Related papers: Matrix-Free Multigrid with Algebraically Consisten…
This work presents a novel agglomeration-based multilevel preconditioner designed to accelerate the convergence of iterative solvers for linear systems arising from the discontinuous Galerkin discretization of the monodomain model in…
We discuss the ill conditioning of the matrix for the discretised Poisson equation in the small aspect ratio limit, and motivate this problem in the context of nonhydrostatic ocean modelling. Efficient iterative solvers for the Poisson…
Finite element schemes based on discontinuous Galerkin methods possess features amenable to massively parallel computing accelerated with general purpose graphics processing units (GPUs). However, the computational performance of such…
Unstructured-mesh ocean models are increasingly used for coastal applications due to their ability to represent complex geometries and apply local grid refinement where needed. However, their broader use has been hindered by their high…
This work studies three multigrid variants for matrix-free finite-element computations on locally refined meshes: geometric local smoothing, geometric global coarsening, and polynomial global coarsening. We have integrated the algorithms…
A 3-dimensional GPU Poisson solver is developed for all possible combinations of free and periodic boundary conditions (BCs) along the three directions. It is benchmarked for various grid sizes and different BCs and a significant…
Methods for solving hyperbolic systems typically depend on unknown ordering (e.g., Gauss-Seidel, or sweep/wavefront/marching methods) to achieve good convergence. For many discretisations, mesh types or decompositions these methods do not…
In this paper, we demonstrate the efficiency of using semi-Lagrangian discontinuous Galerkin methods to solve the drift-kinetic equation using graphic processing units (GPUs). In this setting we propose a second order splitting scheme and a…
High-order Discontinuous Galerkin (DG) methods offer excellent accuracy for turbulent flow simulations, especially when implemented on GPU-oriented architectures that favor very high polynomial orders. On modern GPUs, high-order polynomial…
We generalise a hybridized discontinuous Galerkin method for incompressible flow problems to non-affine cells, showing that with a suitable element mapping the generalised method preserves a key invariance property that eludes most methods,…
We design and investigate a variety of multigrid solvers for high-order local discontinuous Galerkin methods applied to elliptic interface and multiphase Stokes problems. Using the template of a standard multigrid V-cycle, we consider 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…
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…
To numerically solve a generic elliptic equation on two-dimensional domains with rectangular Cartesian grids, we propose a cut-cell geometric multigrid method that features (1) general algorithmic steps that apply to two-dimensional…
Tokamak fusion reactors are actively studied as a means of realizing energy production from plasma fusion. However, due to the substantial cost and time required to construct fusion reactors and run physical experiments, numerical…
The torrential influx of floating-point data from domains like IoT and HPC necessitates high-performance lossless compression to mitigate storage costs while preserving absolute data fidelity. Leveraging GPU parallelism for this task…
High-dimensional transport equations frequently occur in science and engineering. Computing their numerical solution, however, is challenging due to its high dimensionality. In this work we develop an algorithm to efficiently solve the…
Adaptive mesh refinement (AMR) reduces computational costs in CFD by concentrating resolution where needed, but efficiently embedding complex, non-aligned geometries on GPUs remains challenging. We present a GPU-native algorithm for…
We present a polynomial multigrid method for the nodal interior penalty formulation of the Poisson equation on three-dimensional Cartesian grids. Its key ingredient is a weighted overlapping Schwarz smoother operating on element-centered…
We present a novel high-order accurate nodal discontinuous Galerkin (DG) method for solving nonlinear hyperbolic systems of partial differential equations (PDEs) on fully unstructured three-dimensional polyhedral meshes. A mesh generator is…