Related papers: An implementation of tensor product patch smoother…
Optimizing deep learning algorithms currently requires slow, manual derivation, potentially leaving much performance untapped. Methods like FlashAttention have achieved a x6 performance improvement over native PyTorch by avoiding…
We describe an implementation of compressible inviscid fluid solvers with block-structured adaptive mesh refinement on Graphics Processing Units using NVIDIA's CUDA. We show that a class of high resolution shock capturing schemes can be…
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…
A cascadic multigrid method is proposed for the GPE problem based on the multilevel correction scheme. With this new scheme, the ground state eigenvalue problem on the finest space can be solved by smoothing steps on a series of multilevel…
We present the implementation of a trust-region Newton algorithm ExaTron for bound-constrained nonlinear programming problems, fully running on multiple GPUs. Without data transfers between CPU and GPU, our implementation has achieved the…
Subgraph matching is a core operation in graph analytics, supporting a broad spectrum of applications from social network analysis to bioinformatics. Recent GPU-based approaches accelerate subgraph matching by leveraging parallelism but…
The discontinuous Galerkin (DG) finite element method is conservative, lends itself well to parallelization, and is high-order accurate due to its close affinity with the theory of quadrature and orthogonal polynomials. When applied with an…
We analyze a hybrid method that enriches coarse grid finite element solutions with fine scale fluctuations obtained from a neural network. The idea stems from the Deep Neural Network Multigrid Solver (DNN-MG), (Margenberg et al., J Comput…
Sparse tensors appear in many large-scale applications with multidimensional and sparse data. While multidimensional sparse data often need to be processed on manycore processors, attempts to develop highly-optimized GPU-based…
Large sparse symmetric linear systems appear in several branches of science and engineering thanks to the widespread use of the finite element method (FEM). The fastest sparse linear solvers available implement hybrid iterative methods.…
The last decade has seen a shift in the computer systems industry where heterogeneous computing has become prevalent. Graphics Processing Units (GPUs) are now present in supercomputers to mobile phones and tablets. GPUs are used for…
The ability to model, analyze, and predict execution time of computations is an important building block supporting numerous efforts, such as load balancing, performance optimization, and automated performance tuning for high performance,…
Graphics Processing Units (GPUs) consisting of Streaming Multiprocessors (SMs) achieve high throughput by running a large number of threads and context switching among them to hide execution latencies. The number of thread blocks, and hence…
To break the GPU memory wall for scaling deep learning workloads, a variety of architecture and system techniques have been proposed recently. Their typical approaches include memory extension with flash memory and direct storage access.…
We present a novel, quadrature-based finite element integration method for low-order elements on GPUs, using a pattern we call \textit{thread transposition} to avoid reductions while vectorizing aggressively. On the NVIDIA GTX580, which has…
In this paper a local Fourier analysis for multigrid methods on tetrahedral grids is presented. Different smoothers for the discretization of the Laplace operator by linear finite elements on such grids are analyzed. A four-color smoother…
Random sketching is a dimensionality reduction technique that approximately preserves norms and singular values up to some $O(1)$ distortion factor with high probability. The most popular sketches in literature are the Gaussian sketch and…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
Rapid growth in scientific data and a widening gap between computational speed and I/O bandwidth makes it increasingly infeasible to store and share all data produced by scientific simulations. Instead, we need methods for reducing data…
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…