Space--Time Least-Squares Petrov--Galerkin Projection for Nonlinear Model Reduction
نویسندگان
چکیده
منابع مشابه
Space-time least-squares Petrov-Galerkin projection for nonlinear model reduction
This work proposes a space–time least-squares Petrov–Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply (Petrov– )Galerkin projection in the spatial dimension and subsequently apply time integration to numerically resolve the resulting low-dimensional dynamical system, the proposed me...
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We consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input parameters. We explore spectral methods in which the solutions are approximated in a chosen finite-dimensional subspace. It has been shown that the stochastic Galerkin projection technique fails to minimize any measure of...
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The variable projection algorithm of Golub and Pereyra (1973) has proven to be quite valuable in the solution of nonlinear least squares problems in which a substantial number of the parameters are linear. Its advantages are efficiency and, more importantly, a better likelihood of finding a global minimizer rather than a local one. The purpose of our work is to provide a more robust implementat...
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Least-squares Petrov–Galerkin (LSPG) model-reduction techniques such as the Gauss–Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible flow problems where standard Galerkin techniques have failed. However, there has been limited comparative analysis of the two approaches. This is due in part ...
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2019
ISSN: 1064-8275,1095-7197
DOI: 10.1137/17m1120531