Related papers: Parareal algorithms applied to stochastic differen…
In this paper, we propose stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of particles using the Lagrangian formulation, which is modeled by…
We study coarse-graining methods for stochastic differential equations. In particular we consider averaging and a type of projection operator method, sometimes referred to as effective dynamic via conditional expectations. The projection…
This article proposes modifications of the Parareal algorithm for its application to higher index differential algebraic equations (DAEs). It is based on the idea of applying the algorithm to only the differential components of the equation…
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…
We consider a new class of Parareal algorithms, which use ideas from localized reduced basis methods to construct the coarse solver from spectral approximations of the transfer operators mapping initial values for a given time interval to…
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…
In this paper, we propose a model order reduction based adaptive parareal method for time-dependent partial differential equations. By using the data obtained by the fine propagator in each iteration of the plain parareal method together…
In this paper, we consider the problem of accelerating the numerical simulation of time dependent problems by time domain decomposition. The available algorithms enabling such decompositions present severe efficiency limitations and are an…
A type of iterative orthogonally accumulated projection methods for solving linear system of equations are proposed in this paper. This type of methods are applications of accumulated projection(AP) technique proposed recently by authors.…
Stochastic parareal (SParareal) is a probabilistic variant of the popular parallel-in-time algorithm known as parareal. Similarly to parareal, it combines fine- and coarse-grained solutions to an ordinary differential equation (ODE) using a…
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…
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…
This paper investigates gradient recovery schemes for data defined on discretized manifolds. The proposed method, parametric polynomial preserving recovery (PPPR), does not require the tangent spaces of the exact manifolds, and they have…
In this paper, we are concerned with the micro-macro Parareal algorithm for the simulation of initial-value problems. In this algorithm, a coarse (fast) solver is applied sequentially over the time domain, and a fine (time-consuming) solver…
Random projections are random linear maps, sampled from appropriate distributions, that approx- imately preserve certain geometrical invariants so that the approximation improves as the dimension of the space grows. The well-known…
We propose a new modified primal-dual proximal best approximation method for solving convex not necessarily differentiable optimization problems. The novelty of the method relies on introducing memory by taking into account iterates…
In this paper, we propose a class of explicit positivity preserving numerical methods for general stochastic differential equations which have positive solutions. Namely, all the numerical solutions are positive. Under some reasonable…
The Parareal algorithm was invented in 2001 in order to parallelize the solution of evolution problems in the time direction. It is based on parallel fine time propagators called F and sequential coarse time propagators called G, which…
Parareal is a well-known parallel-in-time algorithm that combines a coarse and fine propagator within a parallel iteration. It allows for large-scale parallelism that leads to significantly reduced computational time compared to serial…
A weighted version of the parareal method for parallel-in-time computation of time dependent problems is presented. Linear stability analysis for a scalar weighing strategy shows that the new scheme may enjoy favorable stability properties…