High order implicit time integration schemes on multiresolution adaptive\n grids for stiff PDEs

2016/04/01 by Max Duarte, Duarte, Max, Richard A. Dobbins +3
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1604.00355

openalex publication_date 2016/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider high order, implicit Runge-Kutta schemes to solve time-dependent\nstiff PDEs on dynamically adapted grids generated by multiresolution analysis\nfor unsteady problems disclosing localized fronts. The multiresolution finite\nvolume scheme yields highly compressed representations within a user-defined\naccuracy tolerance, hence strong reductions of computational requirements to\nsolve large, coupled nonlinear systems of equations. SDIRK and RadauIIA\nRunge-Kutta schemes are implemented with particular interest in those with\nL-stability properties and accuracy-based time-stepping capabilities. Numerical\nevidence is provided of the computational efficiency of the numerical strategy\nto cope with highly unsteady problems modeling various physical scenarios with\na broad spectrum of time and space scales.\n

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