Related papers: Fast Stencil Computations using Fast Fourier Trans…
Stencil kernels dominate a range of scientific applications, including seismic and medical imaging, image processing, and neural networks. Temporal blocking is a performance optimization that aims to reduce the required memory bandwidth of…
Quantum subspace diagonalization (QSD) algorithms have emerged as a competitive family of algorithms that avoid many of the optimization pitfalls associated with parameterized quantum circuit algorithms. While the vast majority of the QSD…
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…
In this paper we evaluate the performance of FPGAs for high-order stencil computation using High-Level Synthesis. We show that despite the higher computation intensity and on-chip memory requirement of such stencils compared to first-order…
Finite-difference methods based on high-order stencils are widely used in seismic simulations, weather forecasting, computational fluid dynamics, and other scientific applications. Achieving HPC-level stencil computations on one…
Stencil computation constitutes a cornerstone of scientific computing, serving as a critical kernel in domains ranging from fluid dynamics to weather simulation. While stencil computations are conventionally regarded as memory-bound and…
Current architectures are now equipped with matrix computation units designed to enhance AI and high-performance computing applications. Within these architectures, two fundamental instruction types are matrix multiplication and vector…
Stencils represent a class of computational patterns where an output grid point depends on a fixed shape of neighboring points in an input grid. Stencil computations are prevalent in scientific applications engaging a significant portion of…
Different numerical approaches for the stray-field calculation in the context of micromagnetic simulations are investigated. We compare finite difference based fast Fourier transform methods, tensor grid methods and the finite-element…
We propose a fast collocation method based on Krylov subspace iterative solver on general nonuniform grids for the fractional Laplacian problem, in which the fractional operator is presented in a singular integral formulation. The method is…
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…
The convolution potential arises in a wide variety of application areas, and its efficient and accurate evaluation encounters three challenges: singularity, nonlocality and anisotropy. We introduce a fast algorithm based on a far-field…
Stencil computations are a fundamental kernel in scientific computing, critical for simulations in domains such as fluid dynamics and climate modeling. However, these computations are often memory-bound on traditional High-Performance…
Convolutional neural networks (CNNs) have a large number of variables and hence suffer from a complexity problem for their implementation. Different methods and techniques have developed to alleviate the problem of CNN's complexity, such as…
We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to…
We introduce a fast algorithm for computing sparse Fourier transforms supported on smooth curves or surfaces. This problem appear naturally in several important problems in wave scattering and reflection seismology. The main observation is…
This work presents a GPU thread mapping approach that allows doing fast parallel stencil-like computations on discrete fractals using their compact representation. The intuition behind is to employ two GPU tensor-core accelerated thread…
In this era of diverse and heterogeneous computer architectures, the programmability issues, such as productivity and portable efficiency, are crucial to software development and algorithm design. One way to approach the problem is to step…
Fast linear transforms are ubiquitous in machine learning, including the discrete Fourier transform, discrete cosine transform, and other structured transformations such as convolutions. All of these transforms can be represented by dense…
It is well known that to accelerate stencil codes on CPUs or GPUs and to exploit hardware caches and their lines optimizers must find spatial and temporal locality of array accesses to harvest data-reuse opportunities. On FPGAs there is the…