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Some PINT simulations


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Parallel-in-time solution snapshots (using XBraid) of the velocity magnitude at the 5120th time step (t=2.56s), for unsteady vortex shedding and the compressible Navier-Stokes equations
(Courtesy of J. B. Schroder)



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Simulation of the plasma in the ITER tokamak, using parareal
(Courtesy of D. Samaddar)




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Approximate solution obtained by the time parallel algorithm using diagonalization
(Courtesy of L. Halpern)






Parallel Replica Algorithm for molecular dynamics. Parallel step:
run independent trajectories in parallel (left), and detect the first transition event (right)
(Courtesy of T. Lelièvre)






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Symplectic parareal schemes and structure preserving parallel in time propagators. The right figure shows the energy conservation, after 3 iterations of the algorithm, for a solar system problem
(Courtesy of G. Turinici)





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Coupled Parareal - Optimized Schwarz Waveform Relaxation method, where few (P) iterations of OSWR in the fine propagator are done,  for solving advection-reaction-diffusion problems
(Courtesy of B. D. Quang)






Parareal algorithm for optimal control
(Courtesy of J. Salomon)





Andra test case   A posteriori stopping criteria


A posteriori stopping criteria for global-in-time domain decomposition
for the heat equation in mixed formulations
(Andra test case)
 (Courtesy of S. Ali Hassan)


Two-phase flow    A posteriori for space-time DD


A posteriori stopping criteria for global-in-time domain decomposition for two-phase flow between different rock types (Dense Non-Aqueuous Phase Liquid (DNAPL) infiltration in a low-capillarity lens
(Courtesy of E. Ahmed)







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Others applications of parallel-in-time methods are :
weather forecast, thermal-hydraulic modeling of a real life accidental transient of a reactor, with stiff terms and bifurcations (CATHARE, see the ANR project CINE-PARA), ...

see also www.parallelintime.org