Related papers: A GPU accelerated and error-controlled solver for …

Evaluating the Torontonian function is a central computational challenge in the simulation of Gaussian Boson Sampling (GBS) with threshold detection. In this work, we propose a recursive algorithm providing a polynomial speedup in the exact…

We present a highly general implementation of fast multipole methods on graphics processing units (GPUs). Our two-dimensional double precision code features an asymmetric type of adaptive space discretization leading to a particularly…

We present an efficient and accurate algorithm for solving the Poisson equation in spherical polar coordinates with a logarithmic radial grid and open boundary conditions. The method employs a divide-and-conquer strategy, decomposing the…

We have developed an adaptive multigrid code for solving the Poisson equation in gravitational simulations. Finer rectangular subgrids are adaptively created in locations where the density exceeds a local level-dependent threshold. We…

Discontinuous Galerkin (DG) methods for the numerical solution of partial differential equations have enjoyed considerable success because they are both flexible and robust: They allow arbitrary unstructured geometries and easy control of…

In this paper, we propose and analyze a high-order finite volume method for the Poisson problem based on the reduced discontinuous Galerkin (RDG) space. The main idea is to employ the RDG space as the trial space and the piecewise constant…

3D Gaussian Splatting (3DGS) achieves impressive rendering fidelity and speed for novel view synthesis. However, its substantial data size poses a significant challenge for practical applications. While many compression techniques have been…

The stability of a differentially rotating fluid subject to its own gravity is a problem with applications across wide areas of astrophysics--from protoplanetary discs (PPDs) to entire galaxies. The shearing box formalism offers a…

This paper presents a spectral element finite element scheme that efficiently solves elliptic problems on unstructured hexahedral meshes. The discrete equations are solved using a matrix-free preconditioned conjugate gradient algorithm. An…

We present a multi-block finite-difference solver for massively parallel Direct Numerical Simulations (DNS) of incompressible flows. The algorithm combines the versatility of a multi-block solver with the method of eigenfunctions…

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…

This paper presents a numerical method for variable coefficient elliptic PDEs with mostly smooth solutions on two dimensional domains. The PDE is discretized via a multi-domain spectral collocation method of high local order (order 30 and…

We present a simple and effective multigrid-based Poisson solver of second-order accuracy in both gravitational potential and forces in terms of the one, two and infinity norms. The method is especially suitable for numerical simulations…

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 propose a GPU-accelerated distributed optimization algorithm for controlling multi-phase optimal power flow in active distribution systems with dynamically changing topologies. To handle varying network configurations and enable…

As a first approximation beyond linearity, the nonlinear Schr\"odinger equation (NLSE) reliably describes a broad class of physical systems. Though numerical solutions of this model are well-established, these methods can be computationally…

We describe our contribution as industrial stakeholders to the existing open-source GPU4PySCF project (https: //github.com/pyscf/gpu4pyscf), a GPU-accelerated Python quantum chemistry package. We have integrated GPU acceleration into other…

[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…

Obtaining a thermodynamically accurate phase diagram through numerical calculations is a computationally expensive problem that is crucially important to understanding the complex phenomena of solid state physics, such as superconductivity.…

We present a set of rules to guide the design of GPU algorithms. These rules are grounded on the principle of reducing waste in GPU utility to achieve good speed up. In accordance to these rules, we propose GPU algorithms for 2D…