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Geometric programming (GP) provides a power tool for solving a variety of optimization problems. In the real world, many applications of geometric programming (GP) are engineering design problems in which some of the problem parameters are…
Linear solvers are key components in any software platform for scientific and engineering computing. The solution of large and sparse linear systems lies at the core of physics-driven numerical simulations relying on partial differential…
In this paper, we introduce a quasi-Newton method optimized for efficiently solving quasi-linear elliptic equations and systems, with a specific focus on GPU-based computation. By approximating the Jacobian matrix with a combination of…
The current paper reports on the implementation of a numerical solver on the Graphic Processing Units (GPU) to model reactive gas mixture with detailed chemical kinetics. The solver incorporates high-order finite volume methods for solving…
We deal with the numerical solution of the compressible Euler equations with the aid of the discontinuous Galerkin (DG) method with focus on the goal-oriented error estimates and adaptivity. We analyze the adjoint consistency of the DG…
This paper introduces open-source computational fluid dynamics software named open computational fluid dynamic code for scientific computation with graphics processing unit (GPU) system (OpenCFD-SCU), developed by the authors for direct…
The quest for quantum degenerate Fermi gases interacting through the anisotropic and long-range dipole-dipole interaction is an exciting and fast developing branch within the cold-atoms research program. Recent experimental progress in…
Machine learning solvers for partial differential equations (PDEs) have attracted growing interest. However, most existing approaches, such as neural network solvers, rely on stochastic training, which is inefficient and typically requires…
This paper introduces a framework for solving alternating current optimal power flow (ACOPF) problems using graphics processing units (GPUs). While GPUs have demonstrated remarkable performance in various computing domains, their…
We show how to accelerate the direct solution of the Boltzmann equation using Graphics Processing Units (GPUs). In order to fully exploit the computational power of the GPU, we choose a method of solution which combines a finite difference…
The problem of solving a system of polynomial equations is one of the most fundamental problems in applied mathematics. Among them, the problem of solving a system of binomial equations form a important subclass for which specialized…
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…
This work focuses on the numerical study of a recently published class of Runge-Kutta methods designed for mixed-precision arithmetic. We employ the methods in solving partial differential equations on modern hardware. In particular we…
[Abridged] We present the results of a highly parallel Kepler equation solver using the Graphics Processing Unit (GPU) on a commercial nVidia GeForce 280GTX and the "Compute Unified Device Architecture" programming environment. We apply…
We derive the time-dependent dipolar Gross-Pitaevskii (GP) equation from the N-body Schr{\"o}dinger equation. More precisely we show a norm approximation for the solution of the many body equation as well as the convergence of its one-body…
In this paper we modify a fast heuristic solver for the Linear Sum Assignment Problem (LSAP) for use on Graphical Processing Units (GPUs). The motivating scenario is an industrial application for P2P live streaming that is moderated by a…
Efficient methods for generating samples of wave packet trajectories are needed to build machine learning models for quantum dynamics. However, simulating such data by direct integration of the time-dependent Schrodinger equation can be…
This paper puts forth a coarse grid projection (CGP) multiscale method to accelerate computations of quasigeostrophic (QG) models for large scale ocean circulation. These models require solving an elliptic sub-problem at each time step,…
Geometric Semantic Genetic Programming (GSGP) is a state-of-the-art machine learning method based on evolutionary computation. GSGP performs search operations directly at the level of program semantics, which can be done more efficiently…
Gaussian processes (GP) are a popular and powerful tool for spatial modelling of data, especially data that quantify environmental processes. However, in stationary form, whether covariance is isotropic or anisotropic, GPs may lack the…