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The Preconditioned Conjugate Gradient method is often employed for the solution of linear systems of equations arising in numerical simulations of physical phenomena. While being widely used, the solver is also known for its lack of…
In the next decade, the demands for computing in large scientific experiments are expected to grow tremendously. During the same time period, CPU performance increases will be limited. At the CERN Large Hadron Collider (LHC), these two…
General-relativistic magnetohydrodynamic (GRMHD) simulations have revolutionized our understanding of black hole accretion. Here, we present a graphics processing unit (GPU) accelerated GRMHD code \hammer{} with multi-faceted optimizations…
In the context of cryptanalysis, computing discrete logarithms in large cyclic groups using index-calculus-based methods, such as the number field sieve or the function field sieve, requires solving large sparse systems of linear equations…
Graphics Processing Units (GPUs) are high performance co-processors originally intended to improve the use and quality of computer graphics applications. Once, researchers and practitioners noticed the potential of using GPU for general…
A finite-difference Micromagnetic simulation code written in MATLAB is presented with Graphics Processing Unit (GPU) acceleration. The high performance of Graphics Processing Unit (GPU) is demonstrated compared to a typical Central…
In order to compensate for the higher cost of double double and quad double arithmetic when solving large polynomial systems, we investigate the application of NVIDIA Tesla K20C general purpose graphics processing unit. The focus on this…
The Hermite methods of Goodrich, Hagstrom, and Lorenz (2006) use Hermite interpolation to construct high order numerical methods for hyperbolic initial value problems. The structure of the method has several favorable features for parallel…
The convex hull is a fundamental geometrical structure for many applications where groups of points must be enclosed or represented by a convex polygon. Although efficient sequential convex hull algorithms exist, and are constantly being…
Immersed boundary methods (IBMs) facilitate the simulation of flows around stationary, moving, and deforming bodies on Cartesian grids. However, extending these simulations to the large grid sizes required for realistic flow problems…
Monte Carlo (MC) simulation is commonly considered to be the most accurate dose calculation method in radiotherapy. However, its efficiency still requires improvement for many routine clinical applications. In this paper, we present our…
Graphics Processing Units (GPUs) with high computational capabilities used as modern parallel platforms to deal with complex computational problems. We use this platform to solve large-scale linear programing problems by revised simplex…
Solving quantifier-free non-linear real arithmetic (NRA) problems is a computationally hard task. To tackle this problem, prior work proposed a promising approach based on gradient descent. In this work, we extend their ideas and combine…
Currently, deep neural networks (DNNs)-based models have drawn enormous attention and have been utilized to different domains widely. However, due to the data-driven nature, the DNN models may generate unsatisfying performance on the small…
Recent research has focused on developing GPU-accelerated first-order solvers for linear programming (LP). This line of work, however, has largely overlooked the role of presolving, and thus prior results do not fully reflect the speedups…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…
Systems of polynomial equations arise frequently in computer vision, especially in multiview geometry problems. Traditional methods for solving these systems typically aim to eliminate variables to reach a univariate polynomial, e.g., a…
We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the…
Computational tools for rigorously verifying the performance of large-scale machine learning (ML) models have progressed significantly in recent years. The most successful solvers employ highly specialized, GPU-accelerated branch and bound…
We present a new implementation of the SFUMATO code, called SFUMATO#, for solving self-gravitational radiation hydrodynamics problems using adaptive mesh refinement (AMR) with the CUDA/HIP programming frameworks. The code incorporates a…