Author: Martin Alexander GreplPublisher:
ISBN:
Category :
Languages : en
Pages : 251
Book Description
(Cont.) To this end, we introduce a collateral reduced-basis expansion for the nonaffine and nonlinear terms and employ an inexpensive interpolation procedure to calculate the coefficients for the function approximation - the approach permits an efficient offline-online computational decomposition even in the presence of nonaffine and highly nonlinear terms. Under certain restrictions on the function approximation, we also introduce rigorous a posteriori error estimators for nonaffine and nonlinear problems. Finally, we apply our methods to the solution of inverse and optimal control problems. While the efficient evaluation of the input-output relationship is essential for the real-time solution of these problems, the a posteriori error bounds let us pursue a robust parameter estimation procedure which takes into account the uncertainty due to measurement and reduced-basis modeling errors explicitly (and rigorously). We consider several examples: the nondestructive evaluation of delamination in fiber-reinforced concrete, the dispersion of pollutants in a rectangular domain, the self-ignition of a coal stockpile, and the control of welding quality. Numerical results illustrate the applicability of our methods in the many-query contexts of optimization, characterization, and control.
