相关论文: An OpenCL implementation for the solution of TDSE …

We discuss the development, verification, and performance of a GPU accelerated discontinuous Galerkin method for the solutions of two dimensional nonlinear shallow water equations. The shallow water equations are hyperbolic partial…

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…

In this short communication we introduce a rather simple autonomous system of 2 nonlinearly-coupled first-order Ordinary Differential Equations (ODEs), whose initial-values problem is explicitly solvable by algebraic operations. Its ODEs…

In addressing the demands of industrial high-fidelity computation, the present study introduces a rapid and accurate customized solver developed on the OpenFOAM platform. To enhance computational efficiency, a novel integrated acceleration…

In-Context Learning (ICL) has emerged as a new paradigm in large language models (LLMs), enabling them to perform novel tasks by conditioning on a few examples embedded in the prompt. Yet, the highly nonlinear behavior of ICL for NLP tasks…

The Preconditioned Conjugate Gradient (PCG) method is widely used for solving linear systems of equations with sparse matrices. A recent version of PCG, Pipelined PCG, eliminates the dependencies in the computations of the PCG algorithm so…

Generative AI technology based on Large Language Models (LLM) has been developed and applied to assist or automatically generate program codes. In this paper, we evaluate the capability of existing general LLMs for Basic Linear Algebra…

As in various fields like scientific research and industrial application, the computation time optimization is becoming a task that is of increasing importance because of its highly parallel architecture. The graphics processing unit is…

Performance modeling, a pivotal domain in program cost analysis, currently relies on manually crafted models constrained by various program and hardware limitations, especially in the intricate landscape of GPGPU. Meanwhile, Large Language…

We present a new adaptive parallel algorithm for the challenging problem of multi-dimensional numerical integration on massively parallel architectures. Adaptive algorithms have demonstrated the best performance, but efficient many-core…

We study the problem of executing an application represented by a precedence task graph on a parallel machine composed of standard computing cores and accelerators. Contrary to most existing approaches, we distinguish the allocation and the…

The alternating direction method of multipliers (ADMM) is a powerful operator splitting technique for solving structured convex optimization problems. Due to its relatively low per-iteration computational cost and ability to exploit…

The recent trend of using Graphics Processing Units (GPU's) for high performance computations is driven by the high ratio of price performance for these units, complemented by their cost effectiveness. At first glance, computational fluid…

Probabilistic numerical solvers for ordinary differential equations (ODEs) treat the numerical simulation of dynamical systems as problems of Bayesian state estimation. Aside from producing posterior distributions over ODE solutions and…

Deep learning (DL) frameworks take advantage of GPUs to improve the speed of DL inference and training. Ideally, DL frameworks should be able to fully utilize the computation power of GPUs such that the running time depends on the amount of…

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…

Many graphics and vision problems can be expressed as non-linear least squares optimizations of objective functions over visual data, such as images and meshes. The mathematical descriptions of these functions are extremely concise, but…

With the potential of quantum algorithms to solve intractable classical problems, quantum computing is rapidly evolving and more algorithms are being developed and optimized. Expressing these quantum algorithms using a high-level language…

Realistic reservoir simulation is known to be prohibitively expensive in terms of computation time when increasing the accuracy of the simulation or by enlarging the model grid size. One method to address this issue is to parallelize the…

The open-world assumption in model development suggests that a model might lack sufficient information to adequately handle data that is entirely distinct or out of distribution (OOD). While deep learning methods have shown promising…