Jehanzeb Hameed Chaudhry

Research Group

Graduate Students (Past and Current):

Michael Brown. Research Interest: Lattice Boltzmann Methods
Md Al Amin Molla. Research Interest: Differential Algebraic Equations
Trevor Giannini. Research Interest: Shallow Water Equations
Z. Stevens. PhD Thesis: Robust Un-certainty Quantification with Analysis of Error in Standard and Non-standard Quantities of Interest
Danial Alcala. Masters Thesis: Derivation of Adjoint Based Error Estimates for Nonlinear Ordinary Differential Equations with Application to Multistage SIR Models with Demographics
Jonathan Gutierrez. Masters Thesis: Using Physics-Informed Neural Networks for Multigrid in Time Coarse Grid Equations
Ari Rappaport. Masters Thesis: A Posteriori error analysis for Magnetohydrodynamics.
Nicholas Abel. Masters Thesis: Multi-level Asymptotic Parallel-in-Time Techniques For Highly Oscillatory Hyperbolic PDEs..

Undergraduate Students (Past):

Christopher Leap. Deep learning for predicting Conjugate Gradient iterations for Uncertainty Quantification. Jupyter Notebook on Github
Ari Rappaport. Exploration of Black Box Multigrid for Linear Systems Modeling Resistive MHD, Honors Thesis, (2018)

Jupyter Notebooks

A posteriori error analysis for a non-standard Quantity-of-Interest: First time to a threshold event Jupyter Notebooks on Github
A posteriori error analysis of Schwarz Domain Decomposition Methods Jupyter Notebooks on Github
Monte-Carlo simulations Jupyter Notebooks on Github
Deep learning for predicting Conjugate Gradient iterations for Uncertainty Quantification. Github link

Research Areas

Uncertainty Quantification and Error Estimation

Jehanzeb Chaudhry, Ari Rappaport and John Shadid. An a posteriori error analysis for the equations of stationary incompressible magnetohydrodynamics SIAM Journal on Scientific Computing (2021) [Text, Preprint]
Jehanzeb Chaudhry, Don Estep and Simon Tavener. A posteriori error analysis for Schwarz overlapping domain decomposition methods. BIT Numerical Mathematics (2021) [Text, Preprint]
Vicente Ramm, Jehanzeb H. Chaudhry, Christopher D. Cooper. Efficient mesh refinement for the Poisson-Boltzmann equation with boundary elements. Journal of Computational Chemistry (2021). [Text, Preprint]
Jehanzeb Chaudhry, Don Estep, Zachary Stevens and Simon Tavener. Error estimation and uncertainty quantification for first time to a threshold value. BIT Numerical Mathematics (2021). [Text, [Preprint]
Jehanzeb Chaudhry and Jeb Collins. A posteriori Error Estimation for the Spectral Deferred Correction Method. Journal of Computational and Applied Mathematics (2021). [Text, Preprint]
J. H. Chaudhry, J. N. Shadid and T. Wildey. A Posteriori analysis of an IMEX Entropy-Viscosity formulation for Hyperbolic conservation laws with dissipation. Applied Numerical Mathematics (2019). [Text]
J. H. Chaudhry. A Posteriori Analysis and Efficient Refinement Strategies for the Poisson-Boltzmann Equation SIAM Journal on Scientific Computing (2018). [Text]
J. H. Chaudhry, N. Burch and D. Estep. Efficient Distribution Estimation and Uncertainty Quantification for Elliptic Problems on Domains with Stochastic Boundaries. SIAM/ASA Journal on Uncertainty Quantification (2018). [Text]
J. H. Chaudhry, J. B. Collins and J. N. Shadid. A Posteriori Error Estimation for Multi-Stage Runge-Kutta IMEX Schemes. Applied Numerical Mathematics (2017). [Text]
J. H. Chaudhy, D. Esep and M. Gunzburger. Exploration of Efficient Reduced-Order Modeling and A Posteriori Error Estimation. International Journal for Numerical Methods in Engineering (2017) [Text]
J. H. Chaudhry, D. Estep, S. Tavener, V. Carey, and J. Sandelin. A Posteriori Error Analysis of Two-Stage Computation Methods with Application to Efficient Discretization and the Parareal Algorithm. SIAM Journal on Numerical Analysis (2016).[Text]
J. H. Chaudhry, D. Estep, V. Ginting, J. N. Shadid, and S. Tavenver. A posteriori error analysis of IMEX multi-step time integration methods for advection-diffusion-reaction equations. Computer Methods in Applied Mechanics and Engineering (2015).[Text]
J. H. Chaudhry, D. Estep, V. Ginting, and S. Tavenver. A posteriori analysis of iterative evolution solvers for non-autonomous problems. SIAM/ASA Journal on Uncertainty Quantification (2015).[Text]
A. Johansson, J. H. Chaudhry, V. Carey, D. Estep, V. Ginting, M. Larson, and S. Tavenver. Adaptive finite element solution of multiscale PDE-ODE systems. Computer Methods in Applied Mechanics and Engineering (2015).[Text]
J. H. Chaudhry, D. Estep, V. Ginting, and S. Tavenver. A posteriori analysis of an iterative multi-discretization method for reaction-diffusion systems. Computer Methods in Applied Mechanics and Engineering, 267:1 (2013). [Text]

Continuum Methods for Biomolecular Simuation

Vicente Ramm, Jehanzeb H. Chaudhry, Christopher D. Cooper. Efficient mesh refinement for the Poisson-Boltzmann equation with boundary elements. Journal of Computational Chemistry (2021). [Text, Preprint]
Divya Bohra, Jehanzeb H. Chaudhry, Thomas Burdyny, Evgeny A. Pidko and Wilson A. Smith. Modeling the Electrical Double Layer to Understand the Reaction Environment in a CO2 Electrocatalytic System. Energy & Environmental Science (2019). [Text, Preprint]
J. H. Chaudhry. A Posteriori Analysis and Efficient Refinement Strategies for the Poisson-Boltzmann Equation SIAM Journal on Scientific Computing (2018). [Text]
J. H. Chaudhry, J. Comer, A. Aksimentiev, and L. N. Olson. A stabilized finite element method for modified Poisson-Nernst-Planck equations to determine ion flow through a nanopore. Communications in Computational Physics (2014). [Text or Text ]
J. H. Chaudhry, S. D. Bond, and L. N. Olson. A weighted adaptive least-squares finite element method for the Poisson-Boltzmann equation. Applied Mathematics and Computation (2012). [Text]
J. H. Chaudhry, S. D. Bond, and L. N. Olson. Finite element approximation to a finite-size modified Poisson-Boltzmann equation. Journal of Scientific Computing (2011). [Text]
S. D. Bond, J. H. Chaudhry, E. C. Cyr, and L. N. Olson. A first-order system least-squares finite element method for the Poisson-Boltzmann equation. Journal of Computational Chemistry (2010). [Text]

Reduced Order Modeling

Jehanzeb Hameed Chaudhry, Luke N. Olson, Peter Sentz. A Least-Squares Finite Element Reduced Basis Method. SIAM Journal on Scientific Computing (2021) [Text, Preprint]
J. H. Chaudhy, D. Esep and M. Gunzburger. Exploration of Efficient Reduced-Order Modeling and A Posteriori Error Estimation. International Journal for Numerical Methods in Engineering (2017) [Text]

Finite Element Method for PDEs

J. H. Chaudhry, K. Liu, K. Liu, T. A. Manteuffel, L. N. Olson, and L. Tang. Enhancing Least-Squares finite element methods through a Quantity-of-Interest. SIAM Journal on Numerical Analysis (2014). [Text]
J. H. Chaudhry, J. Comer, A. Aksimentiev, and L. N. Olson. A stabilized finite element method for modified Poisson-Nernst-Planck equations to determine ion flow through a nanopore. Communications in Computational Physics (2014). [Text or Text ]
J. H. Chaudhry, S. D. Bond, and L. N. Olson. A weighted adaptive least-squares finite element method for the Poisson-Boltzmann equation. Applied Mathematics and Computation (2012). [Text]
J. H. Chaudhry, S. D. Bond, and L. N. Olson. Finite element approximation to a finite-size modified Poisson-Boltzmann equation. Journal of Scientific Computing (2011). [Text]
S. D. Bond, J. H. Chaudhry, E. C. Cyr, and L. N. Olson. A first-order system least-squares finite element method for the Poisson-Boltzmann equation. Journal of Computational Chemistry (2010). [Text]
A. Johansson, J. H. Chaudhry, V. Carey, D. Estep, V. Ginting, M. Larson, and S. Tavenver. Adaptive finite element solution of multiscale PDE-ODE systems. Computer Methods in Applied Mechanics and Engineering (2015).[Text]
A. N. Hirani, K. B. Nakshatrala, and J. H. Chaudhry. Numerical method for Darcy flow derived using Discrete Exterior Calculus. International Journal for Computational Methods in Engineering Science and Mechanics. (2015). [Text]

Collaborators:

Partial list of current and past collaborators:

Christopher D. Cooper. (Universidad Tecnica Federico Santa Maria, Chile)
Nishant Panda. (Los Alamos)
Joseph Bishop. (Sandia National Laboratories)
John Shadid. (Sandia National Laboratories)
Don Estep. (Simon Fraser University)
Simon Tavener. (Colorado State University)
Luke Olson. (University of Illinois at Urbana-Champaign)
Max Gunzburger
Eric Cyr. (Sandia National Laboratories)
Tim Wildey. (Sandia National Laboratories)