scholarly journals Spectral Analysis of One-Dimensional High-Contrast Elliptic Problems with Periodic Coefficients

2015 ◽  
Vol 13 (1) ◽  
pp. 72-98 ◽  
Author(s):  
K. D. Cherednichenko ◽  
S. Cooper ◽  
S. Guenneau
Keyword(s):  
Spectral Analysis ◽  
Elliptic Problems ◽  
High Contrast ◽  
Periodic Coefficients ◽  
One Dimensional

scholarly journals Learning Adaptive Coarse Spaces of BDDC Algorithms for Stochastic Elliptic Problems with Oscillatory and High Contrast Coefficients

2021 ◽  
Vol 26 (2) ◽  
pp. 44
Author(s):  
Eric Chung ◽  
Hyea-Hyun Kim ◽  
Ming-Fai Lam ◽  
Lina Zhao
Keyword(s):  
Deep Neural Network ◽  
Elliptic Problems ◽  
Learning Approach ◽  
High Contrast ◽  
Spectral Problems ◽  
Significant Challenge ◽  
Machine Learning Approach ◽  
Balancing Domain Decomposition ◽  
Computationally Expensive ◽  
Coarse Space

In this paper, we consider the balancing domain decomposition by constraints (BDDC) algorithm with adaptive coarse spaces for a class of stochastic elliptic problems. The key ingredient in the construction of the coarse space is the solutions of local spectral problems, which depend on the coefficient of the PDE. This poses a significant challenge for stochastic coefficients as it is computationally expensive to solve the local spectral problems for every realization of the coefficient. To tackle this computational burden, we propose a machine learning approach. Our method is based on the use of a deep neural network (DNN) to approximate the relation between the stochastic coefficients and the coarse spaces. For the input of the DNN, we apply the Karhunen–Loève expansion and use the first few dominant terms in the expansion. The output of the DNN is the resulting coarse space, which is then applied with the standard adaptive BDDC algorithm. We will present some numerical results with oscillatory and high contrast coefficients to show the efficiency and robustness of the proposed scheme.

scholarly journals Spectral Analysis of Sampled Signals in the Linear Canonical Transform Domain

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Bing-Zhao Li ◽  
Tian-Zhou Xu
Keyword(s):  
Spectral Analysis ◽  
Spectral Representation ◽  
Digital Signal ◽  
Sampling Theorem ◽  
Transform Domain ◽  
Linear Canonical Transform ◽  
Two Dimensional ◽  
Research Papers ◽  
One Dimensional ◽  
Uniform Sampling

The spectral analysis of uniform or nonuniform sampling signal is one of the hot topics in digital signal processing community. Theories and applications of uniformly and nonuniformly sampled one-dimensional or two-dimensional signals in the traditional Fourier domain have been well studied. But so far, none of the research papers focusing on the spectral analysis of sampled signals in the linear canonical transform domain have been published. In this paper, we investigate the spectrum of sampled signals in the linear canonical transform domain. Firstly, based on the properties of the spectrum of uniformly sampled signals, the uniform sampling theorem of two dimensional signals has been derived. Secondly, the general spectral representation of periodic nonuniformly sampled one and two dimensional signals has been obtained. Thirdly, detailed analysis of periodic nonuniformly sampled chirp signals in the linear canonical transform domain has been performed.

scholarly journals Two New Spiro-Heterocyclic γ-Lactams from A Marine-Derived Aspergillus fumigatus Strain CUGBMF170049

Marine Drugs ◽  
2019 ◽  
Vol 17 (5) ◽  
pp. 289 ◽  
Author(s):  
Xiuli Xu ◽  
Jiahui Han ◽  
Yanan Wang ◽  
Rui Lin ◽  
Haijin Yang ◽  
...  
Keyword(s):  
Spectral Analysis ◽  
Circular Dichroism ◽  
Aspergillus Fumigatus ◽  
2D Nmr ◽  
Two Dimensional ◽  
One Dimensional ◽  
Helvolic Acid ◽  
Circular Dichroïsm

Two new spiro-heterocyclic γ-lactam derivatives, cephalimysins M (1) and N (2), were isolated from the fermentation cultures of the marine-derived fungus Aspergillus fumigatus CUGBMF17018. Two known analogues, pseurotin A (3) and FD-838 (4), as well as four previously reported helvolic acid derivatives, 16-O-propionyl-16-O-deacetylhelvolic acid (5), 6-O-propionyl-6-O-deacetylhelvolic acid (6), helvolic acid (7), and 1,2-dihydrohelvolic acid (8) were also identified. One-dimensional (1D), two-dimensional (2D) NMR, HRMS, and circular dichroism spectral analysis characterized the structures of the isolated compounds.

Sign in / Sign up

Export Citation Format

Share Document