Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems

被引：12

作者：

Abdulle, Assyr ^{[1
]}

Arjmand, Doghonay ^{[1
]}

Paganoni, Edoardo ^{[1
]}

机构：

[1] Ecole Polytech Fed Lausanne, ANMC, Inst Math, CH-1015 Lausanne, Switzerland

来源：

COMPTES RENDUS MATHEMATIQUE | 2019年 / 357卷 / 06期

基金：

瑞士国家科学基金会;

关键词：

COEFFICIENTS;

D O I：

10.1016/j.crma.2019.05.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper presents two new approaches for finding the homogenized coefficients of multiscale elliptic PDEs. Standard approaches for computing the homogenized coefficients suffer from the so-called resonance error, originating from a mismatch between the true and the computational boundary conditions. Our new methods, based on solutions of parabolic and elliptic cell problems, result in an exponential decay of the resonance error. (C) 2019 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

引用

页码：545 / 551

页数：7

共 15 条

[1] Fourth order Chebyshev methods with recurrence relation [J].

Abdulle, A .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2002, 23 (06) :2041-2054

[2]

Abdulle A., PREPRINT

[3] The heterogeneous multiscale method [J].

Abdulle, Assyr ;

Weinan, E. ;

Engquist, Bjoern ;

Vanden-Eijnden, Eric .

ACTA NUMERICA, 2012, 21 :1-87

[4] A time dependent approach for removing the cell boundary error in elliptic homogenization problems [J].

Arjmand, Doghonay ;

Runborg, Olof .

JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 314 :206-227

[5]

Bensoussan A., 1978, Asymptotic Analysis for Periodic Structures

[6] IMPROVING ON COMPUTATION OF HOMOGENIZED COEFFICIENTS IN THE PERIODIC AND QUASI-PERIODIC SETTINGS [J].

Blanc, Xavier ;

Le Bris, Claude .

NETWORKS AND HETEROGENEOUS MEDIA, 2010, 5 (01) :1-29

[7] Approximations of effective coefficients in stochastic homogenization [J].

Bourgeat, A ;

Piatnitski, A .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2004, 40 (02) :153-165

[8]

Cioranescu D., 1999, An Introduction to Homogenization

[9]

E WN, 2005, J AM MATH SOC, V18, P121

[10] AN OPTIMAL ERROR ESTIMATE IN STOCHASTIC HOMOGENIZATION OF DISCRETE ELLIPTIC EQUATIONS [J].

Gloria, Antoine ;

Otto, Felix .

ANNALS OF APPLIED PROBABILITY, 2012, 22 (01) :1-28

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