Related papers: A simple GPU implementation of spectral-element me…
We propose a novel efficient algorithm to solve Poisson equation in irregular two dimensional domains for electrostatics. It can handle Dirichlet, Neumann or mixed boundary problems in which the filling media can be homogeneous or…
Solving partial differential equations (PDEs) on shapes underpins many shape analysis and engineering tasks; yet, prevailing PDE solvers operate on polygonal/triangle meshes while modern 3D assets increasingly live as neural…
Elliptic Partial Differential Equations (PDEs) play a central role in computing the equilibrium conditions of physical problems (heat, gravitation, electrostatics, etc.). Efficient solutions to elliptic PDEs are also relevant to computer…
We extend the tensor-product direct solver from the Laplacian to the Schr\"odinger operator $-\Delta + V$. When the potential $V_1$ is separable, the operator $-\Delta + V_1$ is inverted or exponentiated at cost $O(N^{1+1/d})$ in $d$…
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…
We present a simple and efficient MATLAB implementation of the linear virtual element method for the three dimensional Poisson equation. The purpose of this software is primarily educational, to demonstrate how the key components of the…
This work presents a GPU thread mapping approach that allows doing fast parallel stencil-like computations on discrete fractals using their compact representation. The intuition behind is to employ two GPU tensor-core accelerated thread…
A spectral method for solving linear partial differential equations (PDEs) with variable coefficients and general boundary conditions defined on rectangular domains is described, based on separable representations of partial differential…
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…
This paper presents a Graphics Processing Units (GPUs) acceleration method of an iterative scheme for gas-kinetic model equations. Unlike the previous GPU parallelization of explicit kinetic schemes, this work features a fast converging…
This work concerns the numerical simulation of the Vlasov-Poisson set of equations using semi- Lagrangian methods on Graphical Processing Units (GPU). To accomplish this goal, modifications to traditional methods had to be implemented.…
Simulations of physical phenomena are essential to the expedient design of precision components in aerospace and other high-tech industries. These phenomena are often described by mathematical models involving partial differential equations…
Fast 4$\pi$ solid angle particle track recognition has been a challenge in particle physics for a long time, especially in using nuclear emulsion detectors. The recent advances in computing technology opened the way for its realization. A…
The discontinuous Galerkin (DG) finite element method is conservative, lends itself well to parallelization, and is high-order accurate due to its close affinity with the theory of quadrature and orthogonal polynomials. When applied with an…
Nowadays, several industrial applications are being ported to parallel architectures. In fact, these platforms allow acquire more performance for system modelling and simulation. In the electric machines area, there are many problems which…
We present a spectral element model for general-purpose simulation of non-overturning nonlinear water waves using the incompressible Navier-Stokes equations (INSE) with a free surface. The numerical implementation of the spectral element…
In this paper we present a methodology for data accesses when solving batches of Tridiagonal and Pentadiagonal matrices that all share the same left-hand-side (LHS) matrix. The intended application is to the numerical solution of Partial…
We present a time-explicit discontinuous Galerkin (DG) solver for the time-domain acoustic wave equation on hybrid meshes containing vertex-mapped hexahedral, wedge, pyramidal and tetrahedral elements. Discretely energy-stable formulations…
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…
This paper presents a grid-free simulation algorithm for the fully three-dimensional Vlasov--Poisson system for collisionless electron plasmas. We employ a standard particle method for the numerical approximation of the distribution…