LANS Informal Seminar
" Reduced basis approximations and a posteriori error estimation: application to fracture analysis"
DATE: February 27, 2008
TIME: - Description:
SPEAKER: Phuong Huynh
LOCATION: Building 221, Room A-261, Argonne National Laboratory
We develop reduced basis approximation and a posteriori error estimation for linear functional outputs of affinely parametrized elliptic partial differential equations. The essential ingredients are (primal-dual) Galerkin projection onto a low dimensional space associated with a smooth parametric manifold dimension reduction; efficient and effective greedy sampling methods for identification of optimal and numerically stable approximations rapid convergence; a posteriori error estimation procedures rigorous and sharp bounds for the linear functional outputs of interest; and Offline-Online computational decomposition strategies minimum marginal cost for high performance in the real-time/embedded (e.g., parameter estimation, control) and many-query (e.g., design optimization, multi-model/scale) contexts. We present illustrative results for several problems, with emphasis on stress intensity factor calculations in fracture mechanics.
Please send questions or suggestions to Jeffrey Larson: jmlarson at anl dot gov.