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

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 …

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 …

Blade-resolved numerical simulations of wind energy applications using full blade and tower
models are presented. The computational methodology combines solution technologies in a …

Soft materials such as rubber, elastomers, and soft biological tissues mechanically deform at
large strain isochorically for all time, or during their initial transient (when a pore fluid …

We provide a new approach for the efficient matrix-free application of the transpose of the
Jacobian for the spectral element method for the adjoint-based solution of partial differential …

We examine a residual and matrix-free Jacobian formulation of compressible and nearly
incompressible (ν→ 0.5) displacement-only linear isotropic elasticity with high-order …

In this thesis, we develop and study efficient solvers for high-order Galerkin methods applied
to fluid flow problems. Many flow problems necessitate implicit time-integration schemes in …