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Yun Bai

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Publications associées (7)

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Fully discrete analysis of the heterogeneous multiscale method for elliptic problems with multiple scales

Assyr Abdulle, Yun Bai

A fully discrete analysis of the finite element heterogeneous multiscale method (FE-HMM) for elliptic problems with N+1 well-separated scales is discussed. The FE-HMM is a numerical homogenization method that relies on a macroscopic scheme (macro FEM) for ...

Oxford Univ Press2015

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A reduced basis finite element heterogeneous multiscale method (RB-FE-HMM) for a class of nonlinear homogenization elliptic problems of nonmonotone type is introduced. In this approach, the solutions of the micro problems needed to estimate the macroscopic ...

Amer Inst Mathematical Sciences2015

Reduced order modelling numerical homogenization

Assyr Abdulle, Yun Bai

A 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 ...

Royal Soc2014

An online-offline homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems

Assyr Abdulle, Gilles Vilmart, Yun Bai

Inspired by recent analyses of the finite element heterogeneous multiscale method and the reduced basis technique for nonlinear problems, we present a simple and concise finite element algorithm for the reliable and efficient resolution of elliptic or para ...

Wiley-Blackwell2014

The characteristic of effective properties of physical processes in heterogeneous media is a basic modeling and computational problem for many applications. As standard numerical discretization of such multiscale problems (e.g. with classical finite elemen ...

EPFL2013

Adaptive reduced basis finite element heterogeneous multiscale method

Assyr Abdulle, Yun Bai

An adaptive reduced basis finite element heterogeneous multiscale method (RB-FE-HMM) is proposed for elliptic problems with multiple scales. The multiscale method is based on the RB-FE-HMM introduced in [A. Abdulle, Y. Bai, Reduced basis finite element het ...

Elsevier2013

Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems

Assyr Abdulle, Yun Bai

A new finite element method for the efficient discretization of elliptic homogenization problems is proposed. These problems, characterized by data varying over a wide range of scales cannot be easily solved by classical numerical methods that need mesh re ...

Elsevier2012