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In this paper we develop and study numerically a model to describe some aspects of sound propagation in the human lung, considered as a deformable and viscoelastic porous medium (the parenchyma) with millions of alveoli filled with air. Transmission of sound through the lung above 1 kHz is known to be highly frequency-dependent. We pursue the key idea that the viscoelastic parenchyma structure is highly heterogeneous on the small scale and use two-scale homogenization techniques to derive effective...
We propose two new algorithms to improve greedy sampling of high-dimensional functions. While the techniques have a substantial degree of generality, we frame the discussion in the context of methods for empirical interpolation and the development of reduced basis techniques for high-dimensional parametrized functions. The first algorithm, based on a saturation assumption of the error in the greedy algorithm, is shown to result in a significant reduction of the workload over the standard greedy...
In error analysis of reduced basis approximations to affinely parametrized partial differential equations, the construction of lower bounds for the coercivity and inf-sup
stability constants is essential. In [Huynh ,
(2007) 473–478], the authors presented an efficient
method, compatible with an off-line/on-line strategy, where the on-line computation is reduced to
minimizing a linear functional under a few linear constraints. These constraints depend on nested sets of parameters...
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