Related papers: Massively parallel-in-space-time, adaptive finite …
It is found that the wave functions of the Gross-Pitaevskii equation (GPE) often vary significantly in different spatial regions, with some components exhibiting sharp variations while others remain smooth. Solving the GPE on a single mesh,…
We propose, analyze, and test new iterative solvers for large-scale systems of linear algebraic equations arising from the finite element discretization of reduced optimality systems defining the finite element approximations to the…
The parallel linear equations solver capable of effectively using 1000+ processors becomes the bottleneck of large-scale implicit engineering simulations. In this paper, we present a new hierarchical parallel master-slave-structural…
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 derive a new parallel-in-time approach for solving large-scale optimization problems constrained by time-dependent partial differential equations arising from fluid dynamics. The solver involves the use of a block circulant approximation…
We present an approach to solving problems in micromechanics that is amenable to massively parallel calculations through the use of graphical processing units and other accelerators. The problems lead to nonlinear differential equations…
We propose a new computational framework that combines the recently developed time-parallel (TP) and the compound wavelet matrix (CWM) methods. The framework, termed tpCWM, offers significant computational acceleration by making…
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…
Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…
In this paper, we consider the problem of stochastic optimization, where the objective function is in terms of the expectation of a (possibly non-convex) cost function that is parametrized by a random variable. While the convergence speed…
In this paper we combine the Parareal parallel-in-time method together with spatial parallelization and investigate this space-time parallel scheme by means of solving the three-dimensional incompressible Navier-Stokes equations.…
In order to run Computational Fluid Dynamics (CFD) codes on large scale infrastructures, parallel computing has to be used because of the computational intensive nature of the problems. In this paper we investigate the ADAPT platform where…
To overcome the communication bottlenecks observed in state-of-the-art parallel time-dependent flow solvers at extreme scales, an asynchronous computing approach that relaxes communication and synchronization at a mathematical level was…
We introduce an adaptive superconvergent finite element method for a class of mixed formulations to solve partial differential equations involving a diffusion term. It combines a superconvergent postprocessing technique for the primal…
An adaptive method for parabolic partial differential equations that combines sparse wavelet expansions in time with adaptive low-rank approximations in the spatial variables is constructed and analyzed. The method is shown to converge and…
We propose a decomposition framework for the parallel optimization of the sum of a differentiable function and a (block) separable nonsmooth, convex one. The latter term is typically used to enforce structure in the solution as, for…
The parallel full approximation scheme in space and time (PFASST) is a parallel-in-time integrator that allows to integrate multiple time-steps simultaneously. It has been shown to extend scaling limits of spatial parallelization strategies…
We consider the parallel-in-time solution of hyperbolic partial differential equation (PDE) systems in one spatial dimension, both linear and nonlinear. In the nonlinear setting, the discretized equations are solved with a preconditioned…
The increasing scale and complexity of large language models (LLMs) pose significant inference latency challenges, primarily due to their autoregressive decoding paradigm characterized by the sequential nature of next-token prediction. By…
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…