Related papers: Time-parallelization of sequential data assimilati…
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…
We present and analyze a parallel implementation of a parallel-in-time collocation method based on $\alpha$-circulant preconditioned Richardson iterations. While many papers explore this family of single-level, time-parallel "all-at-once"…
Time-parallel algorithms, such as Parareal, are well-understood for linear problems, but their convergence analysis for nonlinear, chaotic systems remains limited. This paper introduces a new theoretical framework for analysing…
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…
The time parallel solution of optimality systems arising in PDE constraint optimization could be achieved by simply applying any time parallel algorithm, such as Parareal, to solve the forward and backward evolution problems arising in the…
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…
We give in this paper a convergence result concerning parallel synchronous algorithm for nonlinear fixed point problems with respect to the euclidian norm in $\Rn$. We then apply this result to some problems related to convex analysis like…
Parallel computing is omnipresent in today's scientific computer landscape, starting at multicore processors in desktop computers up to massively parallel clusters. While domain decomposition methods have a long tradition in computational…
We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in…
Recently, the ParaOpt algorithm was proposed as an extension of the time-parallel Parareal method to optimal control. ParaOpt uses quasi-Newton steps that each require solving a system of matching conditions iteratively. The…
Parametric linear programming is a central operation for polyhedral computations, as well as in certain control applications.Here we propose a task-based scheme for parallelizing it, with quasi-linear speedup over large problems.This type…
In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refinement and synchronization techniques and is motivated by…
In this contribution the usage of the Parareal method is proposed for the time-parallel solution of the eddy current problem. The method is adapted to the particular challenges of the problem that are related to the differential algebraic…
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…
A novel approach to solve the problem of distributed state estimation of linear time-invariant systems is proposed in this paper. It relies on the application of parameter estimation-based observers, where the state observation task is…
The relative degree limitation for adaptive observer-based synchronization schemes is overcome. The scheme is extended to nonpassifiable systems. Two synchronization methods are described and justified based on augmented error adaptive…
We present a novel approach to the parallelization of the parabolic fast multipole method for a space-time boundary element method for the heat equation. We exploit the special temporal structure of the involved operators to provide an…
We present an algorithm for the solution of a simultaneous space-time discretization of linear parabolic evolution equations with a symmetric differential operator in space. Building on earlier work, we recast this discretization into a…
The Parareal algorithm allows to solve evolution problems exploiting parallelization in time. Its convergence and stability have been proved under the assumption of regular (smooth) inputs. We present and analyze here a new Parareal…
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…