Related papers: A simple GPU implementation of spectral-element me…
This work presents a GPU-accelerated solver for the unit commitment (UC) problem in large-scale power grids. The solver uses the Primal-Dual Hybrid Gradient (PDHG) algorithm to efficiently solve the relaxed linear subproblem, achieving…
Current trends in the computer graphics community propose leveraging the massive parallel computational power of GPUs to accelerate physically based simulations. Collision detection and solving is a fundamental part of this process. It is…
We develop an algorithm to solve tridiagonal systems of linear equations, which appear in implicit finite-difference schemes of partial differential equations (PDEs), being the time-dependent Schr\"{o}dinger equation (TDSE) an ideal…
Block-tridiagonal systems are prevalent in state estimation and optimal control, and solving these systems is often the computational bottleneck. Improving the underlying solvers therefore has a direct impact on the real-time performance of…
We present Neural Spectral Methods, a technique to solve parametric Partial Differential Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal bases to learn PDE solutions as mappings between spectral…
This paper introduces a second-order method for solving general elliptic partial differential equations (PDEs) on irregular domains using GPU acceleration, based on Ying's kernel-free boundary integral (KFBI) method. The method addresses…
Optimization plays a central role in modern radiation therapy, where it is used to determine optimal treatment machine parameters in order to deliver precise doses adapted to each patient case. In general, solving the optimization problems…
When the molecules of a gaseous system are far apart, say in microscale gas flows where the surface to volume ratio is high and hence the surface forces dominant, the molecule-surface interactions lead to the formation of a local…
An application based on graphical processing units (GPUs) applied to 3-D digital images is described for computing the linear anisotropic elastic properties of heterogeneous materials. The application can also retrieve the property…
We introduce a fusion of GPU accelerated primal heuristics for Mixed Integer Programming. Leveraging GPU acceleration enables exploration of larger search regions and faster iterations. A GPU-accelerated PDLP serves as an approximate LP…
Matrix decompositions are ubiquitous in machine learning, including applications in dimensionality reduction, data compression and deep learning algorithms. Typical solutions for matrix decompositions have polynomial complexity which…
This report presents a comprehensive analysis of the performance of GPU accelerated meshfree CFD solvers for two-dimensional compressible flows in Fortran, C++, Python, and Julia. The programming model CUDA is used to develop the GPU codes.…
We present a method that gives highly accurate electrostatic potentials for systems where we have periodic boundary conditions in two spatial directions but free boundary conditions in the third direction. These boundary conditions are…
A numerical scheme is presented for approximating fractional order Poisson problems in two and three dimensions. The scheme is based on reformulating the original problem posed over $\Omega$ on the extruded domain…
We evaluate the computational performance of the Bernstein-Bezier basis for discontinuous Galerkin (DG) discretizations and show how to exploit properties of derivative and lift operators specific to Bernstein polynomials for an optimal…
The Poisson-Nernst-Planck (PNP) equations are one of the most effective model for describing electrostatic interactions and diffusion processes in ion solution systems, and have been widely used in the numerical simulations of biological…
In recent years, high performance scientific computing on graphics processing units (GPUs) have gained widespread acceptance. These devices are designed to offer massively parallel threads for running code with general purpose. There are…
The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far either suffer from lack of accuracy and/or are limited to very small sizes of the…
We present an efficient implementation for running three-dimensional numerical simulations of fluid-structure interaction problems on single GPUs, based on Nvidia CUDA through Numba and Python. The incompressible flow around moving bodies…
The Monte Carlo method is a powerful technique for computing thermodynamic magnetic states of otherwise unsolvable spin Hamiltonians, but the method becomes computationally prohibitive with increasing number of spins and the simulation of…