相关论文: ShyLU node: On-node Scalable Solvers and Precondit…

We discuss an approach for solving sparse or dense banded linear systems ${\bf A} {\bf x} = {\bf b}$ on a Graphics Processing Unit (GPU) card. The matrix ${\bf A} \in {\mathbb{R}}^{N \times N}$ is possibly nonsymmetric and moderately large;…

As supercomputers become larger with powerful Graphics Processing Unit (GPU), traditional direct eigensolvers struggle to keep up with the hardware evolution and scale efficiently due to communication and synchronization demands.…

The SPIKE family of linear system solvers provides parallelism using a block tridiagonal partitioning. Typically SPIKE-based solvers are applied to banded systems, resulting in structured off-diagonal blocks with non-zeros elements…

We demonstrate algorithm-based fault tolerance for silent, transient data corruption in "black-box" preconditioners. We consider both additive Schwarz domain decomposition with an ILU(k) subdomain solver, and algebraic multigrid, both…

We present SPDL (Scalable and Performant Data Loading), an open-source, framework-agnostic library designed for efficiently loading array data to GPU. Data loading is often a bottleneck in AI applications, and is challenging to optimize…

Inversion of sparse matrices with standard direct solve schemes is robust, but computationally expensive. Iterative solvers, on the other hand, demonstrate better scalability; but, need to be used with an appropriate preconditioner (e.g.,…

We present a cross-architecture high-order heterogeneous Navier-Stokes simulation solver, XFluids, for compressible reacting multicomponent flows on different platforms. The multi-component reacting flows are ubiquitous in many scientific…

Task-based programming models have proven to be a robust and versatile way to approach development of applications for distributed environments. They provide natural programming patterns with high performance. However, execution on this…

The evaluation of new microprocessor designs is constrained by slow, cycle-accurate simulators that rely on unrepresentative benchmark traces. This paper introduces a novel deep learning framework for high-fidelity, ``in-the-wild''…

Transformer-based models are the state-of-the-art for Natural Language Understanding (NLU) applications. Models are getting bigger and better on various tasks. However, Transformer models remain computationally challenging since they are…

This paper presents a lightweight, open-source and high-performance python package for solving peridynamics problems in solid mechanics. The development of this solver is motivated by the need for fast analysis tools to achieve the large…

Fast, scalable decoding architectures that operate in a block-wise parallel fashion across space and time are essential for real-time fault-tolerant quantum computing. We introduce a scalable AI-based pre-decoder for the surface code that…

In this paper, we revisit an auxiliary space preconditioning method proposed by Xu [Computing 56, 1996], in which low-order finite element spaces are employed as auxiliary spaces for solving linear algebraic systems arising from high-order…

This paper introduces sTiles, a GPU-accelerated framework for factorizing sparse structured symmetric matrices. By leveraging tile algorithms for fine-grained computations, sTiles uses a structure-aware task execution flow to handle…

We present a scalable parallel solver for numerical constraint satisfaction problems (NCSPs). Our parallelization scheme consists of homogeneous worker solvers, each of which runs on an available core and communicates with others via the…

The paper proposes a combination of the subdomain deflation method and local algebraic multigrid as a scalable distributed memory preconditioner that is able to solve large linear systems of equations. The implementation of the algorithm is…

Linear operators and optimisation are at the core of many algorithms used in signal and image processing, remote sensing, and inverse problems. For small to medium-scale problems, existing software packages (e.g., MATLAB, Python numpy and…

We investigate the potential of Graphics Processing Units (GPUs) to solve large-scale nonlinear programs with a dynamic structure. Using ExaModels, a GPU-accelerated automatic differentiation tool, and the interior-point solver MadNLP, we…

Here we present an implementation of Primal-Dual Affine scaling method to solve linear optimization problem on GPU based systems. Strategies to convert the system generated by complementary slackness theorem into a symmetric system are…

We propose Paraiso, a domain specific language embedded in functional programming language Haskell, for automated tuning of explicit solvers of partial differential equations (PDEs) on GPUs as well as multicore CPUs. In Paraiso, one can…