Related papers: A Matrix-Free Galerkin Multigrid Solver and Failur…

In axisymmetric fusion reactors, the equilibrium magnetic configuration can be expressed in terms of the solution to a semi-linear elliptic equation known as the Grad-Shafranov equation, the solution of which determines the poloidal…

In this work we investigate the parallel scalability of the numerical method developed in Guthrey and Rossmanith [The regionally implicit discontinuous Galerkin method: Improving the stability of DG-FEM, SIAM J. Numer. Anal. (2019)]. We…

Implicit methods and GPU parallelization are two distinct yet powerful strategies for accelerating high-order CFD algorithms. However, few studies have successfully integrated both approaches within high-speed flow solvers. The core…

This work presents a novel methodology for speeding up the assembly of stiffness matrices for laminate composite 3D structures in the context of isogeometric and finite element discretizations. By splitting the involved terms into their…

We present a high-order discontinuous Galerkin (DG) solver of the compressible Navier-Stokes equations for cloud formation processes. The scheme exploits an underlying parallelized implementation of the ADER-DG method with dynamic adaptive…

This paper introduces a novel staggered discontinuous Galerkin (SDG) method tailored for solving elliptic equations on polytopal meshes. Our approach utilizes a primal-dual grid framework to ensure local conservation of fluxes,…

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…

Matrix Factorization (MF) has been widely applied in machine learning and data mining. A large number of algorithms have been studied to factorize matrices. Among them, stochastic gradient descent (SGD) is a commonly used method.…

We study Hibridizable Discontinuous Galerkin (HDG) discretizations for a class of non-linear interior elliptic boundary value problems posed in curved domains where both the source term and the diffusion coefficient are non-linear. We…

Numerical climate- and weather-prediction requires the fast solution of the equations of fluid dynamics. Discontinuous Galerkin (DG) discretisations have several advantageous properties. They can be used for arbitrary domains and support a…

Waves are all around us--be it in the form of sound, electromagnetic radiation, water waves, or earthquakes. Their study is an important basic tool across engineering and science disciplines. Every wave solver serving the computational…

Machine Learning (ML) models execute several parallel computations including Generalized Matrix Multiplication, Convolution, Dropout, etc. These computations are commonly executed on Graphics Processing Units (GPUs), by dividing the…

General Matrix Multiplication (GEMM) is a crucial algorithm for various applications such as machine learning and scientific computing, and an efficient GEMM implementation is essential for the performance of these systems. While…

This study presents novel strategies for improving the node-level performance of matrix-free evaluation of continuous and discontinuous Galerkin spatial discretizations on unstructured tetrahedral grids. In our approach the underlying…

Communication-avoiding Krylov methods require solving small dense Gram systems at each outer iteration. We present a low-synchronization approach based on Forward Gauss--Seidel (FGS), which exploits the structure of Gram matrices arising…

We present an interface and an implementation of the General Matrix Multiply (GEMM) routine for multiple small matrices processed simultaneously on NVIDIA graphics processing units (GPUs). We focus on matrix sizes under 16. The…

Incorporation of plasmonic nanostructures in the design of photoconductive devices (PCDs) has significantly improved their optical-to-terahertz conversion efficiency. However, this improvement comes at the cost of increased complexity for…

Graph Neural Networks (GNNs) present a fundamental hardware challenge by fusing irregular, memory-bound graph traversals with regular, compute-intensive dense matrix operations. While frameworks such as PyTorch Geometric (PyG) and Deep…

The macro-element variant of the hybridized discontinuous Galerkin (HDG) method combines advantages of continuous and discontinuous finite element discretization. In this paper, we investigate the performance of the macro-element HDG method…

We present a GPU-accelerated version of a high-order discontinuous Galerkin discretization of the unsteady incompressible Navier-Stokes equations. The equations are discretized in time using a semi-implicit scheme with explicit treatment of…