Related papers: PittPack: An Open-Source Poisson's Equation Solver…
We propose a spectral solver for the Poisson equation on a square domain, achieving optimal complexity through the ultraspherical spectral method and the alternating direction implicit (ADI) method. Compared with the state-of-the-art…
In this paper, a parallel overlapping domain decomposition preconditioner is proposed to solve the linear system of equations arising from the extended finite element discretization of elastic crack problems. The algorithm partitions the…
We demonstrate that scalable neuromorphic hardware can implement the finite element method, which is a critical numerical method for engineering and scientific discovery. Our approach maps the sparse interactions between neighboring finite…
Upcoming many core processors are expected to employ a distributed memory architecture similar to currently available supercomputers, but parallel pattern mining algorithms amenable to the architecture are not comprehensively studied. We…
In this work, we investigated the feasibility of applying deep learning techniques to solve Poisson's equation. A deep convolutional neural network is set up to predict the distribution of electric potential in 2D or 3D cases. With proper…
We design a variational quantum algorithm to solve multi-dimensional Poisson equations with mixed boundary conditions that are typically required in various fields of computational science. Employing an objective function that is formulated…
The expedient design of precision components in aerospace and other high-tech industries requires simulations of physical phenomena often described by partial differential equations (PDEs) without exact solutions. Modern design problems…
We study the scalability of consensus-based distributed optimization algorithms by considering two questions: How many processors should we use for a given problem, and how often should they communicate when communication is not free?…
Algorithms for computing All-Pairs Shortest-Paths (APSP) are critical building blocks underlying many practical applications. The standard sequential algorithms, such as Floyd-Warshall and Johnson, quickly become infeasible for large input…
Computer-aided engineering techniques are indispensable in modern engineering developments. In particular, partial differential equations are commonly used to simulate the dynamics of physical phenomena, but very large systems are often…
This paper presents a multiscale approach to efficiently compute approximate optimal transport plans between point sets. It is particularly well-suited for point sets that are in high-dimensions, but are close to being intrinsically…
With the development of machine learning and Big Data, the concepts of linear and non-linear optimization techniques are becoming increasingly valuable for many quantitative disciplines. Problems of that nature are typically solved using…
PDE-constrained inverse problems are some of the most challenging and computationally demanding problems in computational science today. Fine meshes that are required to accurately compute the PDE solution introduce an enormous number of…
Efficiently solving Poisson equations on complex, irregular domains remains a fundamental challenge in scientific computing, as classical iterative solvers often suffer from prohibitive runtime due to ill-conditioned systems. While neural…
We introduce a numerical strategy to efficiently solve the out-of-equilibrium Dyson equation in the transient regime. By discretizing the equation into a compact matrix form and applying state-of-the-art matrix compression techniques, we…
We introduce the Poisson tensor completion (PTC) estimator that exploits inter-sample relationships to compute a low-rank Poisson tensor decomposition of the frequency histogram for samples of a multivariate distribution. Our crucial…
We present a new method for real-time non-rigid dense correspondence between point clouds based on structured shape construction. Our method, termed Deep Point Correspondence (DPC), requires a fraction of the training data compared to…
We present hipBone, an open source performance-portable proxy application for the Nek5000 (and NekRS) CFD applications. HipBone is a fully GPU-accelerated C++ implementation of the original NekBone CPU proxy application with several novel…
Scanning devices often produce point clouds exhibiting highly uneven distributions of point samples across the surfaces being captured. Different point cloud subsampling techniques have been proposed to generate more evenly distributed…
Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in…