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Solving inverse problems and achieving statistical rigour in landscape evolution models requires running many model realizations. Parallel computation is necessary to achieve this in a reasonable time. However, no previous algorithm is…

Computational Engineering, Finance, and Science · Computer Science 2019-01-23 Richard Barnes

This paper proposes a parallel in time (called also time parareal) method to solve Volterra integral equations of the second kind. The parallel in time approach follows the same spirit as the domain decomposition that consists of breaking…

Numerical Analysis · Mathematics 2016-11-26 Xianjuan Li , Tao Tang , Chuanju Xu

The adjoint method, recently introduced by Evans, is used to study obstacle problems, weakly coupled systems, cell problems for weakly coupled systems of Hamilton-Jacobi equations, and weakly coupled systems of obstacle type. In particular,…

Analysis of PDEs · Mathematics 2013-03-13 Filippo Cagnetti , Diogo Gomes , Hung Tran

This paper presents a highly-parallelizable parallel-in-time algorithm for efficient solution of nonlinear time-periodic problems. It is based on the time-periodic extension of the Parareal method, known to accelerate sequential…

Numerical Analysis · Mathematics 2020-07-08 Iryna Kulchytska-Ruchka , Sebastian Schöps

In this paper, we present a method that enables solving in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets…

Optimization and Control · Mathematics 2012-03-13 Yvon Maday , Mohamed-Kamel Riahi , Julien Salomon

The ParaOpt algorithm was recently introduced as a time-parallel solver for optimal-control problems with a terminal-cost objective, and convergence results have been presented for the linear diffusive case with implicit-Euler time…

Numerical Analysis · Mathematics 2023-05-09 Arne Bouillon , Giovanni Samaey , Karl Meerbergen

Recently, ParaExp was proposed for the time integration of linear hyperbolic problems. It splits the time interval of interest into sub-intervals and computes the solution on each sub-interval in parallel. The overall solution is decomposed…

Numerical Analysis · Mathematics 2018-03-14 Melina Merkel , Innocent Niyonzima , Sebastian Schöps

In this paper, we present a method that enables to solve in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets…

Optimization and Control · Mathematics 2011-10-19 Yvon Maday , Julien Salomon , Kamel Riahi

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

We develop and implement a parallel flatPERM algorithm \cite{G97,PK04} with mutually interacting parallel flatPERM sequences and use it to sample self-avoiding walks in 2 and 3 dimensions. Our data show that the parallel implementation…

Statistical Mechanics · Physics 2020-08-26 S Campbell , EJ Janse van Rensburg

We consider the usage of parallel-in-time algorithms of the Parareal and multigrid-reduction-in-time (MGRIT) methodologies for the parallel-in-time solution of the eddy current problem. Via application of these methods to a two-dimensional…

Numerical Analysis · Mathematics 2018-11-01 Stephanie Friedhoff , Jens Hahne , Iryna Kulchytska-Ruchka , Sebastian Schöps

In 2008, Maday and Ronquist introduced an interesting new approach for the direct parallel-in-time (PinT) solution of time-dependent PDEs. The idea is to diagonalize the time stepping matrix, keeping the matrices for the space…

Numerical Analysis · Mathematics 2021-04-15 Martin J. Gander , Jun Liu , Shu-Lin Wu , Xiaoqiang Yue , Tao Zhou

A parallel time integration method for nonlinear partial differential equations is proposed. It is based on a new implementation of the Paraexp method for linear partial differential equations (PDEs) employing a block Krylov subspace…

Numerical Analysis · Mathematics 2015-09-16 G. L. Kooij , M. A. Botchev , B. J. Geurts

An algorithm is discussed for converting a class of recursive processes to a parallel system. It is argued that this algorithm can be superior to certain methods currently found in the literature for an important subset of problems. The…

Computational Physics · Physics 2009-11-10 W. R. Gibbs

A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate…

Numerical Analysis · Mathematics 2009-09-16 Stefan Engblom

With steadily increasing parallelism for high-performance architectures, simulations requiring a good strong scalability are prone to be limited in scalability with standard spatial-decomposition strategies at a certain amount of parallel…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-03-01 Martin Schreiber , Adam Peddle , Terry Haut , Beth Wingate

Optimization has been widely used to generate smooth trajectories for motion planning. However, existing trajectory optimization methods show weakness when dealing with large-scale long trajectories. Recent advances in parallel computing…

Robotics · Computer Science 2025-07-18 Jiajun Yu , Nanhe Chen , Guodong Liu , Chao Xu , Fei Gao , Yanjun Cao

For time-dependent partial differential equations, parallel-in-time integration using the "parallel full approximation scheme in space and time" (PFASST) is a promising way to accelerate existing space-parallel approaches beyond their…

Numerical Analysis · Mathematics 2018-06-07 Matthias Bolten , Dieter Moser , Robert Speck

Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…

Numerical Analysis · Mathematics 2026-03-24 G. H. M. Araújo , O. A. Krzysik , H. De Sterck

Recent advances in random-walk particle-tracking have enabled direct simulation of mixing and reactions on particles by allowing the particles to interact with each other using a multi-point mass transfer scheme. The mass transfer scheme…

Computational Physics · Physics 2019-04-22 Nicholas B. Engdahl , Michael J. Schmidt , David A. Benson