Related papers: Accelerating High-Order Finite Element Simulations…
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…
Largely due to their increased native capacity for numerical intensity and power efficiency, reduced-precision floating-point computing resources, primarily used in artificial intelligence (AI) applications, have expanded at a greater rate…
This paper is devoted to GPU kernel optimization and performance analysis of three tensor-product operators arising in finite element methods. We provide a mathematical background to these operations and implementation details. Achieving…
Quantum circuit simulation provides the foundation for the development of quantum algorithms and the verification of quantum supremacy. Among the various methods for quantum circuit simulation, tensor network contraction has been increasing…
As the demand for AI computation rapidly increases, more hardware is being developed to efficiently perform the low-precision matrix multiplications required by such workloads. However, these operations are generally not directly applicable…
Faster explicit elastic wavefield simulations are required for large and complex three-dimensional media using a structured finite element method. Such wavefield simulations are suitable for GPUs, which have exhibited improved computational…
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…
Efficient simulation of quantum circuits has become indispensable with the rapid development of quantum hardware. The primary simulation methods are based on state vectors and tensor networks. As the number of qubits and quantum gates grows…
As GPU architectures rapidly evolve to meet the growing demands of exascale computing and machine learning, the performance implications of architectural innovations remain poorly understood across diverse workloads. NVIDIA Blackwell (B200)…
The rapid growth of artificial intelligence (AI) has made low-precision formats such as FP16, FP8, and, most recently, block-scaled FP4 the primary focus of modern GPUs, where Tensor Cores now deliver orders-of-magnitude higher throughput…
The NVIDIA Volta GPU microarchitecture introduces a specialized unit, called "Tensor Core" that performs one matrix-multiply-and-accumulate on 4x4 matrices per clock cycle. The NVIDIA Tesla V100 accelerator, featuring the Volta…
Fast Fourier Transform (FFT) is an essential tool in scientific and engineering computation. The increasing demand for mixed-precision FFT has made it possible to utilize half-precision floating-point (FP16) arithmetic for faster speed and…
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,…
Tensor Core is a mixed-precision matrix-matrix multiplication unit on NVIDIA GPUs with a theoretical peak performance of more than 300 TFlop/s on Ampere architectures. Tensor Cores were developed in response to the high demand of dense…
Computing on graphics processors is maybe one of the most important developments in computational science to happen in decades. Not since the arrival of the Beowulf cluster, which combined open source software with commodity hardware to…
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…
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…
A high fidelity flow simulation for complex geometries for high Reynolds number ($Re$) flow is still very challenging, which requires more powerful computational capability of HPC system. However, the development of HPC with traditional CPU…
This study presents a comprehensive multi-level analysis of the NVIDIA Hopper GPU architecture, focusing on its performance characteristics and novel features. We benchmark Hopper's memory subsystem, highlighting improvements in the L2…
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…