A space-time multigrid method for parabolic partial differential equations
SIAM Journal on Scientific Computing
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Accelerating the convergence of spectral deferred correction methods
Journal of Computational Physics
Arbitrary order Krylov deferred correction methods for differential algebraic equations
Journal of Computational Physics
Analysis of the Parareal Time-Parallel Time-Integration Method
SIAM Journal on Scientific Computing
On the choice of correctors for semi-implicit Picard deferred correction methods
Applied Numerical Mathematics
Parallel High-Order Integrators
SIAM Journal on Scientific Computing
The institute for cyber-enabled research: regional organization to promote computation in science
Proceedings of the Conference on Extreme Science and Engineering Discovery Environment: Gateway to Discovery
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In this work, we discuss a family of parallel implicit time integrators for multi-core and potentially multi-node or multi-gpgpu systems. The method is an extension of Revisionist Integral Deferred Correction (RIDC) by Christlieb, Macdonald and Ong (SISC-2010) which constructed parallel explicit time integrators. The key idea is to re-write the defect correction framework so that, after initial startup costs, each correction loop can be lagged behind the previous correction loop in a manner that facilitates running the predictor and correctors in parallel.In this paper, we show that RIDC provides a framework to use p cores to generate a pth-order implicit solution to an initial value problem (IVP) in approximately the same wall clock time as a single core, backward Euler implementation (p驴12). The construction, convergence and stability of the schemes are presented, along with supporting numerical evidence.