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In this paper we analyze, evaluate, and improve the performance of training generalized linear models on modern CPUs. We start with a state-of-the-art asynchronous parallel training algorithm, identify system-level performance bottlenecks,…

Machine Learning · Computer Science 2018-12-20 Nikolas Ioannou , Celestine Dünner , Kornilios Kourtis , Thomas Parnell

We study preconditioned gradient-based optimization methods where the preconditioning matrix has block-diagonal form. Such a structural constraint comes with the advantage that the update computation is block-separable and can be…

Machine Learning · Computer Science 2020-12-08 Celestine Mendler-Dünner , Aurelien Lucchi

Center-based models are used to simulate the mechanical behavior of biological cells during embryonic development or cancer growth. To allow for the simulation of biological populations potentially growing from a few individual cells to…

Numerical Analysis · Mathematics 2022-07-27 Per Lötstedt , Sonja Mathias

This report considers linear multistep methods through time filtering. The approach has several advantages. It is modular and requires the addition of only one line of additional code. Error estimation and variable timesteps is…

Numerical Analysis · Mathematics 2017-08-22 Ahmet Guzel , William Layton

In this paper, we present a method that enables solving in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets…

Optimization and Control · Mathematics 2012-03-13 Yvon Maday , Mohamed-Kamel Riahi , Julien Salomon

Simulating large-scale microswimmer dynamics in viscous fluid poses significant challenges due to the coupled high spatial and temporal complexity. Conventional high-performance computing (HPC) methods often address these two dimensions in…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-04-15 Ruixiang Huang , Weifan Liu

We study a space-time finite element method for a system of poromechanics with memory effects that are modeled by a convolution integral. In the literature, the system is referred to as the Biot-Allard model. We recast the model as a…

Numerical Analysis · Mathematics 2025-04-10 Jakob S. Stokke , Markus Bause , Florin A. Radu

In this work we are interested in effectively solving the quasi-static, linear Biot model for poromechanics. We consider the fixed-stress splitting scheme, which is a popular method for iteratively solving Biot's equations. It is well-known…

Numerical Analysis · Mathematics 2021-05-24 Erlend Storvik , Jakub Wiktor Both , Kundan Kumar , Jan Martin Nordbotten , Florin Adrian Radu

We describe how long-term solar system orbit integration could be implemented on a parallel computer. The interesting feature of our algorithm is that each processor is assigned not to a planet or a pair of planets but to a time-interval.…

Astrophysics · Physics 2009-10-28 Prasenjit Saha , Joachim Stadel , Scott Tremaine

Inverse source problems arise often in real-world applications, such as localizing unknown groundwater contaminant sources. Being different from Tikhonov regularization, the quasi-boundary value method has been proposed and analyzed as an…

Numerical Analysis · Mathematics 2022-01-11 Yi Jiang , Jun Liu , Xiang-Sheng Wang

In-memory computing (IMC) has been shown to be a promising approach for solving binary optimization problems while significantly reducing energy and latency. Building on the advantages of parallel computation, we propose an IMC-compatible…

In this note we exploit polynomial preconditioners for the Conjugate Gradient method to solve large symmetric positive definite linear systems in a parallel environment. We put in connection a specialized Newton method to solve the matrix…

Numerical Analysis · Mathematics 2020-11-30 Luca Bergamaschi , Angeles Martinez

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…

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

Biot's equations of poroelasticity contain a parabolic system for the evolution of the pressure, which is coupled with a quasi-stationary equation for the stress tensor. Thus, it is natural to extend the existing work on isogeometric…

Numerical Analysis · Mathematics 2021-02-17 Jeremias Arf , Bernd Simeon

In this paper, we consider partitioned numerical methods for quasi-static multiple-network poroelasticity (MPET) equations, generalizations of the Biot model in poroelasticity for multiple pore networks. Two partitioned numerical methods…

Numerical Analysis · Mathematics 2024-12-20 Jeonghun J. Lee

In this article, we derive a new, fast, and robust preconditioned iterative solution strategy for the all-at-once solution of optimal control problems with time-dependent PDEs as constraints, including the heat equation and the non-steady…

Numerical Analysis · Mathematics 2020-07-17 Santolo Leveque , John W. Pearson

We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…

Numerical Analysis · Mathematics 2022-10-10 Sergio Blanes

In this paper, we propose a parallel space-time domain decomposition method for solving an unsteady source identification problem governed by the linear convection-diffusion equation. Traditional approaches require to solve repeatedly a…

Optimization and Control · Mathematics 2015-08-26 Xiaomao Deng , Xiao-chuan Cai , Jun Zou

We study higher-order space-time variational discretisations for modeling complex processes in porous media that include fluid and structure interactions which are of fundamental importance in many engineering fields with applications in…

Numerical Analysis · Mathematics 2018-05-03 Uwe Köcher , Markus Bause

We describe a method for time-critical decision making involving sequential tasks and stochastic processes. The method employs several iterative refinement routines for solving different aspects of the decision making problem. This paper…

Artificial Intelligence · Computer Science 2013-03-08 Thomas L. Dean , Leslie Pack Kaelbling , Jak Kirman , Ann Nicholson