Principal Investigator Anthony Patera
A web site has been established and is intended for mechanical engineering educators and students who wish to (1) incorporate solutions to the partial differential equations of continuum mechanics into class discussions, or (2) integrate solutions to the partial differential equations of continuum mechanics into assignments or projects.
We hope that practicing mechanical engineers will also have interest in the site as a demonstration of newly available simulation-based tools for characterization, design, optimization, and control.
Research comprises a number of illustrative Problems in acoustics, solid mechanics, heat transfer, and fluid dynamics. Each problem is characterized by a vector of $P$ input parameters and an associated input domain $\mathcal{D}$; and a set of $J$ scalar outputs representing engineering quantities of interest.
The software evaluates the input-output relationship rapidly and reliably: we provide -- typically in milliseconds -- both (a) an accurate prediction for the output, and (b) a certificate of fidelity that rigorously bounds the error in our prediction relative to a highly accurate "truth" finite element solution. We thus achieve educationally (and design) relevant "interactive timescales" with little or no compromise in accuracy or certainty.
The software also includes a Visualization Option which renders the relevant field variables. This feature is somewhat slower and more memory-intensive, but also more "physical" and colorful.
In addition to Forward Problems, we also consider Inverse Problems.