Search results for: convergence method

Authors: H. Abderrezek, M. N. Harmas

Abstract:

DC-DC converters are widely used as reliable power source for many industrial and military applications, computers and electronic devices. Several control methods were developed for DC-DC converters control mostly with asymptotic convergence. Synergetic control (SC) is a proven robust control approach and will be used here in a so-called terminal scheme to achieve finite time convergence. Lyapunov synthesis is adopted to assure controlled system stability. Furthermore particle swarm optimization (PSO) algorithm, based on an integral time absolute of error (ITAE) criterion will be used to optimize controller parameters. Simulation of terminal synergetic control of a DC-DC converter is carried out for different operating conditions and results are compared to classic synergetic control performance, that which demonstrate the effectiveness and feasibility of the proposed control method.

Keywords: DC-DC converter, PSO, finite time, terminal, synergetic control

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Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi

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The main purpose of this paper is to present the Modified Newmark Method of buckling analysis frame considering the effect of the axial load. The discussion will be restricted to plane frameworks containing a constant cross-section for each element. In addition, it is assumed that the frames are prevented from out-of-plane deflection. In this method, stiffness matrix of the structure is considered to be constant. The most important advantage of such a method is that it obtains both upper and lower critical loads. The advanced of the present method is fast convergence, ability to use computer simulations, and ability to model structures with semi-rigid support conditions using linear and rotational spring.

Keywords: buckling, stability, frame, modified newmark method

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Authors: Zainab A. Bu Sinnah, David I. Graham

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The Lattice Boltzmann Method has been developed and used to simulate both steady and unsteady fluid flow problems such as turbulent flows, multiphase flow and flows in the vascular system. As an example, the study of blood flow and its properties can give a greater understanding of atherosclerosis and the flow parameters which influence this phenomenon. The blood flow in the vascular system is driven by a pulsating pressure gradient which is produced by the heart. As a very simple model of this, we simulate plane channel flow under periodic forcing. This pulsatile flow is essentially the standard Poiseuille flow except that the flow is driven by the periodic forcing term. Moment boundary conditions, where various moments of the particle distribution function are specified, are applied at solid walls. We used a second-order single relaxation time model and investigated grid convergence using two distinct approaches. In the first approach, we fixed both Reynolds and Womersley numbers and varied relaxation time with grid size. In the second approach, we fixed the Womersley number and relaxation time. The expected second-order convergence was obtained for the second approach. For the first approach, however, the numerical method converged, but not necessarily to the appropriate analytical result. An explanation is given for these observations.

Keywords: Lattice Boltzmann method, single relaxation time, pulsatile flow, moment based boundary condition

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Authors: Tan Zhang, Zhongjian Wang, Jack Xin, Zhiwen Zhang

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We aim to efficiently compute the spreading speeds of reaction-diffusion-advection (RDA) fronts in divergence-free random flows under the Kolmogorov-Petrovsky-Piskunov (KPP) nonlinearity. We study a stochastic interacting particle method (IPM) for the reduced principal eigenvalue (Lyapunov exponent) problem of an associated linear advection-diffusion operator with spatially random coefficients. The Fourier representation of the random advection field and the Feynman-Kac (FK) formula of the principal eigenvalue (Lyapunov exponent) form the foundation of our method implemented as a genetic evolution algorithm. The particles undergo advection-diffusion and mutation/selection through a fitness function originated in the FK semigroup. We analyze the convergence of the algorithm based on operator splitting and present numerical results on representative flows such as 2D cellular flow and 3D Arnold-Beltrami-Childress (ABC) flow under random perturbations. The 2D examples serve as a consistency check with semi-Lagrangian computation. The 3D results demonstrate that IPM, being mesh-free and self-adaptive, is simple to implement and efficient for computing front spreading speeds in the advection-dominated regime for high-dimensional random flows on unbounded domains where no truncation is needed.

Keywords: KPP front speeds, random flows, Feynman-Kac semigroups, interacting particle method, convergence analysis

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Authors: Yildiray Keskin, Omer Acan, Murat Akkus

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In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations.

Keywords: fractional diffusion equations, Caputo fractional derivative, reduced differential transform method, partial

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Authors: Pius W. Molo Chin

Abstract:

Real life problems such as the Huxley equation are always modeled as nonlinear differential equations. These problems need accurate and reliable methods for their solutions. In this paper, we propose a nonstandard finite difference method in time and the Galerkin combined with the compactness method in the space variables. This coupled method, is used to analyze a two dimensional Huxley equation for the existence and uniqueness of the continuous solution of the problem in appropriate spaces to be defined. We proceed to design a numerical scheme consisting of the aforementioned method and show that the scheme is stable. We further show that the stable scheme converges with the rate which is optimal in both the L2 as well as the H1-norms. Furthermore, we show that the scheme replicates the decaying qualities of the exact solution. Numerical experiments are presented with the help of an example to justify the validity of the designed scheme.

Keywords: Huxley equations, non-standard finite difference method, Galerkin method, optimal rate of convergence

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Authors: A. Baviskar, C. Sandeep, K. Shankar

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Solving Multi-objective Optimization Problems requires faster convergence and better spread. Though existing Evolutionary Algorithms (EA's) are able to achieve this, the computation effort can further be reduced by hybridizing them with innovative strategies. This study is focuses on converging to the pareto front faster while adapting the advantages of Strength Pareto Evolutionary Algorithm-II (SPEA-II) for a better spread. Two different approaches based on optimizing the objective functions independently are implemented. In the first method, the decision variables corresponding to the optima of individual objective functions are strategically used to guide the search towards the pareto front. In the second method, boundary points of the pareto front are calculated and their decision variables are seeded to the initial population. Both the methods are applied to different constrained and unconstrained multi-objective test functions. It is observed that proposed guided search based algorithm gives better convergence and diversity than several well-known existing algorithms (such as NSGA-II and SPEA-II) in considerably less number of iterations.

Keywords: boundary points, evolutionary algorithms (EA's), guided search, strength pareto evolutionary algorithm-II (SPEA-II)

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Authors: Bruna Luisa Ramos Prado Vasques, Mariane Rembold Petraglia, Antonio Petraglia

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This paper investigates MIMO (Multiple-Input Multiple-Output) adaptive filtering techniques for the application of supervised source separation in the context of convolutive mixtures. From the observation that there is correlation among the signals of the different mixtures, an improvement in the NSAF (Normalized Subband Adaptive Filter) algorithm is proposed in order to accelerate its convergence rate. Simulation results with mixtures of speech signals in reverberant environments show the superior performance of the proposed algorithm with respect to the performances of the NLMS (Normalized Least-Mean-Square) and conventional NSAF, considering both the convergence speed and SIR (Signal-to-Interference Ratio) after convergence.

Keywords: adaptive filtering, multi-rate processing, normalized subband adaptive filter, source separation

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Authors: Giorgi Dalakishvili, Goderdzi G. Didebulidze, Maya Todua

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The possibility of sporadic E (Es) layer formation in the mid-latitude nighttime lower thermosphere by horizontal homogeneous and inhomogeneous (vertically and horizontally changing) winds is investigated in 3D by analytical and numerical solutions of continuity equation for dominant heavy metallic ions Fe+. The theory of influence of wind velocity direction, value, and its shear on formation of sporadic E is developed in case of presence the effect of horizontally changing wind (the effect of horizontal convergence). In this case, the horizontal wind with horizontal shear, characterized by compressibility and/or vortices, can provide an additional influence on heavy metallic ions Fe+ horizontal convergence and Es layers density, which can be formed by their vertical convergence caused as by wind direction and values and by its horizontal shear as well. The horizontal wind value and direction have significant influence on ion vertical drift velocity and its minimal negative values of divergence necessary for development of ion vertical convergence into sporadic E type layer. The horizontal wind horizontal shear, in addition to its vertical shear, also influences the ion drift velocity value and its vertical changes and correspondingly on formation of sporadic E layer and its density. The atmospheric gravity waves (AGWs), with relatively smaller horizontal wave length than planetary waves and tidal motion, can significantly influence location of ion vertical drift velocity nodes (where Es layers formation expectable) and its vertical and horizontal shear providing ion vertical convergence into thin layer. Horizontal shear can cause additional influence in the Es layers density than in the case of only wind value and vertical shear only. In this case, depending on wind direction and value in the height region of the lower thermosphere about 90-150 km occurs heavy metallic ions (Fe+) vertical convergence into thin sporadic E type layer. The horizontal wind horizontal shear also can influence on ions horizontal convergence and density and location Es layers. The AGWs modulate the horizontal wind direction and values and causes ion additional horizontal convergence, while the vertical changes (shear) causes additional vertical convergence than in the case without vertical shear. Influence of horizontal shear on sporadic E density and the importance of vertical compressibility of the lower thermosphere, which also can be influenced by AGWs, is demonstrated numerically. For the given wavelength and background wind, the predictability of formation Es layers and its possible location regions are shown. Acknowledgements: This study was funded by Georgian Shota Rustaveli National Science Foundation Grant no. FR17-357.

Keywords: in-homogeneous, sporadic E, thermosphere, wind

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Authors: Angelo I. Aquino, Luis Ma. T. Bo-ot

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We use the Homotopy Analysis Method (HAM) to solve the system of equations modeling the two-level system and extract results which will pinpoint to turbulent behavior. We look at multi-valued solutions as indicative of turbulence or turbulent-like behavior. We take dierent specic cases which result in multi-valued velocities. The solutions are in series form and application of HAM ensures convergence in some region.

Keywords: multivalued solutions, homotopy analysis method, two-level system, equation

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Authors: Hudson Akewe

Abstract:

This research presents complementary results with wider applications on convergence and rate of convergence of classical fixed point theory in Banach spaces to the world of the theory of fixed points of mappings defined in classes of spaces of measurable functions, known in the literature as modular function spaces. The study gives a comprehensive survey of various iterative fixed point results for the classes of multivalued ρ-contractive-like, ρ-quasi-contractive-like, ρ-quasi-contractive, ρ-Zamfirescu and ρ-contraction mappings in the framework of modular function spaces. An example is presented to demonstrate the applicability of the implicit-type iterative schemes to the system of ordinary differential equations. Furthermore, numerical examples are given to show the rate of convergence of the various explicit Kirk-type and implicit Kirk-type iterative schemes under consideration. Our results complement the results obtained on normed and metric spaces in the literature. Also, our methods of proof serve as a guide to obtain several similar improved results for nonexpansive, pseudo-contractive, and accretive type mappings.

Keywords: implicit Kirk-type iterative schemes, multivalued mappings, convergence results, fixed point

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Authors: Agrinë Baraku

Abstract:

This paper focuses on the convergence of the internet, fake news, and democracy. This paper will examine the convergence of these concepts, the tenets of democracy which are affected by the ever-increasing exposure to fake news, and whether the impact strengthens or can further weaken countries with fragile democracies. To demonstrate the convergence and the impact and to further the discussion about this topic, the case of Kosovo is explored. Its position in the Western Balkans makes it even more susceptible to the pressure stemming from geopolitical interests, which intersect with the generation of fake news by different international actors. Domestically, through data generated by Kantar (Index) Kosova Longitudinal Study on Media Measurement Survey (MMS), which focused on media viewership, the trend among Kosovar citizens is traced and then inserted into a bigger landscape, which is compounded by tenuous circumstances and challenges that Kosovo faces. Attention will be paid to what this can tell about where Kosovo currently is and the possibilities of what can be done regarding the phenomenon that is taking place.

Keywords: democracy, disinformation, internet, social media, fake news

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Authors: Philippe Gugler

Abstract:

This contribution reflects some important questions regarding inter alia the economic development occurring in the light of the ASEAN’s goal of creating the ASEAN Economic Community (AEC) by 2015. We observe a continuing economic growth of GDP per capita over recent years despite the negative effects of the world economic crisis. IMF forecasts indicate that this trend will continue. The paper focuses on the analysis and comparison of economic growth trends of ASEAN countries.

Keywords: ASEAN, convergence, divergence, economic growth, globalization, integration

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Authors: R. Sabre

Abstract:

This work focuses on the symmetric alpha stable process with continuous time frequently used in modeling the signal with indefinitely growing variance, often observed with an unknown additive error. The objective of this paper is to estimate this error from discrete observations of the signal. For that, we propose a method based on the smoothing of the observations via Jackson polynomial kernel and taking into account the width of the interval where the spectral density is non-zero. This technique allows avoiding the “Aliasing phenomenon” encountered when the estimation is made from the discrete observations of a process with continuous time. We have studied the convergence rate of the estimator and have shown that the convergence rate improves in the case where the spectral density is zero at the origin. Thus, we set up an estimator of the additive error that can be subtracted for approaching the original signal without error.

Keywords: spectral density, stable processes, aliasing, non parametric

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Authors: Olusola Ezekiel Abolarin, Gift E. Noah

Abstract:

This research work considered an innovative procedure to numerically approximate higher-order Initial value problems (IVP) of ordinary differential equations (ODE) using the Legendre polynomial as the basis function. The proposed method is a half-step, self-starting Block integrator employed to approximate fourth and fifth order IVPs without reduction to lower order. The method was developed through a collocation and interpolation approach. The basic properties of the method, such as convergence, consistency and stability, were well investigated. Several test problems were considered, and the results compared favorably with both exact solutions and other existing methods.

Keywords: initial value problem, ordinary differential equation, implicit off-grid block method, collocation, interpolation

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Authors: Belloufi Mohammed, Sellami Badreddine

Abstract:

Conjugate gradient methods have played a special role for solving large scale optimization problems due to the simplicity of their iteration, convergence properties and their low memory requirements. In this work, we propose a new class of conjugate gradient methods which ensures sufficient descent. Moreover, we propose a new search direction with the Wolfe line search technique for solving unconstrained optimization problems, a global convergence result for general functions is established provided that the line search satisfies the Wolfe conditions. Our numerical experiments indicate that our proposed methods are preferable and in general superior to the classical conjugate gradient methods in terms of efficiency and robustness.

Keywords: unconstrained optimization, conjugate gradient method, sufficient descent property, numerical comparisons

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Authors: Safeer Hussain Khan

Abstract:

In this paper, we prove a strong convergence result using a recently introduced iterative process with contractive-like operators. This improves and generalizes corresponding results in the literature in two ways: the iterative process is faster, operators are more general. In the end, we indicate that the results can also be proved with the iterative process with error terms.

Keywords: contractive-like operator, iterative process, fixed point, strong convergence

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Authors: Sifeddine Abderrahmani, Sonia Bouafia

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The finite element method is the most practical tool for the analysis of structures, whatever the geometrical shape and behavior. It is extensively used in many high-tech industries, such as civil or military engineering, for the modeling of bridges, motor bodies, fuselages, and airplane wings. Additionally, experience demonstrates that engineers like modeling their structures using the most basic finite elements. Numerous models of finite elements may be utilized in the numerical analysis depending on the interpolation field that is selected, and it is generally known that convergence to the proper value will occur considerably more quickly with a good displacement pattern than with a poor pattern, saving computation time. The method for creating finite elements using the strain approach (S.B.A.) is presented in this presentation. When the results are compared with those provided by equivalent displacement-based elements, having the same total number of degrees of freedom, an excellent convergence can be obtained through some application and validation tests using recently developed membrane elements, plate bending elements, and flat shell elements. The effectiveness and performance of the strain-based finite elements in modeling structures are proven by the findings for deflections and stresses.

Keywords: finite elements, plate bending, strain approach, displacement formulation, shell element

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Authors: Malika El Kyal, Ahmed Machmoum

Abstract:

We prove the superlinear convergence of asynchronous multi-splitting methods applied to differential equations. This study is based on the technique of nested sets. It permits to specify kind of the convergence in the asynchronous mode.The main characteristic of an asynchronous mode is that the local algorithm not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays to be substantial and unpredictable. Note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: parallel methods, asynchronous mode, multisplitting, ODE

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Authors: Guangyuan Zhao, Nan Huang, Xuesong Han, Xu Huang

Abstract:

In order to solve the problem of sample dilution in the traditional particle filter algorithm and achieve accurate state estimation in a nonlinear system, a particle filter method based on an improved artificial bee colony (ABC) algorithm was proposed. The algorithm simulated the process of bee foraging and optimization and made the high likelihood region of the backward probability of particles moving to improve the rationality of particle distribution. The opposition-based learning (OBL) strategy is introduced to optimize the initial population of the artificial bee colony algorithm. The convergence factor is introduced into the neighborhood search strategy to limit the search range and improve the convergence speed. Finally, the crossover and mutation operations of the genetic algorithm are introduced into the search mechanism of the following bee, which makes the algorithm jump out of the local extreme value quickly and continue to search the global extreme value to improve its optimization ability. The simulation results show that the improved method can improve the estimation accuracy of particle filters, ensure the diversity of particles, and improve the rationality of particle distribution.

Keywords: particle filter, impoverishment, state estimation, artificial bee colony algorithm

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Authors: S. H. Arnaud Kanga, O. Hili, S. Dabo-Niang

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Spatial prediction is an issue appealing and attracting several fields such as agriculture, environmental sciences, ecology, econometrics, and many others. Although multiple non-parametric prediction methods exist for spatial data, those are based on the conditional expectation. This paper took a different approach by examining a non-parametric spatial predictor of the conditional quantile. The study especially observes the stationary multidimensional spatial process over a rectangular domain. Indeed, the proposed quantile is obtained by inverting the conditional distribution function. Furthermore, the proposed estimator of the conditional distribution function depends on three kernels, where one of them controls the distance between spatial locations, while the other two control the distance between observations. In addition, the almost complete convergence and the convergence in mean order q of the kernel predictor are obtained when the sample considered is alpha-mixing. Such approach of the prediction method gives the advantage of accuracy as it overcomes sensitivity to extreme and outliers values.

Keywords: conditional quantile, kernel, nonparametric, stationary

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Authors: Aymen Laadhari

Abstract:

We present in this paper a fully implicit finite element method tailored for the numerical modeling of inextensible fluidic membranes in a surrounding Newtonian fluid. We consider a highly simplified version of the Canham-Helfrich model for phospholipid membranes, in which the bending force and spontaneous curvature are disregarded. The coupled problem is formulated in a fully Eulerian framework and the membrane motion is tracked using the level set method. The resulting nonlinear problem is solved by a Newton-Raphson strategy, featuring a quadratic convergence behavior. A monolithic solver is implemented, and we report several numerical experiments aimed at model validation and illustrating the accuracy of the proposed method. We show that stability is maintained for significantly larger time steps with respect to an explicit decoupling method.

Keywords: finite element method, level set, Newton, membrane

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Authors: A. Cerrato Casado, C. Guigou, P. Jean

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In this investigation, the particle swarm optimization (PSO) algorithm is used to perform the inversion of the dispersion curves in the spectral analysis of surface waves (SASW) method. This inverse problem usually presents complicated solution spaces with many local minima that make difficult the convergence to the correct solution. PSO is a metaheuristic method that was originally designed to simulate social behavior but has demonstrated powerful capabilities to solve inverse problems with complex space solution and a high number of variables. The dispersion curve of the synthetic soils is constructed by the vertical flexibility coefficient method, which is especially convenient for soils where the stiffness does not increase gradually with depth. The reason is that these types of soil profiles are not normally dispersive since the dominant mode of Rayleigh waves is usually not coincident with the fundamental mode. Multiple synthetic soil profiles have been tested to show the characteristics of the convergence process and assess the accuracy of the final soil profile. In addition, the inversion procedure is applied to multiple real soils and the final profile compared with the available information. The combination of the vertical flexibility coefficient method to obtain the dispersion curve and the PSO algorithm to carry out the inversion process proves to be a robust procedure that is able to provide good solutions for complex soil profiles even with scarce prior information.

Keywords: dispersion, inverse problem, particle swarm optimization, SASW, soil profile

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Authors: M. S. Turan, Dimple

Abstract:

Due to implementation of IFRS by several developed and developing countries, India has no option other than to converge their accounting standards with IFRS. There are over 10,000 listed companies required to implement IFRS in India. IFRS based financial information presented by a company is different from the same information provided by Indian GAAPs. In this study, we have brought out and analyzed the effect of IFRS reporting on the financial statements of selected companies. The results reveal that convergence with IFRS brought prominent positive variations in the values of quick ratio, debt/equity ratio, proprietary ratio and net profit ratio, while negative variation is brought in the values of current ratio, debt to total assets ratio, operating profit ratio, return on capital employed and return on shareholders’ equity ratios. It also presents significant changes in the values of items of balance sheet, profit and loss account and cash flow statement.

Keywords: IFRS, reporting standards, convergence process, results

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Authors: Farangiz Davranbekova

Abstract:

Subject: The study explores the impact of Over-the-Top services in the sports rights market, focusing on football games. This impact is analysed in the big five European football markets. The research entails how the pay-TV market is combating the disruptors' entry, how the fans are adjusting to these changes and how leagues and football clubs are orienting in the transitional period of more choice. Aims and methods: The research aims to offer a general overview of the impact of OTT players in the football rights market. A theoretical framework of Jenkins’ five layers of convergence is implemented to analyse the transition the sports rights market is witnessing from various angles. The empirical analysis consists of secondary research data as and seven expert interviews from three different clusters. The findings are bound by the combination of the two methods offering general statements. Findings: The combined secondary data as well as expert interviews, conducted on five layers of convergence found: 1. Technological convergence presents that football content is accessible through various devices with innovative digital features, unlike the traditional TV set box. 2. Social convergence demonstrates that football fans multitask using various devices on social media when watching the games. These activities are complementary to traditional TV viewing. 3. Cultural convergence points that football fans have a new layer of fan engagement with leagues, clubs and other fans using social media. Additionally, production and consumption lines are blurred. 4. Economic convergence finds that content distribution is diversifying and/or eroding. Consumers now have more choices, albeit this can be harmful to them. Entry barriers are decreased, and bigger clubs feel more powerful. 5. Global convergence shows that football fans are engaging with not only local fans but with fans around the world that social media sites enable. Recommendation: A study on smaller markets such as Belgium or the Netherlands would benefit the study on the impact of OTT. Additionally, examination of other sports will shed light on this matter. Lastly, once the direct-to-consumer model is fully taken off in Europe, it will be of importance to examine the impact of such transformation in the market.

Keywords: sports rights, OTT, pay TV, football

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Authors: E. Tandis, E. Assareh

Abstract:

Designing the optimal shape of MW wind turbine blades is provided in a number of cases through evolutionary algorithms associated with mathematical modeling (Blade Element Momentum Theory). Evolutionary algorithms, among the optimization methods, enjoy many advantages, particularly in stability. However, they usually need a large number of function evaluations. Since there are a large number of local extremes, the optimization method has to find the global extreme accurately. The present paper introduces a new population-based hybrid algorithm called Genetic-Based Bees Algorithm (GBBA). This algorithm is meant to design the optimal shape for MW wind turbine blades. The current method employs crossover and neighborhood searching operators taken from the respective Genetic Algorithm (GA) and Bees Algorithm (BA) to provide a method with good performance in accuracy and speed convergence. Different blade designs, twenty-one to be exact, were considered based on the chord length, twist angle and tip speed ratio using GA results. They were compared with BA and GBBA optimum design results targeting the power coefficient and solidity. The results suggest that the final shape, obtained by the proposed hybrid algorithm, performs better compared to either BA or GA. Furthermore, the accuracy and speed convergence increases when the GBBA is employed

Keywords: Blade Design, Optimization, Genetic Algorithm, Bees Algorithm, Genetic-Based Bees Algorithm, Large Wind Turbine

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Authors: Maryam Moosavi, Hadi Khatibzadeh

Abstract:

The main purpose of this paper is to study the proximal point algorithm for quasi-nonexpansive mappings in Hadamard spaces. △-convergence and strong convergence of cyclic resolvents for a finite family of quasi-nonexpansive mappings one to a fixed point of the mappings are established

Keywords: Fixed point, Hadamard space, Proximal point algorithm, Quasi-nonexpansive sequence of mappings, Resolvent

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Authors: Aymen Laadhari, Gábor Székely

Abstract:

This paper is concerned with the development of a fully implicit and purely Eulerian fluid-structure interaction method tailored for the modeling of the large deformations of elastic membranes in a surrounding Newtonian fluid. We consider a simplified model for the mechanical properties of the membrane, in which the surface strain energy depends on the membrane stretching. The fully Eulerian description is based on the advection of a modified surface tension tensor, and the deformations of the membrane are tracked using a level set strategy. The resulting nonlinear problem is solved by a Newton-Raphson method, featuring a quadratic convergence behavior. A monolithic solver is implemented, and we report several numerical experiments aimed at model validation and illustrating the accuracy of the presented method. We show that stability is maintained for significantly larger time steps.

Keywords: finite element method, implicit, level set, membrane, Newton method

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Authors: Samaneh Rahimirshnani, Hossein Jafari

Abstract:

In this paper, we consider fluid queueing processes fed by an isonormal Gaussian process. We study the correlation structure of the queueing process and the rate of convergence of the running supremum in the queueing process. The Malliavin calculus techniques are applied to obtain relations that show the workload process inherits the dependence properties of the input process. As examples, we consider two isonormal Gaussian processes, the sub-fractional Brownian motion (SFBM) and the fractional Brownian motion (FBM). For these examples, we obtain upper bounds for the covariance function of the queueing process and its rate of convergence to zero. We also discover that the rate of convergence of the queueing process is related to the structure of the covariance function of the input process.

Keywords: queue length process, Malliavin calculus, covariance function, fractional Brownian motion, sub-fractional Brownian motion

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Authors: Geetanjali Panda, Suvrakanti Chakraborty

Abstract:

In this paper, Newton-like descent methods are proposed for unconstrained optimization problems, which use q-derivatives of the gradient of an objective function. First, a local scheme is developed with alternative sufficient optimality condition, and then the method is extended to a global scheme. Moreover, a variant of practical Newton scheme is also developed introducing a real sequence. Global convergence of these schemes is proved under some mild conditions. Numerical experiments and graphical illustrations are provided. Finally, the performance profiles on a test set show that the proposed schemes are competitive to the existing first-order schemes for optimization problems.

Keywords: Descent algorithm, line search method, q calculus, Quasi Newton method

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