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Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…

Numerical Analysis · Mathematics 2026-03-24 G. H. M. Araújo , O. A. Krzysik , H. De Sterck

This paper presents a concurrent global-local numerical method for solving multiscale parabolic equations in divergence form. The proposed method employs hybrid coefficient to provide accurate macroscopic information while preserving…

Numerical Analysis · Mathematics 2026-04-14 Yulei Liao , Yang Liu , Pingbing Ming

We present and analyse a micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations with separation between the (fast) time-scale of individual trajectories and the (slow) time-scale of the…

Numerical Analysis · Mathematics 2017-12-04 Kristian Debrabant , Giovanni Samaey , Przemysław Zieliński

Pseudo-arclength continuation is a well-established method for generating a numerical curve approximating the solution of an underdetermined system of nonlinear equations. It is an inherently sequential predictor-corrector method in which…

Numerical Analysis · Mathematics 2013-12-13 Dhavide Aruliah , Lennaert van Veen , Alex Dubitski

Computational fluid dynamics (CFD) is a powerful tool for modeling turbulent flow and is commonly used for urban microclimate simulations. However, traditional CFD methods are computationally intensive, requiring substantial hardware…

The paper investigates a non-intrusive parallel time integration with multigrid for space-fractional diffusion equations in two spatial dimensions. We firstly obtain a fully discrete scheme via using the linear finite element method to…

Numerical Analysis · Mathematics 2018-05-18 Xiaoqiang Yue , Shi Shu , Xiaowen Xu , Weiping Bu , Kejia Pan

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.…

Computational Engineering, Finance, and Science · Computer Science 2017-05-18 Roberto Croce , Daniel Ruprecht , Rolf Krause

This report discusses the implementation of two parallel algorithms on a distributed memory system for studying vortex dynamics in type-II superconductors. These algorithms are the same as that implemented for classical molecular dynamics…

Superconductivity · Physics 2007-05-23 Mahesh Chandran

Despite the growing interest in parallel-in-time methods as an approach to accelerate numerical simulations in atmospheric modelling, improving their stability and convergence remains a substantial challenge for their application to…

Numerical Analysis · Mathematics 2023-10-27 João Guilherme Caldas Steinstraesser , Pedro da Silva Peixoto , Martin Schreiber

A parallel 2D+1 split-step Fourier method with Crank-Nicholson scheme running on multi-core shared memory architectures is developed to study the propagation of ultra-short high-intensity laser pulses in air. The parallel method achieves a…

Optics · Physics 2015-07-23 Cunliang Ma , Wenbin Lin

We review several parallel tempering schemes and examine their main ingredients for accuracy and efficiency. The present study covers two selection methods of temperatures and several choices for the exchange of replicas, including a recent…

Statistical Mechanics · Physics 2015-06-16 A. Malakis , T. Papakonstantinou

A unified approach to energy-efficient power control, applicable to a large family of receivers including the matched filter, the decorrelator, the (linear) minimum-mean-square-error detector (MMSE), and the individually and jointly optimal…

Information Theory · Computer Science 2007-07-13 Farhad Meshkati , H. Vincent Poor , Stuart C. Schwartz , Dongning Guo

In modelling time series data coming from different sources, frequencies can easily vary since some variable can be measured at higher frequencies, others, at lower frequencies. Given data measured over spatial units and at varying…

Methodology · Statistics 2025-03-05 Vladimir A. Malabanan , Joseph Ryan G. Lansangan , Erniel B. Barrios

Spectral methods for solving partial differential equations (PDEs) and stochastic partial differential equations (SPDEs) often use Fourier or polynomial spectral expansions on either uniform and non-uniform grids. However, while very widely…

Numerical Analysis · Mathematics 2025-07-30 Channa Hatharasinghe , Run Yan Teh , Jesse van Rhijn , Peter D. Drummond , Margaret D. Reid

We propose in this paper the Wavelet-based Edge Multiscale Parareal (WEMP) Algorithm to efficiently solve parabolic equations with heterogeneous coefficients. This algorithm combines the advantages of multiscale methods that can deal with…

Numerical Analysis · Mathematics 2021-08-18 Guanglian Li , Jiuhua Hu

This paper presents a novel parallel-in-time algorithm able to compute time-periodic solutions of problems where the period is not given. Exploiting the idea of the multiple shooting method, the proposed approach calculates the initial…

Numerical Analysis · Mathematics 2020-07-08 Iryna Kulchytska-Ruchka , Sebastian Schöps

Diffusion models have emerged as a powerful class of generative models across various modalities, including image, video, and audio synthesis. However, their deployment is often limited by significant inference latency, primarily due to the…

Machine Learning · Computer Science 2025-10-14 Kunyun Wang , Bohan Li , Kai Yu , Minyi Guo , Jieru Zhao

We present a full implementation of the parareal algorithm---an integration technique to solve differential equations in parallel---in the Julia programming language for a fully general, first-order, initial-value problem. We provide a…

Mathematical Software · Computer Science 2018-12-17 Tyler M. Masthay , Saverio Perugini

A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…

Numerical Analysis · Mathematics 2017-11-23 Sabyasachi Chatterjee , Amit Acharya , Zvi Artstein

The present study is an extension of the work done in Parareal convergence for oscillatory pdes with finite time-scale separation (2019), A. G. Peddle, T. Haut, and B. Wingate, [16], and An asymptotic parallel-in-time method for highly…

Numerical Analysis · Mathematics 2023-03-17 Juliane Rosemeier , Terry Haut , Beth Wingate