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Spectral deferred corrections (SDC) is an iterative approach for constructing higher- order accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of…

Computational Engineering, Finance, and Science · Computer Science 2017-06-14 R. W. Grout , H. Kolla , M. L. Minion , J. B. Bell

We introduce a fast solver for the phase field crystal (PFC) and functionalized Cahn-Hilliard (FCH) equations with periodic boundary conditions on a rectangular domain that features the preconditioned Nesterov accelerated gradient descent…

Numerical Analysis · Mathematics 2023-03-22 Jea-Hyun Park , Abner Salgado , Steven Wise

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…

Numerical Analysis · Mathematics 2024-12-03 Jianguo Huang , Yuejin Xu

This paper introduces Exp-ParaDiag, a novel time-parallel method that combines the strength of exponential integrators into the ParaDiag framework. We develop and analyze Exp-ParaDiag based on first and second order accurate exponential…

Numerical Analysis · Mathematics 2026-03-05 Gobinda Garai , Nagaiah Chamakuri

We provide improved parallel approximation algorithms for the important class of packing and covering linear programs. In particular, we present new parallel $\epsilon$-approximate packing and covering solvers which run in…

Data Structures and Algorithms · Computer Science 2015-11-23 Di Wang , Michael Mahoney , Nishanth Mohan , Satish Rao

The space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell ADER-WENO finite-volume limiting was used for simulation of multidimensional reacting flows with detonation waves. The presented numerical…

Fluid Dynamics · Physics 2024-09-23 I. S. Popov

Many astrophysical simulations involve extreme dynamic range of timescales around 'special points' in the domain (e.g. black holes, stars, planets, disks, galaxies, shocks, mixing interfaces), where processes on small scales couple strongly…

Instrumentation and Methods for Astrophysics · Physics 2026-05-11 Philip F. Hopkins , Elias R. Most

In 2008, Maday and Ronquist introduced an interesting new approach for the direct parallel-in-time (PinT) solution of time-dependent PDEs. The idea is to diagonalize the time stepping matrix, keeping the matrices for the space…

Numerical Analysis · Mathematics 2021-04-15 Martin J. Gander , Jun Liu , Shu-Lin Wu , Xiaoqiang Yue , Tao Zhou

Large-scale optimization problems that involve thousands of decision variables have extensively arisen from various industrial areas. As a powerful optimization tool for many real-world applications, evolutionary algorithms (EAs) fail to…

Neural and Evolutionary Computing · Computer Science 2023-09-26 Peng Yang , Ke Tang , Xin Yao

The numerical simulation of atherosclerotic plaque growth is computationally prohibitive, since it involves a complex cardiovascular fluid-structure interaction (FSI) problem with a characteristic time scale of milliseconds to seconds, as…

Numerical Analysis · Mathematics 2023-08-09 Stefan Frei , Alexander Heinlein

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…

Computational Geometry · Computer Science 2020-10-01 Camille Coti , David Monniaux , Hang Yu

In view of the rapid rise of the number of cores in modern supercomputers, time-parallel methods that introduce concurrency along the temporal axis are becoming increasingly popular. For the solution of time-dependent partial differential…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-09-22 Andrea Arteaga , Daniel Ruprecht , Rolf Krause

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…

Optimization and Control · Mathematics 2020-04-07 Atal Narayan Sahu , Aritra Dutta , Aashutosh Tiwari , Peter Richtárik

The recent years have witnessed advances in parallel algorithms for large scale optimization problems. Notwithstanding demonstrated success, existing algorithms that parallelize over features are usually limited by divergence issues under…

Machine Learning · Computer Science 2017-12-08 An Bian , Xiong Li , Yuncai Liu , Ming-Hsuan Yang

We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex, continuously differentiable and possibly nonlinear, while the non-relaxed constraint set is…

Optimization and Control · Mathematics 2019-08-09 Brian Dandurand , Natashia Boland , Jeffrey Christiansen , Andrew Eberhard , Fabricio Oliveira

This paper presents parallel-in-time state estimation methods for systems with Slow-Rate inTegrated Measurements (SRTM). Integrated measurements are common in various applications, and they appear in analysis of data resulting from…

Computation · Statistics 2024-10-02 Fatemeh Yaghoobi , Simo Särkkä

We develop the uniform sparse Fast Fourier Transform (usFFT), an efficient, non-intrusive, adaptive algorithm for the solution of elliptic partial differential equations with random coefficients. The algorithm is an adaption of the sparse…

Numerical Analysis · Mathematics 2022-09-05 Lutz Kämmerer , Daniel Potts , Fabian Taubert

We investigate the parallel performance of Parallel Spectral Deferred corrections, a numerical approach that provides small-scale parallelism for the numerical solution of initial value problems. The scheme is applied to the shallow-water…

Computational Engineering, Finance, and Science · Computer Science 2026-03-04 Philip Freese , Sebastian Götschel , Thibaut Lunet , Daniel Ruprecht , Martin Schreiber

Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…

Quantitative Methods · Quantitative Biology 2016-04-29 Jonathan U. Harrison , Christian A. Yates

We present a parallel time-stepping method for fluid-structure interactions. The interaction between the incompressible Navier-Stokes equations and a hyperelastic solid is formulated in a fully monolithic framework. Discretization in space…

Numerical Analysis · Mathematics 2022-01-19 Nils Margenberg , Thomas Richter