High order implicit time integration schemes on multiresolution adaptive grids for stiff PDEs
Abstract
We consider high order, implicit Runge-Kutta schemes to solve time-dependent stiff PDEs on dynamically adapted grids generated by multiresolution analysis for unsteady problems disclosing localized fronts. The multiresolution finite volume scheme yields highly compressed representations within a user-defined accuracy tolerance, hence strong reductions of computational requirements to solve large, coupled nonlinear systems of equations. SDIRK and RadauIIA Runge-Kutta schemes are implemented with particular interest in those with L-stability properties and accuracy-based time-stepping capabilities. Numerical evidence is provided of the computational efficiency of the numerical strategy to cope with highly unsteady problems modeling various physical scenarios with a broad spectrum of time and space scales.
Cite
@article{arxiv.1604.00355,
title = {High order implicit time integration schemes on multiresolution adaptive grids for stiff PDEs},
author = {Max Duarte and Richard Dobbins and Mitchell Smooke},
journal= {arXiv preprint arXiv:1604.00355},
year = {2016}
}