Related papers: A Customized 3D GPU Poisson Solver for Free Bounda…
We develop a matrix-free Full Approximation Storage (FAS) multigrid solver based on staggered finite differences and implemented on GPU in MATLAB. To enhance performance, intermediate variables are reused, and an X-shape Multi-Color…
We present the numerical methods, programming methodology, verification, and performance assessment of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit…
The Poisson equation occurs in many areas of science and engineering. Here we focus on its numerical solution for an equation in d dimensions. In particular we present a quantum algorithm and a scalable quantum circuit design which…
Hybrid computational architectures based on the joint power of Central Processing Units and Graphic Processing Units (GPUs) are becoming popular and powerful hardware tools for a wide range of simulations in biology, chemistry, engineering,…
This work deals with the CPU-GPU heterogeneous code acceleration of a finite-volume CFD solver utilizing multiple CPUs and GPUs at the same time. First, a high-level description of the CFD solver called SENSEI, the discretization of SENSEI,…
We describe the GPU implementation of shifted or multimass iterative solvers for sparse linear systems of the sort encountered in lattice gauge theory. We provide a generic tool that can be used by those without GPU programming experience…
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…
Many problems in geophysical and atmospheric modelling require the fast solution of elliptic partial differential equations (PDEs) in "flat" three dimensional geometries. In particular, an anisotropic elliptic PDE for the pressure…
Gaussian processes (GPs) provide a powerful framework for extrapolation, interpolation, and noise removal in regression and classification. This paper considers constraining GPs to arbitrarily-shaped domains with boundary conditions. We…
This work presents a multigrid preconditioned high order immersed finite difference solver to accurately and efficiently solve the Poisson equation on complex 2D and 3D domains. The solver employs a low order Shortley-Weller multigrid…
In this paper, we present a parallel higher-order boundary integral method to solve the linear Poisson-Boltzmann (PB) equation. In our method, a well-posed boundary integral formulation is used to ensure the fast convergence of Krylov…
CFD is a ubiquitous technique central to much of computational simulation such as that required by aircraft design. Solving of the Poisson equation occurs frequently in CFD and there are a number of possible approaches one may leverage. The…
In recent years, GPU-accelerated optimization solvers based on second-order methods (e.g., interior-point methods) have gained momentum with the advent of mature and efficient GPU-accelerated direct sparse linear solvers, such as cuDSS.…
Adaptive finite elements combined with geometric multigrid solvers are one of the most efficient numerical methods for problems such as the instationary Navier-Stokes equations. Yet despite their efficiency, computations remain expensive…
We present the GPU implementation of the general-purpose interior-point solver Clarabel for convex optimization problems with conic constraints. We introduce a mixed parallel computing strategy that processes linear constraints first, then…
These notes accompany the open-source code published in GitHub which implements a GPU-based line-segment, surface-triangle intersection algorithm in CUDA. It mentions some relevant works and discusses issues specific to this implementation.…
We study exact sparse linear regression with an $\ell_0-\ell_2$ penalty and develop a branch-and-bound (BnB) algorithm explicitly designed for GPU execution. Starting from a perspective reformulation, we derive an interval relaxation that…
This paper presents the RBG-Maxwell framework, a relativistic collisional plasma simulator on GPUs. We provide detailed discussions on the fundamental equations, numerical algorithms, implementation specifics, and key testing outcomes. The…
The multiresolution Gaussian process (GP) has gained increasing attention as a viable approach towards improving the quality of approximations in GPs that scale well to large-scale data. Most of the current constructions assume full…
The solution of linear systems of equations is a central task in a number of scientific and engineering applications. In many cases the solution of linear systems may take most of the simulation time thus representing a major bottleneck in…