scholarly journals Locally Adaptive Greedy Approximations for Anisotropic Parameter Reduced Basis Spaces

2013 ◽  
Vol 35 (6) ◽  
pp. A2417-A2441 ◽  
Author(s):  
Yvon Maday ◽  
Benjamin Stamm
Keyword(s):  
Reduced Basis ◽  
Anisotropic Parameter ◽  
Locally Adaptive ◽  
Greedy Approximations

scholarly journals Reduced basis approximations of the solutions to spectral fractional diffusion problems

2020 ◽  
Vol 28 (3) ◽  
pp. 147-160
Author(s):  
Andrea Bonito ◽  
Diane Guignard ◽  
Ashley R. Zhang
Keyword(s):  
Computational Cost ◽  
Fractional Power ◽  
Reaction Diffusion ◽  
Fractional Diffusion ◽  
Diffusion Problem ◽  
Quadrature Point ◽  
Reduced Basis ◽  
Fast Evaluation ◽  
Bottle Neck ◽  
Diffusion Problems

AbstractWe consider the numerical approximation of the spectral fractional diffusion problem based on the so called Balakrishnan representation. The latter consists of an improper integral approximated via quadratures. At each quadrature point, a reaction–diffusion problem must be approximated and is the method bottle neck. In this work, we propose to reduce the computational cost using a reduced basis strategy allowing for a fast evaluation of the reaction–diffusion problems. The reduced basis does not depend on the fractional power s for 0 < smin ⩽ s ⩽ smax < 1. It is built offline once for all and used online irrespectively of the fractional power. We analyze the reduced basis strategy and show its exponential convergence. The analytical results are illustrated with insightful numerical experiments.

Effect of Dynamic Soft Elasticity on Vibration of Embedded Nematic Elastomer Timoshenko Beams

2018 ◽  
Vol 10 (05) ◽  
pp. 1850058 ◽  
Author(s):  
Dong Zhao ◽  
Ying Liu
Keyword(s):  
Low Frequency ◽  
Beam Theory ◽  
Timoshenko Beams ◽  
Analysis Method ◽  
Anisotropic Parameter ◽  
Nematic Elastomer ◽  
Dissipation Mechanism ◽  
Viscous Media ◽  
Complex Modal Analysis ◽  
Soft Elasticity

This paper addresses the transverse vibration of a nematic elastomer (NE) beam embedded in soft viscoelastic surroundings with the aim to clarify a new dissipation mechanism caused by dynamic soft elasticity of this soft material. Based on the viscoelasticity theory of NEs in low-frequency limit and the Timoshenko beam theory, the governing equation of motion is derived by using the Hamilton principle and energy method, and is solved by the complex modal analysis method. The dependence of vibration property on the intrinsic parameters of NEs (director rotation time, rubber relaxation time, anisotropic parameter) and foundation (spring, shear and damping constants) are discussed in detail. The results show that dynamic soft elasticity leads to anomalous anisotropy of energy transfer and attenuation. The relative stiffer foundation would restraint the rubber dissipation of viscoelastic beams, but has less influence on the director rotation dissipation, which is particular for NE beams. This study would provide a useful guidance in the dynamic design of NE apparatus embedded in soft viscous media.

Adaptive Greedy Approximations

1997 ◽  
Vol 13 (1) ◽  
pp. 57-98 ◽  
Author(s):  
G. Davis
Keyword(s):  
Greedy Approximations
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