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Simulations of physical phenomena are essential to the expedient design of precision components in aerospace and other high-tech industries. These phenomena are often described by mathematical models involving partial differential equations…

Computational Physics · Physics 2017-01-05 Daniel Magee , Kyle E Niemeyer

In this paper, a parallel overlapping domain decomposition preconditioner is proposed to solve the linear system of equations arising from the extended finite element discretization of elastic crack problems. The algorithm partitions the…

Computational Engineering, Finance, and Science · Computer Science 2021-12-07 Tian Wei , Huang Jingjing , Chen Rongliang , Jiang Yi

Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…

Optimization and Control · Mathematics 2022-06-22 Sebastián J. Ferraro , David Martín de Diego , Rodrigo Takuro Sato Martín de Almagro

We propose three semi-decoupled algorithms for efficiently solving a four-field thermoporoelastic model. The first two algorithms adopt a sequential strategy: at the initial time step, all variables are computed simultaneously using a…

Numerical Analysis · Mathematics 2025-12-02 Ziliang Li , Mingchao Cai , Jingzhi Li , Qiang Liu

We present and analyze a parallel implementation of a parallel-in-time collocation method based on $\alpha$-circulant preconditioned Richardson iterations. While many papers explore this family of single-level, time-parallel "all-at-once"…

Numerical Analysis · Mathematics 2023-02-16 Gayatri Caklovic , Robert Speck , Martin Frank

Efficient solutions of large-scale, ill-conditioned and indefinite algebraic equations are ubiquitously needed in numerous computational fields, including multiphysics simulations, machine learning, and data science. Because of their…

Mathematical Software · Computer Science 2026-05-25 Xiaoye Sherry Li , Yang Liu

We propose an efficient algorithm for the immersed boundary method on distributed-memory architectures, with the computational complexity of a completely explicit method and excellent parallel scaling. The algorithm utilizes the…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-01-29 Jeffrey K. Wiens , John M. Stockie

We study the numerical approximation of a time-dependent variational mean field game system with local couplings and either periodic or Neumann boundary conditions. Following a variational approach, we employ a finite difference…

Numerical Analysis · Mathematics 2026-01-06 Heidi Wolles Ljósheim , Dante Kalise , John W. Pearson , Francisco J. Silva

In this paper we present an algebraic dimension-oblivious two-level domain decomposition solver for discretizations of elliptic partial differential equations. The proposed parallel solver is based on a space-filling curve partitioning…

Numerical Analysis · Mathematics 2026-05-01 Michael Griebel , Marc Alexander Schweitzer , Lukas Troska

In this paper we present two strategies to enable "parallelization across the method" for spectral deferred corrections (SDC). Using standard low-order time-stepping methods in an iterative fashion, SDC can be seen as preconditioned Picard…

Numerical Analysis · Mathematics 2017-03-24 Robert Speck

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…

Numerical Analysis · Mathematics 2024-05-30 Bernhard Heinzelreiter , John W. Pearson

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

This paper combines the use of high order finite element methods with parallel preconditioners of domain decomposition type for solving electromagnetic problems arising from brain microwave imaging. The numerical algorithms involved in such…

Computational Physics · Physics 2020-03-23 M. Bonazzoli , V. Dolean , F. Rapetti , P. -H. Tournier

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…

Computational Physics · Physics 2015-06-11 Ran Xu , Bin Liu , Yuan Dong

This paper presents algorithms for temporal parallelization of Bayesian smoothers. We define the elements and the operators to pose these problems as the solutions to all-prefix-sums operations for which efficient parallel scan-algorithms…

Computation · Statistics 2020-02-21 Simo Särkkä , Ángel F. García-Fernández

We consider the numerical solution of large scale time-harmonic Maxwell equations. To this day, this problem remains difficult, in particular because the equations are neither Hermitian nor semi-definite. Our approach is to compare…

Numerical Analysis · Mathematics 2025-07-18 Elise Fressart , Sébastien Dubois , Loïc Gouarin , Marc Massot , Michel Nowak , Nicole Spillane

We develop a space-time spectral element method for topology optimization of transient heat conduction. The forward problem is discretized with summation-by-parts (SBP) operators, and interface/boundary and initial/terminal conditions are…

Numerical Analysis · Mathematics 2026-01-15 Sarah Nataj , Magnus Appel , Joe Alexandersen

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

Smoothing filter is the method of choice for image preprocessing and pattern recognition. We present a new concurrent method for smoothing 2D object in binary case. Proposed method provides a parallel computation while preserving the…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-04-01 Ramzi Mahmoudi , Mohamed Akil

In this paper, we aim to solve the system of equations governing linear elasticity in parallel using domain decomposition. Through a non-overlapping decomposition of the domain, our approach aims to target the resulting interface problem,…

Optimization and Control · Mathematics 2015-01-29 James Turner , Michal Kocvara , Daniel Loghin