Abstract: We present a nonlinear registration-based model reduction procedure for rapid and reliable solution of parameterized two-dimensional steady conservation laws. This class of problems is challenging for model reduction techniques due to the presence of nonlinear terms in the equations and also due to the presence of parameter-dependent sharp gradient regions that cannot be adequately represented through linear approximation spaces. Our approach builds on the following ingredients: (i) a general (i.e., independent of the underlying equation) registration procedure for the computation of a parametric mapping that tracks moving features of the solution field; (ii) an hyper-reduced least-squares Petrov-Galerkin reduced-order model for the rapid and reliable estimation of the solution field; (iii) a greedy procedure driven by a residual-based error indicator for efficient exploration of the parameter domain; and (iv) an adaptive mesh refinement technique for the definition of an accurate discretization for all parameter values. We present results for a representative nonlinear problem in steady aerodynamics to demonstrate the effectiveness and the mathematical soundness of our proposal.

Biography: Tommaso Taddei is a junior research scientist at Inria Bordeaux. He is also a member of the Institute of Mathematics in Bordeaux (IMB). His research focuses on model reduction methods for parameterized PDEs and data assimilation methods with applications in continuum mechanics.

Before joining Inria in 2018, he was a post-doctoral associate in the group of Professor Yvon Maday at Laboratoire Jacques-Louis Lions, and a PhD student in the group of Professor Anthony Patera in the Department of Mechanical Engineering at MIT.