Related papers: Semi-Lagrangian Vlasov simulation on GPUs
In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier-Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with…
Semi-Lagrangian (SL) schemes are known as a major numerical tool for solving transport equations with many advantages and have been widely deployed in the fields of computational fluid dynamics, plasma physics modeling, numerical weather…
The singular value decomposition (SVD) is a powerful tool in modern numerical linear algebra, which underpins computational methods such as principal component analysis (PCA), low-rank approximations, and randomized algorithms. Many…
This paper considers the discontinuous Galerkin (DG) methods for solving the Vlasov-Maxwell (VM) system, a fundamental model for collisionless magnetized plasma. The DG methods provide accurate numerical description with conservation and…
This work discusses the performance of a modern numerical scheme for fluid dynamical problems on modern high-performance computing architectures. Our code implements a spatial nodal discontinuous Galerkin scheme that we test up to an order…
A novel domain-decomposition least-squares Petrov-Galerkin (DD-LSPG) model-reduction method applicable to parameterized systems of nonlinear algebraic equations (e.g., arising from discretizing a parameterized partial-differential-equations…
This paper introduces cuHALLaR, a GPU-accelerated implementation of the HALLaR method proposed in Monteiro et al. 2024 for solving large-scale semidefinite programming (SDP) problems. We demonstrate how our Julia-based implementation…
A fast multigrid solver is presented for high-order accurate Stokes problems discretised by local discontinuous Galerkin (LDG) methods. The multigrid algorithm consists of a simple V-cycle, using an element-wise block Gauss-Seidel smoother.…
This paper constitutes our initial effort in developing sparse grid discontinuous Galerkin (DG) methods for high-dimensional partial differential equations (PDEs). Over the past few decades, DG methods have gained popularity in many…
The recent trend of using Graphics Processing Units (GPU's) for high performance computations is driven by the high ratio of price performance for these units, complemented by their cost effectiveness. At first glance, computational fluid…
The latest Graphics Processing Units (GPUs) are reported to reach up to 200 billion floating point operations per second (200 Gflops) and to have price performance of 0.1 cents per M flop. These facts raise great interest in the…
In this paper we propose a new spatially high order accurate semi-implicit discontinuous Galerkin (DG) method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured curved meshes. While the…
Designing efficient and scalable sparse linear algebra kernels on modern multi-GPU based HPC systems is a daunting task due to significant irregular memory references and workload imbalance across the GPUs. This is particularly the case for…
In this paper we present a new high order semi-implicit DG scheme on two-dimensional staggered triangular meshes applied to different nonlinear systems of hyperbolic conservation laws such as advection-diffusion models, incompressible…
We present the GPU calculation with the common unified device architecture (CUDA) for the Wolff single-cluster algorithm of the Ising model. Proposing an algorithm for a quasi-block synchronization, we realize the Wolff single-cluster Monte…
In many applications of practical interest, solutions of partial differential equation models arise as critical points of an underlying (energy) functional. If such solutions are saddle points, rather than being maxima or minima, then the…
A novel and scalable geometric multi-level algorithm is presented for the numerical solution of elliptic partial differential equations, specially designed to run with high occupancy of streaming processors inside Graphics Processing…
This paper develops and analyses semi-discrete numerical method for two dimensional Vlasov-Stokes' system with periodic boundary condition. The method is based on coupling of semi-discrete discontinuous Galerkin method for the Vlasov…
This paper reviews the adaptive sparse grid discontinuous Galerkin (aSG-DG) method for computing high dimensional partial differential equations (PDEs) and its software implementation. The C\texttt{++} software package called AdaM-DG,…
GPU has a significantly higher performance in single-precision computing than that of double precision. Hence, it is important to take a maximal advantage of the single precision in the CG inverter, using the mixed precision method. We have…