153 citations · 333 across the 25 of their papers we have counts for
28 papers
Global error estimators for parametric monotone nonlinearities and neural approximations
Pablo Cortés Castillo, Wolfgang Dahmen, Jay Gopalakrishnan
We construct computable error estimators, which double as loss functions for neural networks, for a class of parametric nonlinear partial differential equations with a monotonicity…
Fortin operators for DPG advection discretizations
Pablo Cortés Castillo, Jay Gopalakrishnan
We construct Fortin operators for discontinuous Petrov-Galerkin (DPG) discretizations of the advection equation with a piecewise constant divergence-free advection vector , on s…
Divergence-conforming velocity and vorticity approximations for incompressible fluids obtained with minimal facet coupling
Jay Gopalakrishnan, Lukas Kogler, Philip L. Lederer +1
We introduce two new lowest order methods, a mixed method, and a hybrid Discontinuous Galerkin (HDG) method, for the approximation of incompressible flows. Both methods use diverge…
Computing leaky modes of optical fibers using a FEAST algorithm for polynomial eigenproblems
Jay Gopalakrishnan, Benjamin Quanah Parker, Pieter Vandenberge
An efficient contour integral technique to approximate a cluster of nonlinear eigenvalues of a polynomial eigenproblem, circumventing certain large inversions from a linearization,…
Convergence analysis of some tent-based schemes for linear hyperbolic systems
Dow Drake, Jay Gopalakrishnan, Joachim Schöberl +1
Finite element methods for symmetric linear hyperbolic systems using unstructured advancing fronts (satisfying a causality condition) are considered in this work. Convergence resul…
An Explicit Mapped Tent Pitching Scheme for Maxwell Equations
Jay Gopalakrishnan, Matthias Hochsteger, Joachim Schöberl +1
We present a new numerical method for solving time dependent Maxwell equations, which is also suitable for general linear hyperbolic equations. It is based on an unstructured parti…