The Elastohydrodynamic Problem Expressed in Terms of Extended Variational Formulation

1986 ◽  
Vol 108 (4) ◽  
pp. 557-564 ◽  
Author(s):  
Antonio Strozzi
Keyword(s):  
Convergence Rate ◽  
Variational Formulation ◽  
Numerical Experiments ◽  
Numerical Results ◽  
Lubricated Contacts ◽  
Relaxation Scheme

The elastohydrodynamic problem is revisited in terms of an extended variational formulation, where the corresponding functional exhibits minimum properties in the solution neighborhood. Such features are exploited in the development of a relaxation-type solver. The numerical results indicate that the convergence rate of the proposed relaxation scheme becomes increasingly poor as the solution of the elastohydrodynamic problem is approached. A polyalgorithm based on a combination between relaxation-type and Newton-type schemes is proposed. The numerical experiments referred to various sealing profiles of increasing foundation compliance show that the proposed procedure is particularly advantageous in the case of soft lubricated contacts.

scholarly journals An efficient algorithm for estimating the parameters of superimposed exponential signals in multiplicative and additive noise

2013 ◽  
Vol 23 (1) ◽  
pp. 117-129 ◽  
Author(s):  
Jiawen Bian ◽  
Huiming Peng ◽  
Jing Xing ◽  
Zhihui Liu ◽  
Hongwei Li
Keyword(s):  
Parameter Estimation ◽  
Convergence Rate ◽  
Efficient Algorithm ◽  
Numerical Experiments ◽  
Additive Noise ◽  
Mean Squared Errors ◽  
Least Squares Estimators ◽  
The Mean ◽  
Newton Raphson ◽  
Raphson Algorithm

This paper considers parameter estimation of superimposed exponential signals in multiplicative and additive noise which are all independent and identically distributed. A modified Newton-Raphson algorithm is used to estimate the frequencies of the considered model, which is further used to estimate other linear parameters. It is proved that the modified Newton- Raphson algorithm is robust and the corresponding estimators of frequencies attain the same convergence rate with Least Squares Estimators (LSEs) under the same noise conditions, but it outperforms LSEs in terms of the mean squared errors. Finally, the effectiveness of the algorithm is verified by some numerical experiments.

scholarly journals CONVERGENCE OF COMONOTONE HISTOPOLATING SPLINES

2015 ◽  
Vol 20 (1) ◽  
pp. 124-138 ◽  
Author(s):  
Helle Hallik ◽  
Peeter Oja
Keyword(s):  
Convergence Rate ◽  
Finite Number ◽  
Numerical Results ◽  
Quadratic Polynomial

The convergence rate of histopolation on an interval with combined splines of class C1 having linear/linear rational or quadratic polynomial pieces is studied. The function to histopolate may have finite number of derivative zeros and established convergence rate depends mainly on the behaviour of the derivative near its zeros. Given numerical results are completely consistent with theoretical ones.

scholarly journals Parallel in Time Algorithms for Nonlinear Iterative Methods

2018 ◽  
Vol 63 ◽  
pp. 248-257 ◽  
Author(s):  
Mustafa Gaja ◽  
Olga Gorynina
Keyword(s):  
Boundary Condition ◽  
Structural Analysis ◽  
Iterative Methods ◽  
Numerical Experiments ◽  
Numerical Results ◽  
Contact Boundary ◽  
Nonlinear Structural Analysis ◽  
Nonlinear Structural

In this paper we investigate the feasibility of applying the Parareal algorithm [5, 6] for quasi-static nonlinear structural analysis problems. We describe how this proposal has been realized and present some preliminary numerical results of applying this algorithm to a beam undergoing nonlinear deflection with a contact boundary condition. Further numerical experiments are needed to provide an evidence for the effciency of the method.

A Filtered-Davidson Method for Large Symmetric Eigenvalue Problems

2017 ◽  
Vol 7 (1) ◽  
pp. 21-37 ◽  
Author(s):  
Cun-Qiang Miao
Keyword(s):  
Convergence Rate ◽  
Chebyshev Polynomials ◽  
Numerical Experiments ◽  
Eigenvalue Problems ◽  
Cubic Convergence ◽  
Davidson Method ◽  
Filtering Technique ◽  
Matrix Vector ◽  
Three Term Recurrence Relation ◽  
Symmetric Eigenvalue Problems

AbstractFor symmetric eigenvalue problems, we constructed a three-term recurrence polynomial filter by means of Chebyshev polynomials. The new filtering technique does not need to solve linear systems and only needs matrix-vector products. It is a memory conserving filtering technique for its three-term recurrence relation. As an application, we use this filtering strategy to the Davidson method and propose the filtered-Davidson method. Through choosing suitable shifts, this method can gain cubic convergence rate locally. Theory and numerical experiments show the efficiency of the new filtering technique.

An optimized Schwarz method with relaxation for the Helmholtz equation: the negative impact of overlap

2019 ◽  
Vol 53 (1) ◽  
pp. 249-268
Author(s):  
Yongxiang Liu ◽  
Xuejun Xu
Keyword(s):  
Convergence Rate ◽  
Helmholtz Equation ◽  
Domain Decomposition ◽  
Negative Impact ◽  
Mesh Size ◽  
Careful Analysis ◽  
Numerical Results ◽  
Wave Number ◽  
Convergence Behavior ◽  
Schwarz Method

In this paper we study how the overlapping size influences the convergence rate of an optimized Schwarz domain decomposition (DD) method with relaxation in the two subdomain case for the Helmholtz equation. Through choosing suitable parameters, we find that the convergence rate is independent of the wave number k and mesh size h, but sensitively depends on the overlapping size. Furthermore, by careful analysis, we obtain that the convergence behavior deteriorates with the increase of the overlapping size. Numerical results which confirm our theory are given.

GENERATION OF BRIGHT MATTER-WAVE SOLITON PATTERNS IN MIXTURES OF BOSE–EINSTEIN CONDENSATES WITH CUBIC AND QUINTIC NONLINEARITIES

2014 ◽  
Vol 28 (04) ◽  
pp. 1450003 ◽  
Author(s):  
DIDIER BELOBO BELOBO ◽  
GERMAIN HUBERT BEN-BOLIE ◽  
TIMOLÉON CRÉPIN KOFANÉ
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Numerical Experiments ◽  
Modulational Instability ◽  
Numerical Results ◽  
Matter Wave ◽  
Bright Solitons ◽  
Bose Einstein

The modulational instability (MI) of binary condensates with cubic-quintic nonlinearities is investigated. Using a linear stability analysis, a gain of instability is derived then, effects of the quintic nonlinearities on the instability gain are identified. To be precise, attractive intraspecie quintic nonlinearities enhance the instability, while repulsive quintic intraspecie nonlinearities soften the instability. Besides, small attractive and large repulsive quintic inter-species nonlinearities increase the instability. Numerical experiments quite well corroborate the analytical predictions. Further numerical results show effects of the cubic and the quintic nonlinearities on the propagation of trains of bright solitons generated.

Spectral Element Discretization of the Stokes Equations in Deformed Axisymmetric Geometries

2011 ◽  
Vol 3 (4) ◽  
pp. 448-469 ◽  
Author(s):  
Zakaria Belhachmi ◽  
Andreas Karageorghis
Keyword(s):  
Variational Formulation ◽  
Numerical Experiments ◽  
Spectral Element Method ◽  
Stokes System ◽  
Stokes Equations ◽  
Spectral Element ◽  
Azimuthal Direction ◽  
Element Discretization ◽  
Polynomial Series ◽  
Truncated Fourier Series

AbstractIn this paper, we study the numerical solution of the Stokes system in deformed axisymmetric geometries. In the azimuthal direction the discretization is carried out by using truncated Fourier series, thus reducing the dimension of the problem. The resulting two-dimensional problems are discretized using the spectral element method which is based on the variational formulation in primitive variables. The meridian domain is subdivided into elements, in each of which the solution is approximated by truncated polynomial series. The results of numerical experiments for several geometries are presented.

A New Preconditioned Generalised AOR Method for the Linear Complementarity Problem Based on a Generalised Hadjidimos Preconditioner

2012 ◽  
Vol 2 (2) ◽  
pp. 94-107 ◽  
Author(s):  
Cuiyu Liu ◽  
Chenliang Li
Keyword(s):  
Convergence Rate ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Numerical Experiments ◽  
Linear Complementarity ◽  
New Method ◽  
Aor Method

AbstractA new generalised Hadjidimos preconditioner and preconditioned generalised AOR method for the solution of the linear complementarity problem are presented. The convergence and convergence rate of the new method are analysed, and numerical experiments demonstrate that it is efficient.

Using Q-Learning and Genetic Algorithms to Improve the Efficiency of Weight Adjustments for Optimal Control and Design Problems

2005 ◽  
Author(s):  
Kaivan Kamali ◽  
Lijun Jiang ◽  
John Yen ◽  
K. W. Wang
Keyword(s):  
Optimal Control ◽  
Genetic Algorithms ◽  
Convergence Rate ◽  
Cost Function ◽  
Design Problem ◽  
Numerical Experiments ◽  
Design Parameters ◽  
Design Problems ◽  
Q Learning ◽  
Layered Approach

In traditional optimal control and design problems, the control gains and design parameters are usually derived to minimize a cost function reflecting the system performance and control effort. One major challenge of such approaches is the selection of weighting matrices in the cost function, which are usually determined via trial and error and human intuition. While various techniques have been proposed to automate the weight selection process, they either can not address complex design problems or suffer from slow convergence rate and high computational costs. We propose a layered approach based on Q-learning, a reinforcement learning technique, on top of genetic algorithms (GA) to determine the best weightings for optimal control and design problems. The layered approach allows for reuse of knowledge. Knowledge obtained via Q-learning in a design problem can be used to speed up the convergence rate of a similar design problem. Moreover, the layered approach allows for solving optimizations that cannot be solved by GA alone. To test the proposed method, we perform numerical experiments on a sample active-passive hybrid vibration control problem, namely adaptive structures with active-passive hybrid piezoelectric networks (APPN). These numerical experiments show that the proposed Q-learning scheme is a promising approach for.

scholarly journals Modified Preconditioned GAOR Methods for Systems of Linear Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xue-Feng Zhang ◽  
Qun-Fa Cui ◽  
Shi-Liang Wu
Keyword(s):  
Linear System ◽  
Convergence Rate ◽  
Least Squares ◽  
Linear Equations ◽  
Generalized Least Squares ◽  
Numerical Results ◽  
Least Squares Problem ◽  
Comparison Results ◽  
Systems Of Linear Equations ◽  
Better Than

Three kinds of preconditioners are proposed to accelerate the generalized AOR (GAOR) method for the linear system from the generalized least squares problem. The convergence and comparison results are obtained. The comparison results show that the convergence rate of the preconditioned generalized AOR (PGAOR) methods is better than that of the original GAOR methods. Finally, some numerical results are reported to confirm the validity of the proposed methods.

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