相关论文: Time-periodic steady-state solution of fluid-struc…
The paper investigates a non-intrusive parallel time integration with multigrid for space-fractional diffusion equations in two spatial dimensions. We firstly obtain a fully discrete scheme via using the linear finite element method to…
This paper presents a novel parallel-in-time algorithm able to compute time-periodic solutions of problems where the period is not given. Exploiting the idea of the multiple shooting method, the proposed approach calculates the initial…
A long-standing issue in the parallel-in-time community is the poor convergence of standard iterative parallel-in-time methods for hyperbolic partial differential equations (PDEs), and for advection-dominated PDEs more broadly. Here, a…
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…
Artificial neural networks are a popular and effective machine learning technique. Great progress has been made parallelizing the expensive training phase of an individual network, leading to highly specialized pieces of hardware, many…
Parallelizing Gated Recurrent Unit (GRU) networks is a challenging task, as the training procedure of GRU is inherently sequential. Prior efforts to parallelize GRU have largely focused on conventional parallelization strategies such as…
Work presented in this paper describes a general algorithm and its finite element implementation for performing concurrent multiple sub-domain simulations in linear structural dynamics. Using this approach one can solve problems in which…
A framework is presented to design multirate time stepping algorithms for two dissipative models with coupling across a physical interface. The coupling takes the form of boundary conditions imposed on the interface, relating the solution…
This paper introduces a parallel-in-time algorithm for efficient steady-state solution of the eddy current problem. Its main idea is based on the application of the well-known multi-harmonic (or harmonic balance) approach as the coarse…
In the realm of big data and machine learning, data-parallel, distributed stochastic algorithms have drawn significant attention in the present days.~While the synchronous versions of these algorithms are well understood in terms of their…
We present a new algorithm for solving linear-quadratic regulator (LQR) problems with linear equality constraints, also known as constrained LQR (CLQR) problems. Our method's sequential runtime is linear in the number of stages and…
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…
The Parareal algorithm, which is related to multiple shooting, was introduced for solving evolution problems in a time-parallel manner. The algorithm was then extended to solve time-periodic problems. We are interested here in time-periodic…
Inspired by the successes of stochastic algorithms in the training of deep neural networks and the simulation of interacting particle systems, we propose and analyze a framework for randomized time-splitting in linear-quadratic optimal…
Parallel-in-time algorithms have been successfully employed for reducing time-to-solution of a variety of partial differential equations, especially for diffusive (parabolic-type) equations. A major failing of parallel-in-time approaches to…
Although convergence of the Parareal and multigrid-reduction-in-time (MGRIT) parallel-in-time algorithms is well studied, results on their optimality is limited. Appealling to recently derived tight bounds of two-level Parareal and MGRIT…
In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…
We consider the parallel-in-time solution of scalar nonlinear conservation laws in one spatial dimension. The equations are discretized in space with a conservative finite-volume method using weighted essentially non-oscillatory (WENO)…
The parareal in time algorithm allows to perform parallel simulations of time dependent problems. This algorithm has been implemented on many types of time dependent problems with some success. Recent contributions have allowed to extend…
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…