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Molecular dynamics models materials by simulating each individual particle's trajectory. Many-body potentials lead to a more accurate trajectory simulation, and are used in materials science and computational chemistry. We present…
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…
Modern GPGPUs provide massive arithmetic throughput, yet many scientific kernels remain limited by memory bandwidth. In particular, repeatedly loading precomputed auxiliary data wastes abundant compute resources while stressing the memory…
The aim of this paper is to apply a high-order discontinuous-in-time scheme to second-order hyperbolic partial differential equations (PDEs). We first discretize the PDEs in time while keeping the spatial differential operators…
Efficient and suitably preconditioned iterative solvers for elliptic partial differential equations (PDEs) of the convection-diffusion type are used in all fields of science and engineering. To achieve optimal performance, solvers have to…
The Simplex tableau has been broadly used and investigated in the industry and academia. With the advent of the big data era, ever larger problems are posed to be solved in ever larger machines whose architecture type did not exist in the…
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…
The present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems. Fast matrix-free operator evaluation on tensor product elements is used to devise a computationally efficient PDE…
The flux vector splitting (FVS) method has firstly been incorporated into the discontinuous Galerkin (DG) framework for reconstructing the numerical fluxes required for the spatial semi-discrete formulation, setting it apart from the…
Stencil computation is one of the most important kernels in various scientific and engineering applications. A variety of work has focused on vectorization and tiling techniques, aiming at exploiting the in-core data parallelism and data…
This paper proposes a matrix-free residual evaluation technique for the hybridizable discontinuous Galerkin method requiring a number of operations scaling only linearly with the number of degrees of freedom. The method results from…
Particle track reconstruction is an important problem in high-energy physics (HEP), necessary to study properties of subatomic particles. Traditional track reconstruction algorithms scale poorly with the number of particles within the…
We present scalable iterative solvers and preconditioning strategies for Hybridizable Discontinuous Galerkin (HDG) discretizations of partial differential equations (PDEs) on graphics processing units (GPUs). The HDG method is implemented…
Modern HPC systems are increasingly relying on greater core counts and wider vector registers. Thus, applications need to be adapted to fully utilize these hardware capabilities. One class of applications that can benefit from this increase…
The third paper in our series on open source MATLAB / GNU Octave implementation of the discontinuous Galerkin (DG) method(s) focuses on a hybridized formulation. The main aim of this ongoing work is to develop rapid prototyping techniques…
Signature kernels have emerged as a powerful tool within kernel methods for sequential data. In the paper "The Signature Kernel is the solution of a Goursat PDE", the authors identify a kernel trick that demonstrates that, for continuously…
Linearized shallow neural networks that are constructed by fixing the hidden-layer parameters have recently shown strong performance in solving partial differential equations (PDEs). Such models, widely used in the random feature method…
Petrov-Galerkin formulations with optimal test functions allow for the stabilization of finite element simulations. In particular, given a discrete trial space, the optimal test space induces a numerical scheme delivering the best…
The modern CPU's design, which is composed of hierarchical memory and SIMD/vectorization capability, governs the potential for algorithms to be transformed into efficient implementations. The release of the AVX-512 changed things radically,…
Vectorization and GPUs will profoundly change graph processing. Traditional graph algorithms tuned for 32- or 64-bit based memory accesses will be inefficient on architectures with 512-bit wide (or larger) instruction units that are already…