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Journal Articles Numerical Algorithms Year : 2023

Interpretation of Parareal as a Two-level Additive Schwarz In Time Preconditioner and Its Acceleration with GMRES

Abstract

We describe an interpretation of parareal as a two-level additive Schwarz preconditioner in the time domain. We show that this twolevel preconditioner in time is equivalent to parareal and to multigrid reduction in time (MGRIT) with F-relaxation. We also discuss the case when additional fine or coarse propagation steps are applied in the preconditioner. This leads to procedures equivalent to MGRIT with FCF-relaxation and to MGRIT with F(CF) 2-relaxation or overlapping parareal. Numerical results show that these variants have faster convergence in some cases. In addition, we also apply a Krylov subspace method, namely GMRES (Generalized Minimal Residual), to accelerate the parareal algorithm. Better convergence is obtained, especially for the advection-reaction-diffusion equation in the case when advection and reaction coefficients are large.
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Dates and versions

hal-04038459 , version 1 (20-03-2023)

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Van-Thanh Nguyen, Laura Grigori. Interpretation of Parareal as a Two-level Additive Schwarz In Time Preconditioner and Its Acceleration with GMRES. Numerical Algorithms, 2023, ⟨10.1007/s11075-022-01492-8⟩. ⟨hal-04038459⟩
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