Adaptive Krylov-Type Time Integration Methods [article]

Paul Tranquilli, Ross Glandon, Adrian Sandu
2019 arXiv   pre-print
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,
more » ... e 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.
arXiv:1910.02514v1 fatcat:d4r4nykh4fbwrmqfagm3uik4aa