Related papers: Acceleration of tensor-product operations for high…
In this paper, we explore the acceleration of tensor product operations in finite element methods, leveraging the computational power of the NVIDIA A100 GPU Tensor Cores. We provide an accessible overview of the necessary mathematical…
In this paper we present a new GPU-oriented mesh optimization method based on high-order finite elements. Our approach relies on node movement with fixed topology, through the Target-Matrix Optimization Paradigm (TMOP) and uses a global…
We extend earlier international efforts to optimise hexahedral-based spectral element methods on GPUs and vectorised CPUs to mixed element meshes additionally involving prismatic, pyramidic, and tetrahedral shapes using tensorial…
High-performance deep learning depends on efficient tensor programs. In recent years, automatic tensor program optimization, also known as tensor compilation, has emerged as the primary approach to generating efficient tensor programs.…
Finite element simulations play a critical role in a wide range of applications, from automotive design to tsunami modeling and computational electromagnetics. Performing these simulations efficiently at the high resolutions needed for…
In this paper, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of…
The paper considers the problem of implementation on graphics processors of numerical integration routines for higher order finite element approximations. The design of suitable GPU kernels is investigated in the context of general purpose…
In this paper, we will present a generalization of the L-tensor product (L-product) including generalization of the well known tensor cosine and T-products that were defined for third-order tensors and based on fast Fourier transform and…
We present a GPU implementation of vertex-patch smoothers for higher order finite element methods in two and three dimensions. Analysis shows that they are not memory bound with respect to GPU DRAM, but with respect to on-chip scratchpad…
This paper is devoted to the development of highly efficient kernels performing vector operations relevant in linear system solvers. In particular, we focus on the low arithmetic intensity operations (i.e., streaming operations) performed…
The paper presents investigations on the implementation and performance of the finite element numerical integration algorithm for first order approximations and three processor architectures, popular in scientific computing, classical CPU,…
Numerical methods such as the Finite Element Method (FEM) have been successfully adapted to utilize the computational power of GPU accelerators. However, much of the effort around applying FEM to GPU's has been focused on high-order FEM due…
Novel methods are presented in this initial study for the fusion of GPU kernels in the artificial compressibility method (ACM), using tensor product elements with constant Jacobians and flux reconstruction. This is made possible through the…
The Nvidia GPU architecture has introduced new computing elements such as the \textit{tensor cores}, which are special processing units dedicated to perform fast matrix-multiply-accumulate (MMA) operations and accelerate \textit{Deep…
Language models are now prevalent in software engineering with many developers using them to automate tasks and accelerate their development. While language models have been tremendous at accomplishing complex software engineering tasks,…
Kernel methods provide an elegant and principled approach to nonparametric learning, but so far could hardly be used in large scale problems, since na\"ive implementations scale poorly with data size. Recent advances have shown the benefits…
Tensor networks are a class of algorithms aimed at reducing the computational complexity of high-dimensional problems. They are used in an increasing number of applications, from quantum simulations to machine learning. Exploiting data…
We introduce a learning-based framework to optimize tensor programs for deep learning workloads. Efficient implementations of tensor operators, such as matrix multiplication and high dimensional convolution, are key enablers of effective…
Accurate hardware performance models are critical to efficient code generation. They can be used by compilers to make heuristic decisions, by superoptimizers as a minimization objective, or by autotuners to find an optimal configuration for…
In the CFD solver Nek5000, the computation is dominated by the evaluation of small tensor operations. Nekbone is a proxy app for Nek5000 and has previously been ported to GPUs with a mixed OpenACC and CUDA approach. In this work, we…