20 citations · 28 across the 4 of their papers we have counts for
7 papers · 1 filter
Discrete Elasticity Exact Sequences on Worsey-Farin Splits
Sining Gong, Jay Gopalakrishnan, Johnny Guzmán +1
We construct conforming finite element elasticity complexes on Worsey-Farin splits in three dimensions. Spaces for displacement, strain, stress, and the load are connected in the e…
Analysis of curvature approximations via covariant curl and incompatibility for Regge metrics
Jay Gopalakrishnan, Michael Neunteufel, Joachim Schöberl +1
The metric tensor of a Riemannian manifold can be approximated using Regge finite elements and such approximations can be used to compute approximations to the Gauss curvature and…
Stability of structure-aware Taylor methods for tents
Jay Gopalakrishnan, Zheng Sun
Structure-aware Taylor (SAT) methods are a class of timestepping schemes designed for propagating linear hyperbolic solutions within a tent-shaped spacetime region. Tents are usefu…
A discrete elasticity complex on three-dimensional Alfeld splits
Snorre H. Christiansen, Jay Gopalakrishnan, Johnny Guzmán +1
We construct conforming finite element elasticity complexes on the Alfeld splits of tetrahedra. The complex consists of vector fields and symmetric tensor fields, interlinked via t…
Structure aware Runge-Kutta time stepping for spacetime tents
Jay Gopalakrishnan, Joachim Schöberl, Christoph Wintersteiger
We introduce a new class of Runge-Kutta type methods suitable for time stepping to propagate hyperbolic solutions within tent-shaped spacetime regions. Unlike standard Runge-Kutta…
Spectral discretization errors in filtered subspace iteration
Jay Gopalakrishnan, Luka Grubišić, Jeffrey Ovall
We consider filtered subspace iteration for approximating a cluster of eigenvalues (and its associated eigenspace) of a (possibly unbounded) selfadjoint operator in a Hilbert space…
Five lectures on DPG methods
Jay Gopalakrishnan
This is a set of lecture notes introducing graduate students to the topic of Discontinuous Petrov-Galerkin (DPG) methods.