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Related papers: PiTSBiCG: Parallel in Time Stable Bi-Conjugate Gra…

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In this article, we propose an accuracy-assuring technique for finding a solution for unsymmetric linear systems. Such problems are related to different areas such as image processing, computer vision, and computational fluid dynamics.…

Mathematical Software · Computer Science 2024-04-23 Mykhailo Havdiak , Jose I. Aliaga , Roman Iakymchuk

This paper deals with a new algorithm called modified trigonometric cubic B-spline differential quadrature method for numerical computation of the time dependent partial differential equations. Specially the numerical computation of the…

Numerical Analysis · Mathematics 2016-11-16 Brajesh Kumar Singh , Pramod Kumar

Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…

Quantum Physics · Physics 2025-10-16 Matteo Vandelli , Francesco Ferrari , Daniele Dragoni

We present a convergence analysis of the parallel-in-time integration method known as the Parareal algorithm for degenerate differential-algebraic systems arising from quasi-static Biot models, which govern coupled flow and deformation in…

Numerical Analysis · Mathematics 2026-01-22 Iñigo Jimenez-Ciga , Francisco Gaspar , Kundan Kumar , Florin A. Radu

Parareal and multigrid reduction in time (MGRiT) are two of the most popular parallel-in-time methods. The idea is to treat time integration in a parallel context by using a multigrid method in time. If $\Phi$ is a (fine-grid) time-stepping…

Numerical Analysis · Mathematics 2019-05-14 Ben S. Southworth

Parallel-in-time methods, such as multigrid reduction-in-time (MGRIT) and Parareal, provide an attractive option for increasing concurrency when simulating time-dependent PDEs in modern high-performance computing environments. While these…

Numerical Analysis · Mathematics 2021-03-04 Hans De Sterck , Robert D. Falgout , Stephanie Friedhoff , Oliver A. Krzysik , Scott P. MacLachlan

We present a new time-stepping algorithm for nonlinear PDEs that exhibit scale separation in time. Our scheme combines asymptotic techniques (which are inexpensive but can have insufficient accuracy) with parallel-in-time methods (which,…

Numerical Analysis · Mathematics 2014-02-24 Terry Haut , Beth Wingate

We propose a parallelizable sparse inverse formulation Gaussian process (SpInGP) for temporal models. It uses a sparse precision GP formulation and sparse matrix routines to speed up the computations. Due to the state-space formulation used…

Machine Learning · Statistics 2017-09-29 Alexander Grigorievskiy , Neil Lawrence , Simo Särkkä

This paper proposes a general formulation for temporal parallelisation of dynamic programming for optimal control problems. We derive the elements and associative operators to be able to use parallel scans to solve these problems with…

Optimization and Control · Mathematics 2022-01-25 Simo Särkkä , Ángel F. García-Fernández

The applicability of the Parareal parallel-in-time integration scheme for the solution of a linear, two-dimensional hyperbolic acoustic-advection system, which is often used as a test case for integration schemes for numerical weather…

Computational Engineering, Finance, and Science · Computer Science 2015-10-09 Daniel Ruprecht , Rolf Krause

In this paper, we introduce two parallel extragradient-proximal methods for solving split equilibrium problems. The algorithms combine the extragradient method, the proximal method and the hybrid (outer approximation) method. The weak and…

Optimization and Control · Mathematics 2015-11-10 Dang Van Hieu

Implicit integration of the viscous term can significantly improve performance in computational fluid dynamics for highly viscous fluids such as lava. We show improvements over our previous proposal for semi-implicit viscous integration in…

We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the…

Numerical Analysis · Mathematics 2015-11-19 Gil Ariel , Seong Jun Kim , Richard Tsai

We introduce a time-parallel algorithm for solving numerically almost integrable Hamiltonian systems in action-angle coordinates. This algorithm is a refinement of that introduced by Saha, Stadel and Tremaine in 1997 (SST97) for the same…

Numerical Analysis · Computer Science 2011-06-21 Hugo Jiménez-Pérez , Jacques Laskar

Parallel-in-time integration has been the focus of intensive research efforts over the past two decades due to the advent of massively parallel computer architectures and the scaling limits of purely spatial parallelization. Various…

Numerical Analysis · Mathematics 2023-09-22 M. J. Gander , T. Lunet , D. Ruprecht , R. Speck

We consider the parallel time integration of the linear advection equation with the Parareal and two-level multigrid-reduction-in-time (MGRIT) algorithms. Our aim is to develop a better understanding of the convergence behaviour of these…

Numerical Analysis · Mathematics 2019-10-15 Oliver A. Krzysik , Hans De Sterck , Scott P. MacLachlan , Stephanie Friedhoff

Time-parallel time integration has received a lot of attention in the high performance computing community over the past two decades. Indeed, it has been shown that parallel-in-time techniques have the potential to remedy one of the main…

Numerical Analysis · Mathematics 2023-09-26 Martin J. Gander , Davide Palitta

Sequential algorithms for the Stable Matching Problem are often too slow in the context of some large scale applications like switch scheduling. Parallel architectures can offer a notable decrease in runtime complexity. We propose a stable…

Data Structures and Algorithms · Computer Science 2024-08-27 Scott Wynn , Alec Kyritsis , Stephora Alberi , Enyue Lu

The growing interest for high dimensional and functional data analysis led in the last decade to an important research developing a consequent amount of techniques. Parallelized algorithms, which consist in distributing and treat the data…

Statistics Theory · Mathematics 2017-10-24 Antoine Godichon-Baggioni , Sofiane Saadane

The paper deals with the developing of the methodological backgrounds for the modeling and simulation of complex dynamical objects. Such backgrounds allow us to perform coordinate transformation and formulate the algorithm of its usage for…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-08-07 Roman Voliansky , Andri Pranolo