Parallel Time Integration

• Applying Parareal on Hyperbolic equations and conservation laws trying to overcome stability issues (multi-stage algorithms?)(idea source: The Parareal Algorithm: A survey of Present work).

• Strategies for reducing the coarse time propagator (idea source: The Parareal Algorithm: A survey of Present work).

• Applying the “multi-step system” idea shown in “parallelization in time of (stochastic) ordinary differential equations” to achieve parallel efficiency close to 1.

• Combining parallelization in time and space.

• Why the Parareal converged faster than the serial version (page 19: The Parareal Algorithm: A survey of Present work)

• The improved PITA algorithm in “A Time-Parallel implicit methodology for the near real time solution of systems of linear oscillators” works better than parareal for first and second order hyperbolic equations.

• Applying parallel time integrators for molecular dynamic applications (idea source: Ahmadia, Yokota and Ketcheson. Also protein folding is mentioned as an application for parallel time integrators in the paper “A Time-Parallel implicit methodology for the near real time solution of systems of linear oscillators”).

Adaptive Mesh Refinement and Local Time Stepping

• As I understood from the paper about integrating Peano into pyclaw, there is an opportunity to improve the load balancing.