12 citations · 20 across the 15 of their papers we have counts for
18 papers
A Weighted Upwind Vector Kinetic Lattice Boltzmann Method For Hyperbolic Conservation Laws
Michael W. Brown, Jehanzeb Chaudhry, John N. Shadid
Vector kinetic lattice Boltzmann (VKLB) methods have recently emerged as a promising framework for solving hyperbolic partial differential equation (PDE) systems. VKLB discretizes…
Adjoint-based A Posteriori Error Analysis for Semi-explicit Index-1 and Hessenberg Index-2 Differential-Algebraic Equations
Jehanzeb H. Chaudhry, Owen L. Lewis, Md Al Amin Molla
In this work we develop adjoint-based analyses for \textit{a posteriori} error estimation for the temporal discretization of differential-algebraic equations (DAEs) of special type…
An Investigation of Physics Informed Neural Networks to solve the Poisson-Boltzmann Equation in Molecular Electrostatics
Martin A. Achondo, Jehanzeb H. Chaudhry, Christopher D. Cooper
Physics-informed neural networks (PINN) is a machine learning (ML)-based method to solve partial differential equations that has gained great popularity due to the fast development…
Adjoint-based Adaptive Multi-Level Monte Carlo for Differential Equations
Jehanzeb Chaudhry, Zachary Stevens
We present a multi-level Monte Carlo (MLMC) algorithm with adaptively refined meshes and accurately computed stopping-criteria utilizing adjoint-based a posteriori error analysis f…
On Computing Coercivity Constants in Linear Variational Problems Through Eigenvalue Analysis
Peter Sentz, Jehanzeb Hameed Chaudhry, Luke N. Olson
In this work, we investigate the convergence of numerical approximations to coercivity constants of variational problems. These constants are essential components of rigorous error…
Error estimation for the time to a threshold value in evolutionary partial differential equations
Jehanzeb Chaudhry, Don Estep, Trevor Giannini +2
We develop an \textit{a posteriori} error analysis for a numerical estimate of the time at which a functional of the solution to a partial differential equation (PDE) first achieve…