Adaptive Krylov-Type Time Integration Methods
Abstract
The Rosenbrock-Krylov family of time integration schemes is an extension of Rosenbrock-W methods that employs a specific Krylov based approximation of the linear system solutions arising within each stage of the integrator. This work proposes an extension of Rosenbrock-Krylov methods to address stability questions which arise for methods making use of inexact linear system solution strategies. Two approaches for improving the stability and efficiency of Rosenbrock-Krylov methods are proposed, one through direct control of linear system residuals and the second through a novel extension of the underlying Krylov space to include stage right hand side vectors. Rosenbrock-Krylov methods employing the new approaches show a substantial improvement in computational efficiency relative to prior implementations.
Cite
@article{arxiv.1910.02514,
title = {Adaptive Krylov-Type Time Integration Methods},
author = {Paul Tranquilli and Ross Glandon and Adrian Sandu},
journal= {arXiv preprint arXiv:1910.02514},
year = {2019}
}