Update pint.bib

Author: joaosteinstraesser

_bibliography/pint.bib

@@ -5134,6 +5134,29 @@ @article{CaiEtAl2021
 	year = {2021},
 }
 
+@phdthesis{Caldas2021,
+	abstract = {This PhD thesis aims to study the coupling of nonlinear shallow water models at different scales, with application to the numerical simulation of urban floods. Accurate simulations in this domain are usually prohibitively expensive due to the small mesh sizes necessary for the spatial discretization of the urban geometry and the associated small time steps constrained by stability conditions. Porosity-based shallow water models have been proposed in the past two decades as an alternative approach, consisting of upscaled models using larger mesh sizes and time steps and being able to provide good global approximations for the solution of the fine shallow water equations, with much smaller computational times. However, small-scale phenomena are not captured by this type of model. Therefore, we seek to formulate a numerical model coupling the fine and upscaled ones, in order to obtain more accurate solutions inside the urban zone, always with reduced computational costs relatively to the simulation of the fine model. The guideline for this objective lays on the use of predictor-corrector iterative parallel-in-time numerical methods, which naturally fit to this fine/coarse formulation. We focus on the parareal, one of the most popular parallel-in-time methods. As a main challenge, temporal parallelization suffers from instabilities and/or slow convergence when applied to hyperbolic or advection-dominated problems, such as the shallow water equations. Therefore, we consider a variant of the method using reduced-order models (ROMs) formulated on-the-fly along parareal iterations, using Proper Orthogonal Decomposition (POD) and the Empirical Interpolation Method (EIM), being able to improve the stability and convergence of the parareal method for solving nonlinear hyperbolic problems. We investigate the limitations of this ROM-based parareal method and we propose a number of modifications that provide further stability and convergence improvements: enrichment of the input snapshot sets used for the model reduction procedure; formulation of local-in-time ROMs; and incorporation of an adaptive parareal approach recently presented in the literature. The original and ROM-based parareal methods, including the proposed improvements, are compared and evaluated in terms of stability, convergence towards the fine solution and numerical speedup obtained in a parallel implementation. In a first part, the methods are formulated, studied and implemented considering a set of numerical simulations coupling the classical shallow water equations (without the porosity concept) at different scales. After this initial study, we implement them for coupling the classical and the porosity-based shallow water models, for the simulation of urban floods.}
+	author = {Caldas Steinstraesser, Jo\~{a}o Guilherme},
+	school = {Universit\'{e} de Montpellier},
+	title = {Coupling large and small scale shallow water models with porosity in the presence of anisotropy},
+	url = {https://www.theses.fr/2021MONTS040},
+	year = {2021}
+}
+
+@article{CaldasEtAl:2021,
+	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.}
+     	author = {Caldas Steinstraesser, Jo\~{a}o Guilherme and Guinot, Vincent and Rousseau, Antoine},
+     	title = {Modified parareal method for solving the two-dimensional nonlinear shallow water equations using finite volumes},
+     	journal = {The SMAI journal of computational mathematics},
+     	pages = {159--184},
+     	publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
+     	volume = {7},
+     	year = {2021},
+     	doi = {10.5802/smai-jcm.75},
+     	language = {en},
+     	url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.75/}
+}
+
 @article{CaliariEtAl2021,
 	author = {Marco Caliari and Lukas Einkemmer and Alexander Moriggl and Alexander Ostermann},
 	doi = {10.1016/j.jcp.2021.110289},
@@ -6317,6 +6340,15 @@ @unpublished{BouillonEtAl2023b
 	year = {2023},
 }
 
+@unpublished{CaldasEtAl2023,
+	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.}
+	author = {Caldas Steinstraesser, Jo\~{a}o Guilherme and da Silva Peixoto, Pedro and Schreiber, Martin},
+	howpublished = {arXiv:2306.09497v1 [math.NA]},
+	title = {Parallel-in-time integration of the shallow water equations on the rotating sphere using Parareal and MGRIT},
+	url = {https://arxiv.org/abs/2306.09497v1},
+	year = {2023}
+}
+
 @article{CarrelEtAl2023,
 	author = {Benjamin Carrel and Martin J. Gander and Bart Vandereycken},
 	doi = {10.1007/s10543-023-00953-3},