000196379 001__ 196379
000196379 005__ 20190316235836.0
000196379 0247_ $$2doi$$a10.1098/rsta.2013.0388
000196379 02470 $$2ISI$$a000338844500010
000196379 037__ $$aARTICLE
000196379 245__ $$aReduced order modelling numerical homogenization
000196379 269__ $$a2014
000196379 260__ $$bRoyal Soc$$c2014$$aLondon
000196379 300__ $$a23
000196379 336__ $$aJournal Articles
000196379 520__ $$aA general framework to combine numerical homogenization and reduced-order modelling techniques for partial differential equations (PDEs) with multiple scales is described. Numerical homogenization methods are usually efficient to approximate the effective solution of PDEs with multiple scales. However, classical numerical homogenization techniques require the numerical solution of a large number of so-called microproblems to approximate the effective data at selected grid points of the computational domain. Such computations become particularly expensive for high-dimensional, time-dependent or nonlinear problems. In this paper, we explain how numerical homogenization method can benefit from reduced-order modelling techniques that allow one to identify offline and online computational procedures. The effective data are only computed accurately at a carefully selected number of grid points (offline stage) appropriately ‘interpolated’ in the online stage resulting in an online cost comparable to that of a single-scale solver. The methodology is presented for a class of PDEs with multiple scales, including elliptic, parabolic, wave and nonlinear problems. Numerical examples, including wave propagation in inhomogeneous media and solute transport in unsaturated porous media, illustrate the proposed method.
000196379 6531_ $$amultiscale method
000196379 6531_ $$areduced basis
000196379 6531_ $$aoscillatory PDEs
000196379 700__ $$0243806$$g189915$$aAbdulle, Assyr
000196379 700__ $$aBai, Yun$$g191177$$0244282
000196379 773__ $$j372$$tPhilosophical Transactions of the Royal Society A$$k2021 20130388
000196379 8564_ $$uhttps://infoscience.epfl.ch/record/196379/files/abd_bai_ROM%20_prep.pdf$$zn/a$$s1888540$$yn/a
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000196379 937__ $$aEPFL-ARTICLE-196379
000196379 973__ $$rNON-REVIEWED$$sPUBLISHED$$aEPFL
000196379 980__ $$aARTICLE