6 papers
Sufficient conditions for QMC analysis of finite elements for parametric differential equations
Vesa Kaarnioja, Andreas Rupp, Jay Gopalakrishnan
Parametric regularity of discretizations of flux vector fields satisfying a balance law is studied under some assumptions on a random parameter that links the flux with an unknown…
Generalizing Riemann curvature to Regge metrics
Jay Gopalakrishnan, Michael Neunteufel, Joachim Schöberl +1
In this paper, we propose a generalization of the Riemann curvature tensor on manifolds (of dimension two or higher) endowed with a Regge metric. Specifically, while all components…
The Johnson-Krizek-Mercier elasticity element in any dimensions
Jay Gopalakrishnan, Johnny Guzman, Jeonghun J. Lee
Mixed methods for linear elasticity with strongly symmetric stresses of lowest order are studied in this paper. On each simplex, the stress space has piecewise linear components wi…
A 2-complex containing Sobolev spaces of matrix fields
Jay Gopalakrishnan, Kaibo Hu, Joachim Schöberl
Using a generalization of complexes, called 2-complexes, this paper defines and analyzes new Sobolev spaces of matrix fields and their interrelationships within a commuting diagram…
DPG loss functions for learning parameter-to-solution maps by neural networks
Pablo Cortés Castillo, Wolfgang Dahmen, Jay Gopalakrishnan
We develop, analyze, and experimentally explore residual-based loss functions for machine learning of parameter-to-solution maps in the context of parameter-dependent families of p…
Guided modes of helical waveguides
Jay Gopalakrishnan, Michael Neunteufel
This paper studies guided transverse scalar modes propagating through helically coiled waveguides. Modeling the modes as solutions of the Helmholtz equation within the three-dimens…