Related papers: A micro-macro parareal algorithm: application to s…
Iterative parallel-in-time algorithms like Parareal can extend scaling beyond the saturation of purely spatial parallelization when solving initial value problems. However, they require the user to build coarse models to handle the…
Parallel-in-time (PinT) techniques have been proposed to solve systems of time-dependent differential equations by parallelizing the temporal domain. Among them, Parareal computes the solution sequentially using an inaccurate (fast) solver,…
In this paper, we consider a recursive estimation problem for linear regression where the signal to be estimated admits a sparse representation and measurement samples are only sequentially available. We propose a convergent parallel…
We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…
In this paper, we present the new "asynchronous truncated multigrid-reduction-in-time" (AT-MGRIT) algorithm for introducing time parallelism to the solution of discretized time-dependent problems. The new algorithm is based on the…
We numerically investigate an adaptive version of the parareal algorithm in the context of molecular dynamics. This adaptive variant has been originally introduced in [F. Legoll, T. Lelievre and U. Sharma, SISC 2022]. We focus here on test…
We present a full implementation of the parareal algorithm---an integration technique to solve differential equations in parallel---in the Julia programming language for a fully general, first-order, initial-value problem. We provide a…
We present a space-time multiscale method for a parabolic model problem with an underlying coefficient that may be highly oscillatory with respect to both the spatial and the temporal variables. The method is based on the framework of the…
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…
We describe a novel algorithm for solving general parametric (nonlinear) eigenvalue problems. Our method has two steps: first, high-accuracy solutions of non-parametric versions of the problem are gathered at some values of the parameters;…
We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…
We consider the initial-boundary value problem for a quasilinear time-fractional diffusion equation, and develop a fully discrete solver combining the parareal algorithm in time with a L1 finite-difference approximation of the Caputo…
While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional numerical solvers still remains a challenge. One strategy to…
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…
We present an explicit multiscale algorithm for solving differential equations for problems with high-frequency modes that can be averaged over by separating and scaling the fast and slow dynamics within a single equation. We introduce a…
A large-scale complex system comprising many, often spatially distributed, dynamical subsystems with partial autonomy and complex interactions are called system of systems. This paper describes an efficient algorithm for model predictive…
A parareal algorithm based on an exponential $\theta$-scheme is proposed for the stochastic Schr\"odinger equation with weak damping and additive noise. It proceeds as a two-level temporal parallelizable integrator with the exponential…
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
We consider a network of sensors deployed to sense a spatio-temporal field and estimate a parameter of interest. We are interested in the case where the temporal process sensed by each sensor can be modeled as a state-space process that is…