An Equation-Free Approach for Second Order Multiscale Hyperbolic Problems in Non-Divergence Form
Abstract
The present study concerns the numerical homogenization of second order hyperbolic equations in non-divergence form, where the model problem includes a rapidly oscillating coefficient function. These small scales influence the large scale behavior, hence their effects should be accurately modelled in a numerical simulation. A direct numerical simulation is prohibitively expensive since a minimum of two points per wavelength are needed to resolve the small scales. A multiscale method, under the equation free methodology, is proposed to approximate the coarse scale behaviour of the exact solution at a cost independent of the small scales in the problem. We prove convergence rates for the upscaled quantities in one as well as in multi-dimensional periodic settings. Moreover, numerical results in one and two dimensions are provided to support the theory.
Cite
@article{arxiv.1708.09446,
title = {An Equation-Free Approach for Second Order Multiscale Hyperbolic Problems in Non-Divergence Form},
author = {Doghonay Arjmand and Gunilla Kreiss},
journal= {arXiv preprint arXiv:1708.09446},
year = {2018}
}