5 papers
Fast multigrid reduction-in-time for advection via modified semi-Lagrangian coarse-grid operators
H. De Sterck, R. D. Falgout, O. A. Krzysik
Many iterative parallel-in-time algorithms have been shown to be highly efficient for diffusion-dominated partial differential equations (PDEs), but are inefficient or even diverge…
Fast solution of fully implicit Runge-Kutta and discontinuous Galerkin in time for numerical PDEs, Part II: nonlinearities and DAEs
Ben S. Southworth, Oliver Krzysik, Will Pazner
Fully implicit Runge-Kutta (IRK) methods have many desirable accuracy and stability properties as time integration schemes, but high-order IRK methods are not commonly used in prac…
Fast solution of fully implicit Runge-Kutta and discontinuous Galerkin in time for numerical PDEs, Part I: the linear setting
Ben S. Southworth, Oliver Krzysik, Will Pazner +1
Fully implicit Runge-Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but high-order IRK methods are not commonly…
Optimizing multigrid reduction-in-time (MGRIT) and Parareal coarse-grid operators for linear advection
Hans De Sterck, Robert D. Falgout, Stephanie Friedhoff +2
Parallel-in-time methods, such as multigrid reduction-in-time (MGRIT) and Parareal, provide an attractive option for increasing concurrency when simulating time-dependent PDEs in m…
On selecting coarse-grid operators for Parareal and MGRIT applied to linear advection
Oliver A. Krzysik, Hans De Sterck, Scott P. MacLachlan +1
We consider the parallel time integration of the linear advection equation with the Parareal and two-level multigrid-reduction-in-time (MGRIT) algorithms. Our aim is to develop a b…