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.

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.

scholarly journals On Monte-Carlo tree search for deterministic games with alternate moves and complete information

2019 ◽  
Vol 23 ◽  
pp. 176-216
Author(s):  
Sylvain Delattre ◽  
Nicolas Fournier
Keyword(s):  
Monte Carlo ◽  
Finite Number ◽  
Optimal Algorithm ◽  
A Priori ◽  
Complete Information ◽  
Random Model ◽  
Numerical Results ◽  
Tree Search ◽  
Monte Carlo Tree Search ◽  
Independence Properties

We consider a deterministic game with alternate moves and complete information, of which the issue is always the victory of one of the two opponents. We assume that this game is the realization of a random model enjoying some independence properties. We consider algorithms in the spirit of Monte-Carlo Tree Search, to estimate at best the minimax value of a given position: it consists in simulating, successively, n well-chosen matches, starting from this position. We build an algorithm, which is optimal, step by step, in some sense: once the n first matches are simulated, the algorithm decides from the statistics furnished by the n first matches (and the a priori we have on the game) how to simulate the (n + 1)th match in such a way that the increase of information concerning the minimax value of the position under study is maximal. This algorithm is remarkably quick. We prove that our step by step optimal algorithm is not globally optimal and that it always converges in a finite number of steps, even if the a priori we have on the game is completely irrelevant. We finally test our algorithm, against MCTS, on Pearl’s game [Pearl, Artif. Intell. 14 (1980) 113–138] and, with a very simple and universal a priori, on the game Connect Four and some variants. The numerical results are rather disappointing. We however exhibit some situations in which our algorithm seems efficient.

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 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.

scholarly journals A Generalized case of Electromagnetic Scattering from a finite number of Ferromagnetic cylinders

2015 ◽  
Vol 4 (3) ◽  
pp. 8 ◽  
Author(s):  
T. Kumar ◽  
N. Kalyanasundaram ◽  
B. K. Lande
Keyword(s):  
Finite Number ◽  
Electromagnetic Scattering ◽  
Scattered Field ◽  
Near Field ◽  
Scattering Problem ◽  
Normal Incidence ◽  
Generalized Solution ◽  
Numerical Results ◽  
Infinite Length ◽  
Angle Of Incidence

A generalized solution of the scattering problem from an array containing a finite number of axially magnetized ferromagnetic cylinders of infinite length placed in free space is presented in this paper. The analysis is carried out by matching the tangential boundary conditions at the surface of each cylinder to find the unknown expansion coefficients of the scattered field. Planar arrays consist of a finite number of ferromagnetic microwires are considered to obtain the numerical results for TMz and TEz polarizations in terms of the variation in scattered field components of the near field and scattering cross section (SCS) with respect to angle of incidence, radius of microwires, spacing among the microwires and operating frequency. For validation purpose, numerical results of the proposed analysis specialized for the case of single microwire and normal incidence for TMz polarization are compared with the results available in the literature for the specialized case and both are found to be matched completely.

scholarly journals Vibration Protection of Mechanical Systems Consisting of Solid And Deformable Bodies

2018 ◽  
Vol 3 (9) ◽  
pp. 18
Author(s):  
Ismail Ibrahimovich Safarov ◽  
Teshaev Muhsin Khudoyberdiyevich
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Numerical Results ◽  
Constructive Method ◽  
Vibration Protection ◽  
Deformable Bodies ◽  
Reaction Forces ◽  
Active Vibration ◽  
Servo Constraints

In this  paper active vibration protection of mechanical systems consisting of solid and deformable bodies is considered. To actively control the oscillations of dissipative mechanical systems, a constructive method is used to determine the structure of the reaction forces of servo constraints. As an example, we consider the system with a finite number of degrees of freedom. Numerical results for various harmonic are also given.

A lattice Boltzmann model for the nonlinear thermistor equations

2020 ◽  
Vol 31 (03) ◽  
pp. 2050043
Author(s):  
Jiao Liu ◽  
Zhenhua Chai ◽  
Baochang Shi
Keyword(s):  
Convergence Rate ◽  
Lattice Boltzmann ◽  
Nonlinear Diffusion ◽  
Numerical Results ◽  
Lattice Boltzmann Model ◽  
Order Convergence ◽  
Poisson Equations ◽  
Second Order Convergence ◽  
Boltzmann Model ◽  
Good Agreement

In this paper, we propose a general and efficient lattice Boltzmann (LB) model for solving the nonlinear thermistor equations, where the nonlinear diffusion and Poisson equations are solved by two LB equations. Through Chapman–Enskog analysis, the nonlinear thermistor equations can be recovered correctly from the present LB model. We then test the model through some numerical simulations, and find that the numerical results are in good agreement with analytical solutions. Additionally, the numerical results also show that the present LB model has a second-order convergence rate in space.

scholarly journals EFFICIENT MULTIPHYSICS ITERATIONS IN MPACT WITH PARTIALLY CONVERGENT CMFD

2021 ◽  
Vol 247 ◽  
pp. 06039
Author(s):  
Qicang Shen ◽  
Brendan Kochunas ◽  
Thomas Downar
Keyword(s):  
Convergence Rate ◽  
Iteration Scheme ◽  
Numerical Results ◽  
Run Time

Partial convergence of CMFD can help to stabilize multiphysics iteration schemes. In this paper, an efficient multiphysics iteration scheme with near-optimal partially convergent CMFD implemented in MPACT is presented. In the new scheme, the feedback intensity of the problem is automatically estimated, and the relative convergence of CMFD solver is adjusted accordingly. Numerical results show that MPACT with near-optimal partially convergent CMFD can have almost the same convergence rate in problems with feedback as those without feedback. For the problems tested here the run time may be reduced by more than 20% and up to 49% compared with that of current MPACT.

scholarly journals Progressive Iterative Approximation with Preconditioners

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1503
Author(s):  
Chengzhi Liu ◽  
Zhongyun Liu
Keyword(s):  
Computational Complexity ◽  
Convergence Rate ◽  
Iterative Methods ◽  
State Of The Art ◽  
Numerical Results ◽  
Iterative Approximation ◽  
Totally Positive ◽  
Positive Bases ◽  
Curve And Surface Fitting ◽  
Methods Numerical

The progressive iterative approximation (PIA) plays an important role in curve and surface fitting. By using the diagonally compensated reduction of the collocation matrix, we propose the preconditioned progressive iterative approximation (PPIA) to improve the convergence rate of PIA. For most of the normalized totally positive bases, we show that the presented PPIA can accelerate the convergence rate significantly in comparison with the weighted progressive iteration approximation (WPIA) and the progressive iterative approximation with different weights (DWPIA). Furthermore, we propose an inexact variant of the PPIA (IPPIA) to reduce the computational complexity of the PPIA. We introduce the inexact solver of the preconditioning system by employing some state-of-the-art iterative methods. Numerical results show that both the PPIA and the IPPIA converge faster than the WPIA and DWPIA, while the elapsed CPU times of the PPIA and IPPIA are less than those of the WPIA and DWPIA.

IMPROVEMENT OF SIMPLER ALGORITHM FOR INCOMPRESSIBLE FLOW ON STAGGERED GRID SYSTEM

2007 ◽  
Vol 18 (07) ◽  
pp. 1149-1155
Author(s):  
T. S. LEE ◽  
Y. P. CHENG ◽  
H. T. LOW
Keyword(s):  
Convergence Rate ◽  
Incompressible Flow ◽  
Numerical Results ◽  
Staggered Grid ◽  
Convergence Criterion ◽  
Grid System ◽  
Numerical Examples ◽  
Simpler Algorithm ◽  
Iteration Number ◽  
Relaxation Factors

In this paper, the updating of the intermediate velocity in the correction stage in SIMPLE-like algorithms on staggered grid is discussed in detail, based on the discussion CLEARER algorithm that is extended from the non-staggered grid to the staggered grid. The performance of SIMPLER and CLEARER algorithms are compared using two numerical examples with reliable solutions. The results show that CLEARER can predict the numerical results as accurately as SIMPLER, and it can also enhance the convergence rate greatly under low under-relaxation factors. In some cases CLEARER algorithm can only need 27% of iteration number required by SIMPLER to reach the same convergence criterion.

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