3 papers
math.NA2026
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…
math.NA2025
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…
physics.chem-ph2024
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…