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_bibliography/pint.bib

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@@ -5140,21 +5140,21 @@ @phdthesis{Caldas2021
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school = {Universit\'{e} de Montpellier},
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title = {Coupling large and small scale shallow water models with porosity in the presence of anisotropy},
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url = {https://www.theses.fr/2021MONTS040},
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year = {2021}
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year = {2021},
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}
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@article{CaldasEtAl:2021,
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abstract = {In this work, the POD-DEIM-based parareal method introduced in [8] is implemented for solving the two-dimensional nonlinear shallow water equations using a finite volume scheme. This method is a variant of the traditional parareal method, first introduced by [22], that improves the stability and convergence for nonlinear hyperbolic problems, and uses reduced-order models constructed via the Proper Orthogonal Decomposition - Discrete Empirical Interpolation Method (POD-DEIM) applied to snapshots of the solution of the parareal iterations. We propose a modification of this parareal method for further stability and convergence improvements. It consists in enriching the snapshots set for the POD-DEIM procedure with extra snapshots whose computation does not require any additional computational cost. The performances of the classical parareal method, the POD-DEIM-based parareal method and our proposed modification are compared using numerical tests with increasing complexity. Our modified method shows a more stable behaviour and converges in fewer iterations than the other two methods.},
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author = {Caldas Steinstraesser, Jo\~{a}o Guilherme and Guinot, Vincent and Rousseau, Antoine},
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title = {Modified parareal method for solving the two-dimensional nonlinear shallow water equations using finite volumes},
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journal = {The SMAI journal of computational mathematics},
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pages = {159--184},
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publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
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volume = {7},
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year = {2021},
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doi = {10.5802/smai-jcm.75},
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language = {en},
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url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.75/}
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author = {Caldas Steinstraesser, Jo\~{a}o Guilherme and Guinot, Vincent and Rousseau, Antoine},
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doi = {10.5802/smai-jcm.75},
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journal = {The SMAI journal of computational mathematics},
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language = {en},
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pages = {159--184},
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publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
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title = {Modified parareal method for solving the two-dimensional nonlinear shallow water equations using finite volumes},
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url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.75/},
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volume = {7},
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year = {2021},
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}
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@article{CaliariEtAl2021,
@@ -6346,7 +6346,7 @@ @unpublished{CaldasEtAl2023
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howpublished = {arXiv:2306.09497v1 [math.NA]},
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title = {Parallel-in-time integration of the shallow water equations on the rotating sphere using Parareal and MGRIT},
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url = {https://arxiv.org/abs/2306.09497v1},
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year = {2023}
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year = {2023},
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}
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@article{CarrelEtAl2023,
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year = {2023},
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}
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@unpublished{SteinstraesserEtAl2023,
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abstract = {Despite the growing interest in parallel-in-time methods as an approach to accelerate numerical simulations in atmospheric modelling, improving their stability and convergence remains a substantial challenge for their application to operational models. In this work, we study the temporal parallelization of the shallow water equations on the rotating sphere combined with time-stepping schemes commonly used in atmospheric modelling due to their stability properties, namely an Eulerian implicit-explicit (IMEX) method and a semi-Lagrangian semi-implicit method (SL-SI-SETTLS). The main goal is to investigate the performance of parallel-in-time methods, namely Parareal and Multigrid Reduction in Time (MGRIT), when these well-established schemes are used on the coarse discretization levels and provide insights on how they can be improved for better performance. We begin by performing an analytical stability study of Parareal and MGRIT applied to a linearized ordinary differential equation depending on the choice of coarse scheme. Next, we perform numerical simulations of two standard tests to evaluate the stability, convergence and speedup provided by the parallel-in-time methods compared to a fine reference solution computed serially. We also conduct a detailed investigation on the influence of artificial viscosity and hyperviscosity approaches, applied on the coarse discretization levels, on the performance of the temporal parallelization. Both the analytical stability study and the numerical simulations indicate a poorer stability behaviour when SL-SI-SETTLS is used on the coarse levels, compared to the IMEX scheme. With the IMEX scheme, a better trade-off between convergence, stability and speedup compared to serial simulations can be obtained under proper parameters and artificial viscosity choices, opening the perspective of the potential competitiveness for realistic models.},
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author = {João Guilherme Caldas Steinstraesser and Pedro da Silva Peixoto and Martin Schreiber},
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howpublished = {arXiv:2306.09497v1 [math.NA]},
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title = {Parallel-in-time integration of the shallow water equations on the rotating sphere using Parareal and MGRIT},
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url = {http://arxiv.org/abs/2306.09497v1},
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year = {2023},
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}
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@unpublished{Trotti2023,
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abstract = {In this work we develop a novel domain splitting strategy for the solution of partial differential equations. Focusing on a uniform discretization of the $d$-dimensional advection-diffusion equation, our proposal is a two-level algorithm that merges the solutions obtained from the discretization of the equation over highly anisotropic submeshes to compute an initial approximation of the fine solution. The algorithm then iteratively refines the initial guess by leveraging the structure of the residual. Performing costly calculations on anisotropic submeshes enable us to reduce the dimensionality of the problem by one, and the merging process, which involves the computation of solutions over disjoint domains, allows for parallel implementation.},
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author = {Ken Trotti},

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