66 citations · 70 across the 3 of their papers we have counts for
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A short note on the accuracy of the discontinuous Galerkin method with reentrant faces
Will Pazner, Terry Haut
We study the convergence of the discontinuous Galerkin (DG) method applied to the advection-reaction equation on meshes with reentrant faces. On such meshes, the upwind numerical f…
Fast solution of fully implicit Runge-Kutta and discontinuous Galerkin in time for numerical PDEs, Part II: nonlinearities and DAEs
Ben S. Southworth, Oliver Krzysik, Will Pazner
Fully implicit Runge-Kutta (IRK) methods have many desirable accuracy and stability properties as time integration schemes, but high-order IRK methods are not commonly used in prac…
Fast solution of fully implicit Runge-Kutta and discontinuous Galerkin in time for numerical PDEs, Part I: the linear setting
Ben S. Southworth, Oliver Krzysik, Will Pazner +1
Fully implicit Runge-Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but high-order IRK methods are not commonly…
High-order matrix-free incompressible flow solvers with GPU acceleration and low-order refined preconditioners
Michael Franco, Jean-Sylvain Camier, Julian Andrej +1
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 polynomi…
High-order partitioned spectral deferred correction solvers for multiphysics problems
Daniel Z. Huang, Will Pazner, Per-Olof Persson +1
We present an arbitrarily high-order, conditionally stable, partitioned spectral deferred correction (SDC) method for solving multiphysics problems using a sequence of pre-existing…
Efficient low-order refined preconditioners for high-order matrix-free continuous and discontinuous Galerkin methods
Will Pazner
In this paper, we design preconditioners for the matrix-free solution of high-order continuous and discontinuous Galerkin discretizations of elliptic problems based on FEM-SEM equi…