Efficient exploitation of exascale architectures requires rethinking of the numerical
algorithms used in many large-scale applications. These architectures favor algorithms that …

Low-rank Tucker and CP tensor decompositions are powerful tools in data analytics. The
widely used alternating least squares (ALS) method, which solves a sequence of over …

In this paper, we develop high-order nodal discontinuous Galerkin (DG) methods for
hyperbolic conservation laws that satisfy invariant domain preserving properties using …

The second paper of this series presents two robust entropy stable shock-capturing methods
for discontinuous Galerkin spectral element (DGSEM) discretizations of the compressible …

We present an implicit large-eddy simulation of transonic buffet over the OAT15A
supercritical airfoil at Mach number 0.73, angle of attack 3.5 deg, and Reynolds number 3× …

At high Reynolds numbers the use of explicit in time compressible flow simulations with
spectral/hp element discretization can become significantly limited by time step. To alleviate …

The present work develops hybrid multigrid methods for high-order discontinuous Galerkin
discretizations of elliptic problems, which are, for example, a key ingredient of …

In this paper, we design preconditioners for the matrix-free solution of high-order continuous
and discontinuous Galerkin discretizations of elliptic problems based on finite element …

Pavarino proved that the additive Schwarz method with vertex patches and a low-order
coarse space gives a $ p $-robust solver for symmetric and coercive problems. However, for …

We present a matrix-free flow solver for high-order finite element discretizations of the
incompressible Navier-Stokes and Stokes equations with GPU acceleration. For high …