Wavelets and Frequency Decomposition Multilevel Methods

1994 ◽  
pp. 261-272
Author(s):  
R. Schneider
Keyword(s):  
Multilevel Methods ◽  
Frequency Decomposition

Preface to the special issue, CMAM 2011, no. 3.

2011 ◽  
Vol 11 (3) ◽  
pp. 272
Author(s):  
Ivan Gavrilyuk ◽  
Boris Khoromskij ◽  
Eugene Tyrtyshnikov
Keyword(s):  
Separation Of Variables ◽  
Numerical Algorithms ◽  
Multilevel Methods ◽  
High Dimensional ◽  
Special Issue ◽  
High Dimensions ◽  
Guiding Principle ◽  
Tensor Methods ◽  
Closed World ◽  
The One

Abstract In the recent years, multidimensional numerical simulations with tensor-structured data formats have been recognized as the basic concept for breaking the "curse of dimensionality". Modern applications of tensor methods include the challenging high-dimensional problems of material sciences, bio-science, stochastic modeling, signal processing, machine learning, and data mining, financial mathematics, etc. The guiding principle of the tensor methods is an approximation of multivariate functions and operators with some separation of variables to keep the computational process in a low parametric tensor-structured manifold. Tensors structures had been wildly used as models of data and discussed in the contexts of differential geometry, mechanics, algebraic geometry, data analysis etc. before tensor methods recently have penetrated into numerical computations. On the one hand, the existing tensor representation formats remained to be of a limited use in many high-dimensional problems because of lack of sufficiently reliable and fast software. On the other hand, for moderate dimensional problems (e.g. in "ab-initio" quantum chemistry) as well as for selected model problems of very high dimensions, the application of traditional canonical and Tucker formats in combination with the ideas of multilevel methods has led to the new efficient algorithms. The recent progress in tensor numerical methods is achieved with new representation formats now known as "tensor-train representations" and "hierarchical Tucker representations". Note that the formats themselves could have been picked up earlier in the literature on the modeling of quantum systems. Until 2009 they lived in a closed world of those quantum theory publications and never trespassed the territory of numerical analysis. The tremendous progress during the very recent years shows the new tensor tools in various applications and in the development of these tools and study of their approximation and algebraic properties. This special issue treats tensors as a base for efficient numerical algorithms in various modern applications and with special emphases on the new representation formats.

Rough Air-Soft Elastohydrodynamic Lubrication

2013 ◽  
Vol 420 ◽  
pp. 30-35
Author(s):  
Khanittha Wongseedakaew ◽  
Jesda Panichakorn
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Modulus Of Elasticity ◽  
Contact Region ◽  
Elastohydrodynamic Lubrication ◽  
Multilevel Methods ◽  
Inlet Temperature ◽  
Film Pressure ◽  
Air Inlet ◽  
Air Film

This paper presents the effects of rough surface air-soft elastohydrodynamic lubrication (EHL) of rollers for soft material under the effect of air molecular slip. The time independent modified Reynolds equation and elasticity equation were solved numerically using finite different method, Newton-Raphson method and multigrid multilevel methods were used to obtain the film pressure profiles and film thickness in the contact region. The effects of amplitude of surface roughness, modulus of elasticity and air inlet temperature are examined. The simulation results showed surface roughness has effect on film thickness but it little effect to air film pressure. When the amplitude of surface roughness and modulus of elasticity increased, the air film thickness decreased but air film pressure increased. However, the air inlet temperature increased when the air film thickness increased.

Modeling consensus emergence in groups using longitudinal multilevel methods

2018 ◽  
Vol 71 (2) ◽  
pp. 255-281 ◽  
Author(s):  
Jonas W. B. Lang ◽  
Paul D. Bliese ◽  
Alex de Voogt
Keyword(s):  
Multilevel Methods

scholarly journals Cascadic multilevel methods for fast nonsymmetric blur- and noise-removal

2010 ◽  
Vol 60 (4) ◽  
pp. 378-396 ◽  
Author(s):  
S. Morigi ◽  
L. Reichel ◽  
F. Sgallari
Keyword(s):  
Noise Removal ◽  
Multilevel Methods

Joint inversion of high-frequency induction and lateral logging sounding data in earth models with tilted principal axes of the electrical resistivity tensor

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Oleg Nechaev ◽  
Viacheslav Glinskikh ◽  
Igor Mikhaylov ◽  
Ilya Moskaev
Keyword(s):  
Electrical Resistivity ◽  
High Frequency ◽  
Joint Inversion ◽  
Finite Element Approximation ◽  
Optimization Method ◽  
Multilevel Methods ◽  
Element Approximation ◽  
Resistivity Tensor ◽  
Principal Axes ◽  
High Frequency Induction

Abstract In this article, we are the first to formulate the direct and inverse problems of resistivity logging on determining the components of the electrical resistivity tensor of rocks from a set of high-frequency induction and lateral logging sounding measurements. Using a finite element approximation, high-order hierarchical basis functions, computationally efficient multilevel methods and a multistart algorithm with the DFO-LS local optimization method, we investigate the capability of reconstructing the horizontal and vertical resistivity components, as well as the tilt of the resistivity tensor principal axes with regard to the study of complex geological objects. A separate consideration is given to a realistic generalized geoelectric model of the unique hydrocarbon source with hard-to-recover reserves, the Bazhenov Formation.

scholarly journals Analysis of Epileptic Activity Based on Brain Mapping of EEG Adaptive Time-Frequency Decomposition

2018 ◽  
pp. 319-328 ◽  
Author(s):  
Maximiliano Bueno-López ◽  
Pablo A. Muñoz-Gutiérrez ◽  
Eduardo Giraldo ◽  
Marta Molinas
Keyword(s):  
Brain Mapping ◽  
Epileptic Activity ◽  
Time Frequency ◽  
Frequency Decomposition ◽  
Adaptive Time
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