scholarly journals Convergence Rates for Greedy Algorithms in Reduced Basis Methods

2011 ◽  
Vol 43 (3) ◽  
pp. 1457-1472 ◽  
Author(s):  
Peter Binev ◽  
Albert Cohen ◽  
Wolfgang Dahmen ◽  
Ronald DeVore ◽  
Guergana Petrova ◽  
...  
Keyword(s):  
Convergence Rates ◽  
Greedy Algorithms ◽  
Reduced Basis ◽  
Reduced Basis Methods

scholarly journals Convergence Rates for Greedy Algorithms in Reduced Basis Methods

2010 ◽  
Author(s):  
Peter Binev ◽  
Albert Cohen ◽  
Wolfgang Dahmen ◽  
Ronald DeVore ◽  
Guergana Petrova ◽  
...  
Keyword(s):  
Convergence Rates ◽  
Greedy Algorithms ◽  
Reduced Basis ◽  
Reduced Basis Methods

scholarly journals Double greedy algorithms: Reduced basis methods for transport dominated problems

2014 ◽  
Vol 48 (3) ◽  
pp. 623-663 ◽  
Author(s):  
Wolfgang Dahmen ◽  
Christian Plesken ◽  
Gerrit Welper
Keyword(s):  
Greedy Algorithms ◽  
Reduced Basis ◽  
Reduced Basis Methods

scholarly journals On Rational Krylov and Reduced Basis Methods for Fractional Diffusion

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tobias Danczul ◽  
Clemens Hofreither
Keyword(s):  
Rational Approximation ◽  
Convergence Rates ◽  
Fractional Diffusion ◽  
Point Of View ◽  
Spectral Interval ◽  
Krylov Methods ◽  
Reduced Basis ◽  
Reduced Basis Methods ◽  
Approximation Classes ◽  
Diffusion Problems

Abstract We establish an equivalence between two classes of methods for solving fractional diffusion problems, namely, Reduced Basis Methods (RBM) and Rational Krylov Methods (RKM). In particular, we demonstrate that several recently proposed RBMs for fractional diffusion can be interpreted as RKMs. This changed point of view allows us to give convergence proofs for some methods where none were previously available. We also propose a new RKM for fractional diffusion problems with poles chosen using the best rational approximation of the function 𝑧 −𝑠 with 𝑧 ranging over the spectral interval of the spatial discretization matrix. We prove convergence rates for this method and demonstrate numerically that it is competitive with or superior to many methods from the reduced basis, rational Krylov, and direct rational approximation classes. We provide numerical tests for some elliptic fractional diffusion model problems.

scholarly journals 4 Reduced basis methods

2020 ◽  
pp. 139-180
Keyword(s):  
Reduced Basis ◽  
Reduced Basis Methods

scholarly journals Stabilized Weighted Reduced Basis Methods for Parametrized Advection Dominated Problems with Random Inputs

2018 ◽  
Vol 6 (4) ◽  
pp. 1475-1502 ◽  
Author(s):  
Davide Torlo ◽  
Francesco Ballarin ◽  
Gianluigi Rozza
Keyword(s):  
Reduced Basis ◽  
Random Inputs ◽  
Reduced Basis Methods

Stochastic Reduced Basis Methods

AIAA Journal ◽  
2002 ◽  
Vol 40 (8) ◽  
pp. 1653-1664 ◽  
Author(s):  
Prasanth B. Nair ◽  
Andrew J. Keane
Keyword(s):  
Reduced Basis ◽  
Reduced Basis Methods

Comparison of advanced reduced-basis methods for transient structural analysis

AIAA Journal ◽  
1993 ◽  
Vol 31 (9) ◽  
pp. 1712-1719 ◽  
Author(s):  
David M. McGowan ◽  
Susan W. Bostic
Keyword(s):  
Structural Analysis ◽  
Reduced Basis ◽  
Reduced Basis Methods
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