Variable Step Size Multiscale Methods for Stiff and Highly Oscillatory\n Dynamical Systems

2013/04/16 by Yoonsang Lee, Björn Engquist, Lee, Yoonsang +1 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1304.4336

openalex publication_date 2013/04/16 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We present a new numerical multiscale integrator for stiff and highly\noscillatory dynamical systems. The new algorithm can be seen as an improved\nversion of the seamless Heterogeneous Multiscale Method by E, Ren, and\nVanden-Eijnden and the method FLAVORS by Tao, Owhadi, and Marsden. It\napproximates slowly changing quantities in the solution with higher accuracy\nthan these other methods while maintaining the same computational complexity.\nTo achieve higher accuracy, it uses variable mesoscopic time steps which are\ndetermined by a special function satisfying moment and regularity conditions.\nDetailed analytical and numerical comparison between the different methods are\ngiven.\n

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• A Dilation-based Seamless Multiscale Method For Elliptic Problems
• Generalised projective integration scheme in equation-free multiscale modelling

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