21 citations · 22 across the 8 of their papers we have counts for
8 papers
Mathematical Modeling and Error Estimation for the Thermal Dunking Problem: A Hierarchical Approach
Theron Guo, Kento Kaneko, Claude Le Bris +1
We consider the thermal dunking problem, in which a solid body is suddenly immersed in a fluid of different temperature, and study both the temporal evolution of the solid and the…
An N-Plus-1 GPT Agency for Critical Solution of Mechanical Engineering Analysis Problems
Anthony Patera, Rohan Abeyaratne
Generative AI, and specifically GPT, can produce a remarkable solution to a mechanical engineering analysis problem - but also, on occasion, a flawed solution. For example, an elem…
Certified Lumped Approximations for the Conduction Dunking Problem
Kento Kaneko, Claude Le Bris, Anthony T. Patera
We consider the dunking problem: a solid body at uniform temperature is placed in a environment characterized by farfield temperature and time-independent s…
Error Estimators for the Small-Biot Lumped Approximation for the Conduction Dunking Problem
Kento Kaneko, Claude Le Bris, Anthony T. Patera
We consider the dunking problem: a solid body at uniform temperature is placed in a environment characterized by farfield temperature and spatially uniform…
Project Artie: An Artificial Student for Disciplines Informed by Partial Differential Equations
Anthony T Patera
We present an Artificial Student, "Artie," for engineering science disciplines in which the mathematical model is a partial differential equation (PDE); Artie considers here the pa…
Randomized residual-based error estimators for parametrized equations
Kathrin Smetana, Olivier Zahm, Anthony T Patera
We propose a randomized a posteriori error estimator for reduced order approximations of parametrized (partial) differential equations. The error estimator has several important pr…
A Reduced Basis Technique for Long-Time Unsteady Turbulent Flows
Lambert Fick, Yvon Maday, Anthony T Patera +1
We present a reduced basis technique for long-time integration of parametrized incompressible turbulent flows. The new contributions are threefold. First, we propose a constrained…
Reduced basis techniques for stochastic problems
Sébastien Boyaval, Claude Le Bris, Tony Lelièvre +3
We report here on the recent application of a now classical general reduction technique, the Reduced-Basis approach initiated in [C. Prud'homme, D. Rovas, K. Veroy, Y. Maday, A. T.…