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A Multiscale Model Reduction Method for Partial Differential Equations

Maolin CiThomas Y. HouZuoqiang Shi — 2014

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We propose a multiscale model reduction method for partial differential equations. The main purpose of this method is to derive an effective equation for multiscale problems without scale separation. An essential ingredient of our method is to decompose the harmonic coordinates into a smooth part and a highly oscillatory part so that the smooth part is invertible and the highly oscillatory part is small. Such a decomposition plays a key role in our construction of the effective equation. We show...

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