Prof. Anthony T Patera

Ford Foundation Professor of Engineering

Primary DLC

Department of Mechanical Engineering

MIT Room: 3-266

Areas of Interest and Expertise

Scientific and Engineering Computation
Numerical Methods and Analysis, in Particular Spectral Element and Finite Element Methods for Partial Differential Equations
Applied Mechanics, in Particular Fluid Dynamics and Transport Phenomena and Stability Theory
Parallel Processing
Singapore-MIT Alliance (SMA)

Research Summary

We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced-basis approximations -- Galerkin projection onto a space W_N spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation -- relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures -- methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage -- in which, given a new parameter value, we calculate the output of interest and associated error bound -- depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.

Recent Work

  • Video

    Anthony Patera - 2019 ICT Conference

    April 16, 2019Conference Video Duration: 26:31

    Artie: An Artificial Heat Transfer Student

    An undergraduate student in heat transfer (or similar engineering science continuum discipline) maps a non-prescriptive problem statement in natural language to a relatively simple mathematical model to a closed-form approximate solution. This classical approach remains relevant even today: to develop design tools which serve to narrow the parameter domain; to provide transparent reference solutions which serve to verify the results of simulation. "Artie" is software which replicates the undergraduate student procedure and further expands the analysis capability to incorporate numerical solution of partial differential equations. Artie may ultimately be capable of an A+ in an MIT heat transfer subject. The latter, in turn, has important implications for education and professional practice: we must adapt our undergraduate curriculum, and we must revisit the roles of engineers. However, many technical challenges remain, in particular related to geometry and image processing, natural language understanding, incorporation of (heat transfer) empirical data and correlations, and assessment of model and approximation error.
    2019 MIT Information and Communication Technologies Conference