Parameter Space: The Final Frontier. Certified Reduced Basis Methods for Real-Time Reliable Solution of Parametrized Partial Differential Equations
Final rept., 15 Feb 2005-14 Nov 2006
MASSACHUSETTS INST OF TECH CAMBRIDGE DEPT OF MECHANICAL ENGINEERING
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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.
- Numerical Mathematics
- Fluid Mechanics