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The increasing number of processing elements and decreas- ing memory to core ratio in modern high-performance platforms makes efficient strong scaling a key requirement for numerical algorithms. In order to achieve efficient scalability on…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-01-14 Michael Lange , Gerard Gorman , Michele Weiland , Lawrence Mitchell , James Southern

A hybrid scheme that utilizes MPI for distributed memory parallelism and OpenMP for shared memory parallelism is presented. The work is motivated by the desire to achieve exceptionally high Reynolds numbers in pseudospectral computations of…

Computational Physics · Physics 2010-03-24 Pablo D. Mininni , Duane L. Rosenberg , Raghu Reddy , Annick Pouquet

We present a highly scalable algorithm for multiplying sparse multivariate polynomials represented in a distributed format. This algo- rithm targets not only the shared memory multicore computers, but also computers clusters or specialized…

Symbolic Computation · Computer Science 2013-04-01 Mickael Gastineau , Jacques Laskar

Parallel implementations of Krylov subspace methods often help to accelerate the procedure of finding an approximate solution of a linear system. However, such parallelization coupled with asynchronous and out-of-order execution often…

Mathematical Software · Computer Science 2023-02-09 Roman Iakymchuk , Jose I. Aliaga

Developing efficient solvers for large-scale multi-term linear matrix equations remains a central challenge in numerical linear algebra and is still largely unresolved. This paper introduces a methodology leveraging CUR decomposition for…

Numerical Analysis · Mathematics 2025-11-19 Saeed Akbari , Damiano Lombardi , Hessam Babaee

This paper presents an efficient technique for matrix-vector and vector-transpose-matrix multiplication in distributed-memory parallel computing environments, where the matrices are unstructured, sparse, and have a substantially larger…

Mathematical Software · Computer Science 2018-12-04 Jonathan Eckstein , Gyorgy Matyasfalvi

We present a novel parallel implementation for large-scale three-dimensional electromagnetic inversion based on a Gauss-Newton framework combined with a rational near-best approximation of the matrix exponential for transient simulations.…

Numerical Analysis · Mathematics 2026-05-20 Ralph-Uwe Börner , Stefan Güttel , Thomas Günther

This paper pushes further the intrinsic capabilities of the GFEM$^{gl}$ global-local approach introduced initially in [1]. We develop a distributed computing approach using MPI (Message Passing Interface) both for the global and local…

Numerical Analysis · Mathematics 2023-02-22 Alexis Salzman , Nicolas Moës

Data structures for efficient sampling from a set of weighted items are an important building block of many applications. However, few parallel solutions are known. We close many of these gaps both for shared-memory and distributed-memory…

Data Structures and Algorithms · Computer Science 2021-07-20 Lorenz Hübschle-Schneider , Peter Sanders

We propose iterative projection methods for solving square or rectangular consistent linear systems Ax = b. Existing projection methods use sketching matrices (possibly randomized) to generate a sequence of small projected subproblems, but…

Numerical Analysis · Mathematics 2023-12-13 Johannes J. Brust , Michael A. Saunders

Sparse linear system solvers are computationally expensive kernels that lie at the heart of numerous applications. This paper proposes a flexible preconditioning framework to substantially reduce the time and energy requirements of this…

Emerging Technologies · Computer Science 2021-07-16 Vasileios Kalantzis , Anshul Gupta , Lior Horesh , Tomasz Nowicki , Mark S. Squillante , Chai Wah Wu

Parallel multigrid is widely used as preconditioners in solving large-scale sparse linear systems. However, the current multigrid library still needs more satisfactory performance for structured grid problems regarding speed and…

Numerical Analysis · Mathematics 2025-06-30 Yi Zong , Peinan Yu , Haopeng Huang , Zhengding Hu , Xinliang Wang , Qin Wang , Chensong Zhang , Xiaowen Xu , Jian Sun , Yongxiao Zhou , Wei Xue

We present variants of the Conjugate Gradient (CG), Conjugate Residual (CR), and Generalized Minimal Residual (GMRES) methods which are both pipelined and flexible. These allow computation of inner products and norms to be overlapped with…

Numerical Analysis · Mathematics 2016-09-16 Patrick Sanan , Sascha M. Schnepp , Dave. A. May

The Simplex tableau has been broadly used and investigated in the industry and academia. With the advent of the big data era, ever larger problems are posed to be solved in ever larger machines whose architecture type did not exist in the…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-05-29 Demetrios Coutinho , Felipe O. Lins e Silva , Daniel Aloise , Samuel , Xavier-de-Souza

Multistep matrix splitting iterations serve as preconditioning for Krylov subspace methods for solving singular linear systems. The preconditioner is applied to the generalized minimal residual (GMRES) method and the flexible GMRES (FGMRES)…

Numerical Analysis · Mathematics 2021-11-09 Keiichi Morikuni

We present the design and optimization of a linear solver on General Purpose GPUs for the efficient and high-throughput evaluation of the marginalized graph kernel between pairs of labeled graphs. The solver implements a preconditioned…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-05-20 Yu-Hang Tang , Oguz Selvitopi , Doru Popovici , Aydın Buluç

The solution of linear systems of equations is a central task in a number of scientific and engineering applications. In many cases the solution of linear systems may take most of the simulation time thus representing a major bottleneck in…

Numerical Analysis · Mathematics 2020-10-28 Giovanni Isotton , Carlo Janna , Massimo Bernaschi

Support for lower precision computation is becoming more common in accelerator hardware due to lower power usage, reduced data movement and increased computational performance. However, computational science and engineering (CSE) problems…

Numerical Analysis · Mathematics 2021-05-18 Jennifer A. Loe , Christian A. Glusa , Ichitaro Yamazaki , Erik G. Boman , Sivasankaran Rajamanickam

The ability to express a program as a hierarchical composition of parts is an essential tool in managing the complexity of software and a key abstraction this provides is to separate the representation of data from the computation. Many…

Programming Languages · Computer Science 2012-10-04 James Hanlon , Simon J. Hollis , David May

Discretizations of infinite-dimensional variational inequalities lead to linear and nonlinear complementarity problems with many degrees of freedom. To solve these problems in a parallel computing environment, we propose two active-set…

Optimization and Control · Mathematics 2007-05-23 Steven J. Benson , Todd S. Munson