diff --git a/_bibliography/pint.bib b/_bibliography/pint.bib index f4279926..1573dfc8 100644 --- a/_bibliography/pint.bib +++ b/_bibliography/pint.bib @@ -8065,15 +8065,6 @@ @article{L2025 year = {2025}, } -@unpublished{LaidinEtAl2025, - abstract = {We present the design of a multiscale parareal method for kinetic equations in the fluid dynamic regime. The goal is to reduce the cost of a fully kinetic simulation using a parallel in time procedure. Using the multiscale property of kinetic models, the cheap, coarse propagator consists in a fluid solver and the fine (expensive) propagation is achieved through a kinetic solver for a collisional Vlasov equation. To validate our approach, we present simulations in the 1D in space, 3D in velocity settings over a wide range of initial data and kinetic regimes, showcasing the accuracy, efficiency, and the speedup capabilities of our method.}, - author = {Tino Laidin and Thomas Rey}, - howpublished = {arXiv:2502.02704v1 [math.NA]}, - title = {A Parareal in time numerical method for the collisional Vlasov equation in the hyperbolic scaling}, - url = {http://arxiv.org/abs/2502.02704v1}, - year = {2025}, -} - @article{LefebvreEtAl2025, author = {Lefebvre, Tom and Vantilborgh, Victor}, doi = {10.1002/oca.70069}, @@ -8123,15 +8114,6 @@ @article{LinEtAl2025 year = {2025}, } -@unpublished{Liu2025, - abstract = {The high cost of sequential time integration is one major constraint that limits the speedup of a time-parallel algorithm like the Parareal algorithm due to the difficulty of coarsening time steps in a stiff numerical problem. To address this challenge, we develop a parallel-in-time approach based on the Parareal algorithm, in which we construct a novel coarse solver using a data-driven method based on Dynamic Mode Decomposition in place of a classic time marching scheme. The proposed solver computes an approximation of the solution using two numerical schemes of different accuracies in parallel, and apply High-Order Dynamic Mode Decomposition (HODMD) to reduce the cost of sequential computations. Compared to the original Parareal algorithm, the proposed approach allows for the construction of low-cost coarse solvers for many complicated stiff problems. We demonstrate through several numerical examples in fluid dynamics that the proposed method can effectively reduce the serial computation cost and improve the parallel speedup of long-time simulations which are hard to accelerate using the original Parareal algorithm.}, - author = {Weifan Liu}, - howpublished = {arXiv:2503.03109v1 [physics.comp-ph]}, - title = {A parallel-in-time method based on the Parareal algorithm and High-Order Dynamic Mode Decomposition with applications to fluid simulations}, - url = {http://arxiv.org/abs/2503.03109v1}, - year = {2025}, -} - @unpublished{LjósheimEtAl2025, abstract = {We study the numerical approximation of a time-dependent variational mean field game system with local couplings and either periodic or Neumann boundary conditions. Following a variational approach, we employ a finite difference discretization and solve the resulting finite-dimensional optimization problem using the Chambolle--Pock primal--dual algorithm. As this involves computing proximal operators and solving ill-conditioned linear systems at each iteration, we propose a general class of parallel-in-time preconditioners based on diagonalization techniques using discrete Fourier transforms. These enable efficient, scalable iterative solvers with robustness across a wide range of viscosities. We further develop fast solvers for the resulting ill-conditioned systems arising at each time step, using exact recursive schemes for structured grids while allowing for other geometries. Numerical experiments confirm the improved performance and parallel scalability of our approach.}, author = {Heidi Wolles Ljósheim and Dante Kalise and John W. Pearson and Francisco J. Silva}, @@ -8844,6 +8826,21 @@ @unpublished{KuleshovEtAl2026 year = {2026}, } +@article{LaidinEtAl2026, + author = {Laidin, Tino and Rey, Thomas}, + doi = {10.1137/25m1731800}, + issn = {1540-3467}, + journal = {Multiscale Modeling & Simulation}, + month = {Sept}, + number = {3}, + pages = {1248–1268}, + publisher = {Society for Industrial & Applied Mathematics (SIAM)}, + title = {A Parallel in Time Numerical Method for the Collisional Vlasov Equation in the Hyperbolic Scaling}, + url = {http://dx.doi.org/10.1137/25m1731800}, + volume = {24}, + year = {2026}, +} + @article{LiangEtAl2026, author = {Liang, Chang-Wen and Hwang, Feng-Nan}, doi = {10.1553/etna_vol66s83}, @@ -8889,6 +8886,19 @@ @unpublished{LinEtAl2026b year = {2026}, } +@article{Liu2026, + author = {Liu, Weifan}, + doi = {10.1016/j.cpc.2026.110416}, + issn = {0010-4655}, + journal = {Computer Physics Communications}, + month = {Sept}, + pages = {110416}, + publisher = {Elsevier BV}, + title = {A parallel-in-time method based on the Parareal algorithm and High-Order Dynamic Mode Decomposition with applications to fluid simulations}, + url = {http://dx.doi.org/10.1016/j.cpc.2026.110416}, + year = {2026}, +} + @unpublished{LuEtAl2026, abstract = {Parabolic optimal control problems arise in numerous scientific and engineering applications. They typically lead to large-scale coupled forward-backward systems that cannot be treated with classical time-stepping schemes and are computationally expensive to solve. Therefore, parallel methods are essential to reduce the computational time required. In this work, we investigate a time domain decomposition approach, namely the time parallel Schwarz method, applied to parabolic optimal control problems. We analyze the convergence behavior and focus on the weak scalability property of this method as the number of time intervals increases. To characterize the spectral radius of the iteration matrix, we present two analysis techniques: the construction of a tailored matrix norm and the application of block Toeplitz matrix theory. Our analyses yield both nonasymptotic bounds on the spectral radius and an asymptotic characterization of the eigenvalues as the number of time intervals tends to infinity. Numerical experiments further confirm our theoretical findings and demonstrate the weak scalability of the time parallel Schwarz method. This work introduces the first theoretical tool for analyzing the weak scalability of time domain decomposition methods, and our results shed light on the suitability of our algorithm for large-scale simulations on modern high-performance computing architectures.}, author = {Liu-Di Lu and Tommaso Vanzan},