Related papers: Asynchronous Time-Parallel Method based on Laplace…

Motivated by large-scale optimization problems arising in the context of machine learning, there have been several advances in the study of asynchronous parallel and distributed optimization methods during the past decade. Asynchronous…

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…

Solving symmetric positive semidefinite linear systems is an essential task in many scientific computing problems. While Jacobi-type methods, including the classical Jacobi method and the weighted Jacobi method, exhibit simplicity in their…

Multigrid methods have been a popular approach for solving linear systems arising from the discretization of partial differential equations (PDEs) for several decades. They are particularly effective for accelerating convergence rates with…

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…

We introduce jaxFMM, an open-source, adaptive, highly parallel point-charge Fast Multipole Method implementation for the Laplace kernel written in JAX. It is based on a non-uniform refinement strategy, which results in extremely concise and…

In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…

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…

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 introduce a method for the fast numerical approximation of linear, second-order parabolic partial differential equations (PDEs for short) with time-independent coefficients based on model order reduction techniques and the Laplace…

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…

We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in…

This paper introduces a novel, fast atomic-snapshot protocol for asynchronous message-passing systems. In the process of defining what ``fast'' means exactly, we spot a few interesting issues that arise when conventional time metrics are…

We present original time-parallel algorithms for the solution of the implicit Euler discretization of general linear parabolic evolution equations with time-dependent self-adjoint spatial operators. Motivated by the inf-sup theory of…

Bayesian inference on non-Gaussian data is often non-analytic and requires computationally expensive approximations such as sampling or variational inference. We propose an approximate inference framework primarily designed to be…

We give in this paper a convergence result concerning parallel asynchronous algorithm with bounded delays to solve a nonlinear fixed point problems. This result is applied to calculate the solution of a strongly monotone operator. Special…

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…

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…

In \emph{Wang et al., A Shifted Laplace Rational Filter for Large-Scale Eigenvalue Problems}, the SLRF method was proposed to compute all eigenvalues of a symmetric definite generalized eigenvalue problem lying in an interval on the real…

This paper proposes a novel class of data-driven acceleration methods for steady-state flow field solvers. The core innovation lies in predicting and assigning the asymptotic limit value for each parameter during iterations based on its own…