High order implicit time integration schemes on multiresolution adaptive grids for stiff PDEs
For computational scientists solving stiff PDEs with localized features, this method reduces computational cost while preserving high accuracy, though it is an incremental combination of existing techniques.
This work develops high-order implicit Runge-Kutta schemes (SDIRK and RadauIIA) on multiresolution adaptive grids for stiff PDEs, achieving strong compression and computational reductions while maintaining user-defined accuracy. Numerical tests demonstrate efficiency for unsteady problems with localized fronts.
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.