AN ADAPTIVE PARAMETRIZED-BACKGROUND DATA-WEAK APPROACH TO VARIATIONAL DATA ASSIMILATION

作者：Taddei Tommaso^*

来源：ESAIM: Mathematical Modelling and Numerical Analysis , 2017, 51(5): 1827-1858.

DOI：10.1051/m2an/2017005

• Variational data assimilation
• parametrized partial differential equations
• model order reduction
• kernel methods

We present an Adaptive Parametrized-Background Data-Weak (APBDW) approach to the steady-state variational data assimilation (state estimation) problem for systems modeled by partial differential equations. The variational formulation is based on the Tikhonov regularization of the PBDW formulation [Y. Maday, A.T. Patera, J.D. Penn and M. Yano, Int. J. Numer. Meth. Eng. 102 (2015) 983-965] for pointwise noisy measurements. We propose an adaptive procedure based on a posteriori estimates of the L(2 )state-estimation error to improve performance. We also present a priori estimates for the L-2 state-estimation error that motivate the approach and guide the adaptive procedure. We provide numerical experiments for a synthetic acoustic problem to illustrate the different elements of the methodology, and we consider an experimental thermal patch configuration to demonstrate the applicability of our approach to real physical systems.

• 出版日期2017-10-24
• 单位MIT