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In this work we investigate the parallel scalability of the numerical method developed in Guthrey and Rossmanith [The regionally implicit discontinuous Galerkin method: Improving the stability of DG-FEM, SIAM J. Numer. Anal. (2019)]. We…
A major bottleneck in scenario-based Sample Average Approximation (SAA) for stochastic programming (SP) is the cost of solving an exact second-stage problem for every scenario, especially when each scenario contains an NP-hard combinatorial…
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…
The discontinuous Galerkin (DG) method is widely being used to solve hyperbolic partial differential equations (PDEs) due to its ability to provide high-order accurate solutions in complex geometries, capture discontinuities, and exhibit…
This paper introduces a fast Central Processing Unit (CPU) implementation of geodesic morphological operations using stream processing. In contrast to the current state-of-the-art, that focuses on achieving insensitivity to the filter sizes…
The present research builds on a recently proposed spatial prediction method for discretized two-dimensional data, based on a suitably modified planar rotator (MPR) spin model from statistical physics. This approach maps the measured data…
We propose a high order discontinuous Galerkin (DG) method for solving nonlinear Fokker-Planck equations with a gradient flow structure. For some of these models it is known that the transient solutions converge to steady-states when time…
In numerical simulations of complex fluid dynamical problems, unphysical negative density or pressure may appear, causing blow-up of the computation. With the aim of obtaining positivity-preserving solutions with multi-scale resolution for…
This paper is concerned with developing accurate and efficient numerical methods for one-dimensional fully nonlinear second order elliptic and parabolic partial differential equations (PDEs). In the paper we present a general framework for…
Online adaptive radiation therapy (ART) promises the ability to deliver an optimal treatment in response to daily patient anatomic variation. A major technical barrier for the clinical implementation of online ART is the requirement of…
The Neural GPU is a recent model that can learn algorithms such as multi-digit binary addition and binary multiplication in a way that generalizes to inputs of arbitrary length. We show that there are two simple ways of improving the…
Three-dimensional neutron transport calculations using the Method of Characteristics (MOC) are highly regarded for their exceptional computational efficiency, precision, and stability. Nevertheless, when dealing with extensive-scale…
Image segmentation plays an important role in computer vision, object detection, traffic control, and video surveillance. Typically, it is a critical step in the 3D reconstruction of a specific organ in medical image processing which…
Graphics Processing Units (GPUs) are employed for a numerical determination of the analytic structure of two-point correlation functions of Quantum Field Theories. These functions are represented through integrals in d-dimensional Euclidean…
GPU has a significantly higher performance in single-precision computing than that of double precision. Hence, it is important to take a maximal advantage of the single precision in the CG inverter, using the mixed precision method. We have…
Stochastic simulation techniques employed for the analysis of portfolios of insurance/reinsurance risk, often referred to as `Aggregate Risk Analysis', can benefit from exploiting state-of-the-art high-performance computing platforms. In…
Model selection in Gaussian processes scales prohibitively with the size of the training dataset, both in time and memory. While many approximations exist, all incur inevitable approximation error. Recent work accounts for this error in the…
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…
We describe the use of Graphics Processing Units (GPUs) for speeding up the code NBODY6 which is widely used for direct $N$-body simulations. Over the years, the $N^2$ nature of the direct force calculation has proved a barrier for…
This paper describes the main features of a pioneering unsteady solver for simulating ideal two-fluid plasmas on unstructured grids, taking profit of GPGPU (General-purpose computing on graphics processing units). The code, which has been…