In this paper we present a unified framework for constructing spectrally equivalent low-order-
refined discretizations for the high-order finite element de Rham complex. This theory covers …

This contribution presents data-locality optimizations of the additive Schwarz method (ASM)
based on the fast-diagonalization method defined on overlapping cell-centric and vertex-star …

The Riesz maps of the de Rham complex frequently arise as subproblems in the
construction of fast preconditioners for more complicated problems. In this work, we present …

We present a novel, highly scalable and optimized solver for turbulent flows based on high-
order discontinuous Galerkin discretizations of the incompressible Navier-Stokes equations …

The Poisson pressure solve resulting from the spectral element discretization of the
incompressible Navier-Stokes equation requires fast, robust, and scalable preconditioning …

The solution to the Poisson equation arising from the spectral element discretization of the
incompressible Navier-Stokes equation requires robust preconditioning strategies. One …

In this article, we present algorithms and implementations for the end-to-end GPU
acceleration of matrix-free low-order-refined preconditioning of high-order finite element …

In this paper we present a new GPU-oriented mesh optimization method based on high-
order finite elements. Our approach relies on node movement with fixed topology, through …

This work describes the development of matrix-free GPU-accelerated solvers for high-order
finite element problems in. The solvers are applicable to grad-div and Darcy problems in …

The solution to the Poisson equation arising from the spectral element discretization of the
incompressible Navier-Stokes equation requires robust preconditioning strategies. Two …