76 citations · 276 across the 15 of their papers we have counts for
9 papers · 1 filter
Entropy Stable Discontinuous Galerkin Methods for Balance Laws in Non-Conservative Form: Applications to the Euler Equations with Gravity
Maciej Waruszewski, Jeremy E. Kozdon, Lucas C. Wilcox +2
In this work a non-conservative balance law formulation is considered that encompasses the rotating, compressible Euler equations for dry atmospheric flows. We develop a semi-discr…
Hybridized Summation-By-Parts Finite Difference Methods
Jeremy E. Kozdon, Brittany A. Erickson, Lucas C. Wilcox
We present a hybridization technique for summation-by-parts finite difference methods with weak enforcement of interface and boundary conditions for second order, linear elliptic p…
Discretely entropy stable weight-adjusted discontinuous Galerkin methods on curvilinear meshes
Jesse Chan, Lucas C. Wilcox
We construct entropy conservative and entropy stable high order accurate discontinuous Galerkin (DG) discretizations for time-dependent nonlinear hyperbolic conservation laws on cu…
Robust Approaches to Handling Complex Geometries with Galerkin Difference Methods
Jeremy E. Kozdon, Lucas C. Wilcox, Thomas Hagstrom +1
The Galerkin difference (GD) basis is a set of continuous, piecewise polynomials defined using a finite difference like grid of degrees of freedom. The one dimensional GD basis fun…
An Energy Stable Approach for Discretizing Hyperbolic Equations with Nonconforming Discontinuous Galerkin Methods
Jeremy E. Kozdon, Lucas C. Wilcox
When nonconforming discontinuous Galerkin methods are implemented for hyperbolic equations using quadrature, exponential energy growth can result even when the underlying scheme wi…
Acceleration of the Implicit-Explicit Non-hydrostatic Unified Model of the Atmosphere (NUMA) on Manycore Processors
Daniel S. Abdi, Francis X. Giraldo, Emil M. Constantinescu +3
We present the acceleration of an IMplicit-EXplicit (IMEX) non-hydrostatic atmospheric model on manycore processors such as GPUs and Intel's MIC architecture. IMEX time integration…
Solving 1D Conservation Laws Using Pontryagin's Minimum Principle
Wei Kang, Lucas C. Wilcox
This paper discusses a connection between scalar convex conservation laws and Pontryagin's minimum principle. For flux functions for which an associated optimal control problem can…
Stable Coupling of Nonconforming, High-Order Finite Difference Methods
Jeremy E. Kozdon, Lucas C. Wilcox
A methodology for handling block-to-block coupling of nonconforming, multiblock summation-by-parts finite difference methods is proposed. The coupling is based on the construction…
Discretely exact derivatives for hyperbolic PDE-constrained optimization problems discretized by the discontinuous Galerkin method
Lucas C. Wilcox, Georg Stadler, Tan Bui-Thanh +1
This paper discusses the computation of derivatives for optimization problems governed by linear hyperbolic systems of partial differential equations (PDEs) that are discretized by…