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An Energy Stable High-Order Cut Cell Discontinuous Galerkin Method with State Redistribution for Wave Propagation
Christina G. Taylor, Lucas C. Wilcox, Jesse Chan
Cut meshes are a type of mesh that is formed by allowing embedded boundaries to "cut" a simple underlying mesh resulting in a hybrid mesh of cut and standard elements. While cut me…
Entropy stable discontinuous Galerkin methods for the shallow water equations with subcell positivity preservation
Xinhui Wu, Nathaniel Trask, Jesse Chan
High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features, and have traditionally required additional filtering, limi…
GPU Acceleration of Hermite Methods for the Simulation of Wave Propagation
Arturo Vargas, Jesse Chan, Thomas Hagstrom +1
The Hermite methods of Goodrich, Hagstrom, and Lorenz (2006) use Hermite interpolation to construct high order numerical methods for hyperbolic initial value problems. The structur…
A Geometric Multigrid Preconditioning Strategy for DPG System Matrices
Nathan V. Roberts, Jesse Chan
The discontinuous Petrov-Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan [15,17] guarantees the optimality of the solution in an energy norm, and provides several featur…