Offline Error Bounds for the Reduced Basis Method

2017 ◽  
pp. 121-136 ◽  
Author(s):  
Robert O’Connor ◽  
Martin Grepl
Keyword(s):  
Error Bounds ◽  
Reduced Basis Method ◽  
Reduced Basis ◽  
Basis Method

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

Fast online simulation of 3D nanophotonic structures by the reduced basis method

2011 ◽  
Author(s):  
Frank Schmidt ◽  
Jan Pomplun ◽  
Lin Zschiedrich ◽  
Sven Burger
Keyword(s):  
Reduced Basis Method ◽  
Reduced Basis ◽  
Online Simulation ◽  
Basis Method ◽  
Nanophotonic Structures
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