Output Error Bounds for the Dirichlet-Neumann Reduced Basis Method

2014 ◽  
pp. 437-445 ◽  
Author(s):  
Immanuel Martini ◽  
Bernard Haasdonk
Keyword(s):  
Error Bounds ◽  
Reduced Basis Method ◽  
Reduced Basis ◽  
Output Error ◽  
Basis Method

EVALUATION OF FLUX INTEGRAL OUTPUTS FOR THE REDUCED BASIS METHOD

2010 ◽  
Vol 20 (03) ◽  
pp. 351-374 ◽  
Author(s):  
JENS L. EFTANG ◽  
EINAR M. RØNQUIST
Keyword(s):  
Finite Element ◽  
Second Order ◽  
Reduced Basis Method ◽  
Reduced Basis ◽  
Numerical Example ◽  
Output Error ◽  
Primal Dual ◽  
Basis Method

In this paper, we consider the evaluation of flux integral outputs from reduced basis solutions to second-order PDEs. In order to evaluate such outputs, a lifting function v⋆ must be chosen. In the standard finite element context, this choice is not relevant, whereas in the reduced basis context, as we show, it greatly affects the output error. We propose two "good" choices for v⋆ and illustrate their effect on the output error by examining a numerical example. We also make clear the role of v⋆ in a more general primal-dual reduced basis approximation framework.

scholarly journals A space-time hp-interpolation-based certified reduced basis method for Burgers' equation

2014 ◽  
Vol 24 (09) ◽  
pp. 1903-1935 ◽  
Author(s):  
Masayuki Yano ◽  
Anthony T. Patera ◽  
Karsten Urban
Keyword(s):  
Error Bounds ◽  
Peclet Number ◽  
Burgers Equation ◽  
Space Time ◽  
Reduced Basis Method ◽  
Reduced Basis ◽  
Element Discretization ◽  
Péclet Number ◽  
Wide Range ◽  
Basis Method

We present a space-time interpolation-based certified reduced basis method for Burgers' equation over the spatial interval (0, 1) and the temporal interval (0, T] parametrized with respect to the Peclet number. We first introduce a Petrov–Galerkin space-time finite element discretization which enjoys a favorable inf–sup constant that decreases slowly with Peclet number and final time T. We then consider an hp interpolation-based space-time reduced basis approximation and associated Brezzi–Rappaz–Raviart a posteriori error bounds. We describe computational offline–online decomposition procedures for the three key ingredients of the error bounds: the dual norm of the residual, a lower bound for the inf–sup constant, and the space-time Sobolev embedding constant. Numerical results demonstrate that our space-time formulation provides improved stability constants compared to classical L2-error estimates; the error bounds remain sharp over a wide range of Peclet numbers and long integration times T, in marked contrast to the exponentially growing estimate of the classical formulation for high Peclet number cases.

scholarly journals Lyapunov-Based Error Bounds for the Reduced-Basis Method

2016 ◽  
Vol 49 (8) ◽  
pp. 1-6 ◽  
Author(s):  
Robert O’Connor
Keyword(s):  
Error Bounds ◽  
Reduced Basis Method ◽  
Reduced Basis ◽  
Basis Method

scholarly journals Application of a reduced basis method for an efficient treatment of structural mechanics problems

PAMM ◽  
2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Sophia Bremm ◽  
Philipp L. Rosendahl ◽  
Wilfried Becker
Keyword(s):  
Structural Mechanics ◽  
Reduced Basis Method ◽  
Reduced Basis ◽  
Efficient Treatment ◽  
Basis Method

High-Order VSIE Based Reduced Basis Method for Fast Modeling of Anisotropic-Metallic Targets

2021 ◽  
pp. 1-1
Author(s):  
Lifeng Wu ◽  
Yanwen Zhao ◽  
Qiangmin Cai ◽  
Zhipeng Zhang ◽  
Jun Hu
Keyword(s):  
High Order ◽  
Reduced Basis Method ◽  
Reduced Basis ◽  
Basis Method

Reduced basis method for real-time inverse scatterometry

2011 ◽  
Author(s):  
Jan Pomplun ◽  
Sven Burger ◽  
Lin Zschiedrich ◽  
Frank Schmidt
Keyword(s):  
Real Time ◽  
Reduced Basis Method ◽  
Reduced Basis ◽  
Basis Method
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