Related papers: Parareal methods for highly oscillatory dynamical …
In this paper, we propose a parallel-in-time algorithm for approximately solving parabolic equations. In particular, we apply the $k$-step backward differentiation formula, and then develop an iterative solver by using the waveform…
In this paper, we investigate the strong convergence analysis of parareal algorithms for stochastic Maxwell equations with the damping term driven by additive noise. The proposed parareal algorithms proceed as two-level temporal…
This paper considers the approximation of the continuous time filtering equation for the case of a multiple timescale (slow-intermediate, and fast scales) that may have correlation between the slow-intermediate process and the observation…
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…
Long-range temporal alignment is critical yet challenging for video restoration tasks. Recently, some works attempt to divide the long-range alignment into several sub-alignments and handle them progressively. Although this operation is…
Nonlinear parabolic equations are frequently encountered in applications and efficient approximating techniques for their solution are of great importance. In order to provide an effective scheme for the temporal approximation of such…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
The parareal algorithm represents an important class of parallel-in-time algorithms for solving evolution equations and has been widely applied in practice. To achieve effective speedup, the choice of the coarse propagator in the algorithm…
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…
This paper proposes an efficient parallelised computation of field/circuit coupled systems co-simulated with the Waveform Relaxation (WR) technique. The main idea of the introduced approach lies in application of the parallel-in-time method…
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…
In this paper, for solving a class of linear parabolic equations in rectangular domains, we have proposed an efficient Parareal exponential integrator finite element method. The proposed method first uses the finite element approximation…
With the advent of supercomputers, multi-processor environments and parallel-in-time (PinT) algorithms offer ways to solve initial value problems for ordinary and partial differential equations (ODEs and PDEs) over long time intervals, a…
To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a…
A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based…
Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article,…
The modeling of atmospheric processes in the context of weather and climate simulations is an important and computationally expensive challenge. The temporal integration of the underlying PDEs requires a very large number of time steps,…
In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…
This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…
Many problems in the geophysical sciences demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially-collected data. Here we introduce a general methodology for the joint…