Krylov Deferred Correction Accelerated Method of Lines Transpose for Parabolic Problems
- ORNL
- University of North Carolina, Chapel Hill
In this paper, a new class of numerical methods for the accurate and efficient solutions of parabolic partial differential equations is presented. Unlike traditional method of lines (MoL), the new {\bf \it Krylov deferred correction (KDC) accelerated method of lines transpose (MoL^T)} first discretizes the temporal direction using Gaussian type nodes and spectral integration, and symbolically applies low-order time marching schemes to form a preconditioned elliptic system, which is then solved iteratively using Newton-Krylov techniques such as Newton-GMRES or Newton-BiCGStab method. Each function evaluation in the Newton-Krylov method is simply one low-order time-stepping approximation of the error by solving a decoupled system using available fast elliptic equation solvers. Preliminary numerical experiments show that the KDC accelerated MoL^T technique is unconditionally stable, can be spectrally accurate in both temporal and spatial directions, and allows optimal time-step sizes in long-time simulations.
- Research Organization:
- Oak Ridge National Laboratory (ORNL)
- Sponsoring Organization:
- SC USDOE - Office of Science (SC)
- DOE Contract Number:
- AC05-00OR22725
- OSTI ID:
- 978778
- Journal Information:
- Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 3 Vol. 227; ISSN JCTPAH; ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
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