719 citations · 1.9k across the 57 of their papers we have counts for
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On the non-uniqueness of the instantaneous frequency
Peyman Tavallali, Thomas Y. Hou
In this article, we investigate the debated Instantaneous Frequency (IF) topic. Here, we show that IF is non-unique inherently. We explain how this non-uniqueness can be quantified…
A sparse decomposition of low rank symmetric positive semi-definite matrices
Thomas Y. Hou, Qin Li, Pengchuan Zhang
Suppose that is symmetric positive semidefinite with rank . Our goal is to decompose into rank-one matrices $\sum_{k=1}^K g_k g_k^T…
Exploring the locally low dimensional structure in solving random elliptic PDEs
Thomas Y. Hou, Qin Li, Pengchuan Zhang
We propose a stochastic multiscale finite element method (StoMsFEM) to solve random elliptic partial differential equations with a high stochastic dimension. The key idea is to sim…
Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods
Eric Chung, Yalchin Efendiev, Thomas Y. Hou
In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to…