Related papers: PittPack: An Open-Source Poisson's Equation Solver…

The discretized Poisson equation matrix (DPEM) in 1D has been shown to require an exponentially large number of terms when decomposed in the Pauli basis when solving numerical linear algebra problems on a quantum computer. Additionally,…

A solver for the Poisson equation for 1D, 2D and 3D regular grids is presented. The solver applies the convolution theorem in order to efficiently solve the Poisson equation in spectral space over a rectangular computational domain.…

Edge-centric distributed computations have appeared as a recent technique to improve the shortcomings of think-like-a-vertex algorithms on large scale-free networks. In order to increase parallelism on this model, edge partitioning -…

Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most…

This work presents Squeeze, an efficient compact fractal processing scheme for tensor core GPUs. By combining discrete-space transformations between compact and expanded forms, one can do data-parallel computation on a fractal with…

It is well known since 1960s that by exploring the tensor product structure of the discrete Laplacian on Cartesian meshes, one can develop a simple direct Poisson solver with an $\mathcal O(N^{\frac{d+1}d})$ complexity in d-dimension, where…

Data accesses between on- and off-chip memories account for a large fraction of overall energy consumption during inference with deep learning networks. We present APack, a simple and effective, lossless, off-chip memory compression…

Abstract interpretation is a general framework for expressing static program analyses. It reduces the problem of extracting properties of a program to computing an approximation of the least fixpoint of a system of equations. The de facto…

For the Poisson equation posed in a domain containing a large number of polygonal perforations, we propose a low-dimensional coarse approximation space based on a coarse polygonal partitioning of the domain. Similarly to other multiscale…

A fast Poisson solver software package PoisFFT is presented. It is available as a free software licensed under the GNU GPL license version 3. The package uses the fast Fourier transform to directly solve the Poisson equation on a uniform…

This paper presents a numerical method for variable coefficient elliptic PDEs with mostly smooth solutions on two dimensional domains. The PDE is discretized via a multi-domain spectral collocation method of high local order (order 30 and…

Physics-Informed Neural Networks (PINN) emerged as a powerful tool for solving scientific computing problems, ranging from the solution of Partial Differential Equations to data assimilation tasks. One of the advantages of using PINN is to…

We study efficient distributed algorithms for the fundamental problem of principal component analysis and leading eigenvector computation on the sphere, when the data are randomly distributed among a set of computational nodes. We propose a…

The Gyrokinetic Toroidal Code at Princeton (GTC-P) is a highly scalable and portable particle-in-cell (PIC) code. It solves the 5D Vlasov-Poisson equation featuring efficient utilization of modern parallel computer architectures at the…

Due to the rapid growth of smart agents such as weakly connected computational nodes and sensors, developing decentralized algorithms that can perform computations on local agents becomes a major research direction. This paper considers the…

We present SuperSCS: a fast and accurate method for solving large-scale convex conic problems. SuperSCS combines the SuperMann algorithmic framework with the Douglas-Rachford splitting which is applied on the homogeneous self-dual embedding…

Alternating least squares is the most widely used algorithm for CP tensor decomposition. However, alternating least squares may exhibit slow or no convergence, especially when high accuracy is required. An alternative approach is to regard…

GPUs are the heart of the latest generations of supercomputers. We efficiently accelerate a compressible multiphase flow solver via OpenACC on NVIDIA and AMD Instinct GPUs. Optimization is accomplished by specifying the directive clauses…

The fast marching method is a widely used numerical method for solving the Eikonal equation arising from a variety of scientific and engineering fields. It is long deemed inherently sequential and an efficient parallel algorithm applicable…

We introduce squared neural Poisson point processes (SNEPPPs) by parameterising the intensity function by the squared norm of a two layer neural network. When the hidden layer is fixed and the second layer has a single neuron, our approach…