The Parareal in Time Algorithm Applied to the Kinetic Neutron Diffusion Equation

Baudron, Anne-Marie; Lautard, Jean-Jacques; Maday, Yvon; Mula, Olga

doi:10.1007/978-3-319-05789-7_41

Cited by 8 publications

(6 citation statements)

References 8 publications

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“…In fact, this package increases with the number of the decomposition contrary to the DDM. We refer to [37] for alternative parallel implementations.…”

Section: Numerical Tests and Discussionmentioning

confidence: 99%

Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model

Baudron

Lautard

Maday

et al. 2014

Journal of Computational Physics

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We present a parareal in time algorithm for the simulation of neutron diffusion transient model. The method is made efficient by means of a coarse solver defined with large time steps and steady control rods model. Using finite element for the space discretization, our implementation provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch-Maurer-Werner (LMW) benchmark [1].

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“…In fact, this package increases with the number of the decomposition contrary to the DDM. We refer to [37] for alternative parallel implementations.…”

Section: Numerical Tests and Discussionmentioning

confidence: 99%

Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model

Baudron

Lautard

Maday

et al. 2014

Journal of Computational Physics

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“…A micro-macro version of the parareal algorithm for singularly perturbed systems of ordinary differential equations (ODEs) has been illustrated in [22], coupling a coarse propagator based on an approximate macroscopic model with fewer degrees of freedom to a fine propagator that accurately simulates the full microscopic dynamics. For other applications, see [23,24] for kinetic transport problems or [25] for reservoir simulation. For a convergence study of the parareal algorithm we refer to [20,26,27,28].…”

Section: Introductionmentioning

confidence: 99%

A hybrid parareal Monte Carlo algorithm for parabolic problems

Dabaghi

Maday

Zoia

2023

Journal of Computational and Applied Mathematics

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“…Given the difficulties already posed by having to solve this problem in a time-stepping framework, perhaps it is not surprising that few papers have considered parallel-in-time (PinT) approaches. To our knowledge, only [11,12,13] and more recently [14], have tested the application of a PinT algorithm (specifically, Parareal [15]) to MHD problems, showing relatively modest speedups of 8-10× using hundreds of processors. However as noted in these works, since the overall time-to-solution for MHD simulations can be prohibitively long (in light of the complexity of the equations involved), even small speedups can have meaningful effects in reducing total time-tosolution, thus making parallel-in-time approaches particularly appealing.…”

Section: Introductionmentioning

confidence: 99%

Space-Time Block Preconditioning for Incompressible Flow

Danieli¹,

Southworth²,

Wathen³

2022

SIAM J. Sci. Comput.

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This work develops an all-at-once space-time preconditioning approach for resistive magnetohydrodynamics (MHD), with a focus on model problems targeting fusion reactor design. We consider parallel-in-time due to the long time domains required to capture the physics of interest, as well as the complexity of the underlying system and thereby computational cost of long-time integration. To ameliorate this cost by using many processors, we thus develop a novel approach to solving the whole space-time system that is parallelizable in both space and time. We develop a space-time block preconditioning for resistive MHD, following the space-time block preconditioning concept first introduced by Danieli et al. in 2022 for incompressible flow, where an effective preconditioner for classic sequential time-stepping is extended to the space-time setting. The starting point for our derivation is the continuous Schur complement preconditioner by Cyr et al. in 2021, which we proceed to generalise in order to produce, to our knowledge, the first space-time block preconditioning approach for the challenging equations governing incompressible resistive MHD. The numerical results are promising for the model problems of island coalescence and tearing mode, with the overhead computational cost associated with space-time preconditioning versus sequential time-stepping being modest and primarily in the range of 2×-5×, which is low for parallel-in-time schemes in general. Additionally, the scaling results for inner (linear) and outer (nonlinear) iterations are flat in the case of fixed time-step size and only grow very slowly in the case of time-step refinement.

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The Parareal in Time Algorithm Applied to the Kinetic Neutron Diffusion Equation

Cited by 8 publications

References 8 publications

Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model

Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model

A hybrid parareal Monte Carlo algorithm for parabolic problems

Space-Time Block Preconditioning for Incompressible Flow

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