Related papers: Finite Element Integration with Quadrature on the …
The automated finite element analysis of complex CAD models using boundary-fitted meshes is rife with difficulties. Immersed finite element methods are intrinsically more robust but usually less accurate. In this work, we introduce an…
Generative Pre-trained Transformer models, known as GPT or OPT, set themselves apart through breakthrough performance across complex language modelling tasks, but also by their extremely high computational and storage costs. Specifically,…
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…
In this paper we develop the first fine-grained rounding error analysis of finite element (FE) cell kernels and assembly. The theory includes mixed-precision implementations and accounts for hardware-acceleration via matrix multiplication…
We present a set of rules to guide the design of GPU algorithms. These rules are grounded on the principle of reducing waste in GPU utility to achieve good speed up. In accordance to these rules, we propose GPU algorithms for 2D…
We report the first CUDA graphics-processing-unit (GPU) implementation of the polymer field-theoretic simulation framework for determining fully fluctuating expectation values of equilibrium properties for periodic and select aperiodic…
We introduce a novel hybrid methodology combining classical finite element methods (FEM) with neural networks to create a well-performing and generalizable surrogate model for forward and inverse problems. The residual from finite element…
In this paper, we present a new immersed finite element scheme for solving elliptic interface problems on unfitted meshes by combining the skeletal finite element method (FEM) with the standard FEM. The skeletal FEM is used for the…
Transformer-based models, such as BERT and ViT, have achieved state-of-the-art results across different natural language processing (NLP) and computer vision (CV) tasks. However, these models are extremely memory intensive during their…
The rapid adaptation of data driven AI models, such as deep learning inference, training, Vision Transformers (ViTs), and other HPC applications, drives a strong need for runtime precision configurable different non linear activation…
Stencil computations are widely used in HPC applications. Today, many HPC platforms use GPUs as accelerators. As a result, understanding how to perform stencil computations fast on GPUs is important. While implementation strategies for…
Graph coloring has been broadly used to discover concurrency in parallel computing. To speedup graph coloring for large-scale datasets, parallel algorithms have been proposed to leverage modern GPUs. Existing GPU implementations either have…
Study of general purpose computation by GPU (Graphics Processing Unit) can improve the image processing capability of micro-computer system. This paper studies the parallelism of the different stages of decimation in time radix 2 FFT…
Convolutional gridding is a processor-intensive step in interferometric imaging. While it is possible to use graphics processing units (GPUs) to accelerate this operation, existing methods use only a fraction of the available flops. We…
Attention accounts for an increasingly dominant fraction of total computation during inference for mixture-of-experts (MoE) models, making efficient acceleration critical. Emerging domain-specific accelerators for large model inference are…
In this paper we study a system of advection-diffusion equations in a bulk domain coupled to an advection-diffusion equation on an embedded surface. Such systems of coupled partial differential equations arise in, for example, the modeling…
In a general graph data structure like an adjacency matrix, when edges are homogeneous, the connectivity of two nodes can be sufficiently represented using a single bit. This insight has, however, not yet been adequately exploited by the…
We present a detailed analysis of the bounds on the integration step in Discrete Element Method (DEM) for simulating collisions and shearing of granular assemblies. We show that, in the numerical scheme, the upper limit for the integration…
Modern transformer-based deep neural networks present unique technical challenges for effective acceleration in real-world applications. Apart from the vast amount of linear operations needed due to their sizes, modern transformer models…
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…