Chimie最新文献_第7页

An adaptive least-squares algorithm for the elliptic Monge–Ampère equation 椭圆型monge - ampantere方程的自适应最小二乘算法

4区化学

Comptes Rendus. Chimie Pub Date : 2023-10-16 DOI: 10.5802/crmeca.222

Alexandre Caboussat, Dimitrios Gourzoulidis, Marco Picasso

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引用次数: 0

Nonlinear compressive reduced basis approximation for PDE’s PDE的非线性压缩降基近似

4区化学

Comptes Rendus. Chimie Pub Date : 2023-09-28 DOI: 10.5802/crmeca.191

Albert Cohen, Charbel Farhat, Yvon Maday, Agustin Somacal

{"title":"Nonlinear compressive reduced basis approximation for PDE’s","authors":"Albert Cohen, Charbel Farhat, Yvon Maday, Agustin Somacal","doi":"10.5802/crmeca.191","DOIUrl":"https://doi.org/10.5802/crmeca.191","url":null,"abstract":"Linear model reduction techniques design offline low-dimensional subspaces that are tailored to the approximation of solutions to a parameterized partial differential equation, for the purpose of fast online numerical simulations. These methods, such as the Proper Orthogonal Decomposition (POD) or Reduced Basis (RB) methods, are very effective when the family of solutions has fast-decaying Karhunen–Loève eigenvalues or Kolmogorov widths, reflecting the approximability by finite-dimensional linear spaces. On the other hand, they become ineffective when these quantities have a slow decay, in particular for families of solutions to hyperbolic transport equations with parameter-dependent shock positions. The objective of this work is to explore the ability of nonlinear model reduction to circumvent this particular situation. To this end, we first describe particular notions of nonlinear widths that have a substantially faster decay for the aforementioned families. Then, we discuss a systematic approach for achieving better performance via a nonlinear reconstruction from the first coordinates of a linear reduced model approximation, thus allowing us to stay in the same “classical” framework of projection-based model reduction. We analyze the approach and report on its performance for a simple and yet instructive univariate test case.","PeriodicalId":10566,"journal":{"name":"Comptes Rendus. Chimie","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135344216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

A second-order resolvent formulation for the analysis of turbulent flow structures 紊流结构分析的二阶解析公式

4区化学

Comptes Rendus. Chimie Pub Date : 2023-09-26 DOI: 10.5802/crmeca.193

Quentin Chevalier, Lesshafft Lutz, André V. G. Cavalieri

引用次数: 0

L’avènement de la science météorologique du XVII e au XIX e siècle 17世纪到19世纪气象学的兴起

4区化学

Comptes Rendus. Chimie Pub Date : 2023-09-15 DOI: 10.5802/crmeca.213

Denis Beaudouin

引用次数: 0

Préface en hommage à Ismaël Boulliau (1605–1694) 向伊斯梅尔·布利奥致敬的序言(1605 - 1694)