Accession Number:

ADA467167

Title:

Parameter Space: The Final Frontier. Certified Reduced Basis Methods for Real-Time Reliable Solution of Parametrized Partial Differential Equations

Descriptive Note:

Final rept., 15 Feb 2005-14 Nov 2006

Corporate Author:

MASSACHUSETTS INST OF TECH CAMBRIDGE DEPT OF MECHANICAL ENGINEERING

Personal Author(s):

Report Date:

2007-03-12

Pagination or Media Count:

13.0

Abstract:

This project is focused on reduced basis approximation methods, associated rigorous and sharp aposteriori error bounds, and offline-online computational strategies for the rapid and reliable solution of parametrized elliptic, parabolic, and more recently hyperbolic partial differential equations relevant to mechanics from the quantum through the meso-scale to the macro-scale. Typical equations and applications of interest include Density Functional Theory for solid state property calculations, the Boltzmann equation for microscale gas flows, the Navier-Stokes equations for natural convection calculations, elasticity for stress intensity factorsbrittle failure, and Helmholtz and the wave equation for acoustic waveguide applications. Of particular interest is real-time and robust parameter estimation with application to detection, nondestructive evaluation, adaptive designoptimization, and control. In the onlinedeployed stage, we can provide results for key engineering outputs in real-time without loss of accuracy or reliability the outputs provided - in milliseconds online - by our approach are provably indistinguishable from the outputs provided - typically in many minutes or even hours - by classical methods.

Subject Categories:

  • Numerical Mathematics
  • Fluid Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE