Search results for: Traveling Salesman Problem

Authors: Tarek M. Mahmoud

Abstract:

Selecting the routes and the assignment of link flow in a computer communication networks are extremely complex combinatorial optimization problems. Metaheuristics, such as genetic or simulated annealing algorithms, are widely applicable heuristic optimization strategies that have shown encouraging results for a large number of difficult combinatorial optimization problems. This paper considers the route selection and hence the flow assignment problem. A genetic algorithm and simulated annealing algorithm are used to solve this problem. A new hybrid algorithm combining the genetic with the simulated annealing algorithm is introduced. A modification of the genetic algorithm is also introduced. Computational experiments with sample networks are reported. The results show that the proposed modified genetic algorithm is efficient in finding good solutions of the flow assignment problem compared with other techniques.

Keywords: Genetic Algorithms, Flow Assignment, Routing, Computer network, Simulated Annealing.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2256

Authors: Hany Alashwal, Safaai Deris, Razib M. Othman

Abstract:

Predicting protein-protein interactions represent a key step in understanding proteins functions. This is due to the fact that proteins usually work in context of other proteins and rarely function alone. Machine learning techniques have been applied to predict protein-protein interactions. However, most of these techniques address this problem as a binary classification problem. Although it is easy to get a dataset of interacting proteins as positive examples, there are no experimentally confirmed non-interacting proteins to be considered as negative examples. Therefore, in this paper we solve this problem as a one-class classification problem using one-class support vector machines (SVM). Using only positive examples (interacting protein pairs) in training phase, the one-class SVM achieves accuracy of about 80%. These results imply that protein-protein interaction can be predicted using one-class classifier with comparable accuracy to the binary classifiers that use artificially constructed negative examples.

Keywords: Bioinformatics, Protein-protein interactions, One-Class Support Vector Machines

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1989

Authors: Usa Sutthisakorn, Samchai Jirapatarasil

Abstract:

This paper aims to present knowledge management for solving economic problem and poverty in Thai community. A community in Thailand is studied as a case study for master plan or social and economic plan which derived form the research people conducted by themselves in their community. The result shows that community uses knowledge management in recording income and expense, analyzing their consumption, and then systematic planning of the production, distribution and consumption in the community. Besides, community enterprises, that people create as the by-products of master plan, can facilitate diverse economic activities which are able to reduce economic problem and poverty. The knowledge that people gain from solving their problem through building community enterprises are both tacit and explicit knowledge. Four styles of knowledge conversion: socialization,externalization, combination and internalization, are used. Besides, knowledge sharing inside the organization, between organizations and its environment are found. Keywordsknowledge management, community enterprise, Thailand.

Keywords: knowledge management, community enterprise, Thailand

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1485

Authors: María L. Jalón, Feargal Brennan

Abstract:

A non-stationary stochastic optimization methodology is applied to an OWC (oscillating water column) to find the design that maximizes the wave energy extraction. Different temporal cycles are considered to represent the long-term variability of the wave climate at the site in the optimization problem. The results of the non-stationary stochastic optimization problem are compared against those obtained by a stationary stochastic optimization problem. The comparative analysis reveals that the proposed non-stationary optimization provides designs with a better fit to reality. However, the stationarity assumption can be adequate when looking at averaged system response.

Keywords: Non-stationary stochastic optimization, oscillating water column, temporal variability, wave energy.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1380

Authors: Christian Meinecke, Bernd Scholz-Reiter

Abstract:

The integrated problem of production and distribution scheduling is relevant in many industrial applications. Thus, many heuristics to solve this integrated problem have been developed in the last decade. Most of these heuristics use a sequential working principal or a single decomposition and integration approach to separate and solve subproblems. A heuristic using a multi step decomposition and integration approach is presented in this paper and evaluated in a case study. The result show significant improved results compared with sequential scheduling heuristics.

Keywords: Production and outbound distribution, integrated planning, heuristic, decomposition and integration.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2468

Authors: Tunjo Perić, Franjo Bratić

Abstract:

In this paper, the goal programming methodology for solving multiple objective problem of the technological variants and production plan optimization has been applied. The optimization criteria are determined and the multiple objective linear programming model for solving a problem of the technological variants and production plan optimization is formed and solved. Then the obtained results are analysed. The obtained results point out to the possibility of efficient application of the goal programming methodology in solving the problem of the technological variants and production plan optimization. The paper points out on the advantages of the application of the goal programming methodology compare to the Surrogat Worth Trade-off method in solving this problem.

Keywords: Goal programming, multi objective programming, production plan, SWT method, technological variants.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1919

Authors: Haroon Altarawneh, Sattam Allahawiah

Abstract:

This paper has two main ideas. Firstly, it describes Evans and Wurster-s concepts “the trade-off between reach and richness", and relates them to the impact of technology on the virtual markets. Authors Evans and Wurster see the transfer of information as a 'trade'off between richness and reach-. Reach refers to the number of people who share particular information, with Richness ['Rich'] being a more complex concept combining: bandwidth, customization, interactivity, reliability, security and currency. Traditional shopping limits the number of shops the shopper is able to visit due to time and other cost constraints; the time spent traveling consequently leaves the shopper with less time to evaluate the product. The paper concludes that although the Web provides Reach, offering Richness and the sense of community required for creating and sustaining relationships with potential clients could be difficult.

Keywords: Internet, Web sites, Richness and Reach, Ecommerce, virtual markets.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3766

Authors: M. Mahdavi, H. Monsef, A. Bagheri

Abstract:

Discrete particle swarm optimization (DPSO) is a powerful stochastic evolutionary algorithm that is used to solve the large-scale, discrete and nonlinear optimization problems. However, it has been observed that standard DPSO algorithm has premature convergence when solving a complex optimization problem like transmission expansion planning (TEP). To resolve this problem an advanced discrete particle swarm optimization (ADPSO) is proposed in this paper. The simulation result shows that optimization of lines loading in transmission expansion planning with ADPSO is better than DPSO from precision view point.

Keywords: ADPSO, TEP problem, Lines loading optimization.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1619

Authors: Sun-Hee Han, Hun-Jung Lim, Tai-Myoung Chung

Abstract:

Vehicular Ad-Hoc Networks (VANET) can provide communications between vehicles or infrastructures. It provides the convenience of driving and the secure driving to reduce accidents. In VANET, the security is more important because it is closely related to accidents. Additionally, VANET raises a privacy issue because it can track the location of vehicles and users- identity when a security mechanism is provided. In this paper, we analyze the problem of an existing solution for security requirements required in VANET, and resolve the problem of the existing method when a key management mechanism is provided for the security operation in VANET. Therefore, we show suitability of the Long Term Evolution (LTE) in VANET for the solution of this problem.

Keywords: VANET, Privacy, Security, LTE

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1818

Authors: Carol B.Collins, M. H. N Tabrizi

Abstract:

The purposes of this paper are to (1) promote excellence in computer science by suggesting a cohesive innovative approach to fill well documented deficiencies in current computer science education, (2) justify (using the authors- and others anecdotal evidence from both the classroom and the real world) why this approach holds great potential to successfully eliminate the deficiencies, (3) invite other professionals to join the authors in proof of concept research. The authors- experiences, though anecdotal, strongly suggest that a new approach involving visual modeling technologies should allow computer science programs to retain a greater percentage of prospective and declared majors as students become more engaged learners, more successful problem-solvers, and better prepared as programmers. In addition, the graduates of such computer science programs will make greater contributions to the profession as skilled problem-solvers. Instead of wearily rememorizing code as they move to the next course, students will have the problem-solving skills to think and work in more sophisticated and creative ways.

Keywords: Algorithms, CASE, Problem-solving, UML.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1387

Authors: Mohd Amaluddin Yusoff

Abstract:

In this paper, we consider the design of pulse shaping filter using orthogonal Hermite-Rodriguez basis functions. The pulse shaping filter design problem has been formulated and solved as a quadratic programming problem with linear inequality constraints. Compared with the existing approaches reported in the literature, the use of Hermite-Rodriguez functions offers an effective alternative to solve the constrained filter synthesis problem. This is demonstrated through a numerical example which is concerned with the design of an equalization filter for a digital transmission channel.

Keywords: channel equalization filter, Hermite-Rodriguez, pulseshaping filter, quadratic programming.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1947

Authors: Fengxia Zheng, Chuanyun Gu

Abstract:

By using a fixed point theorem of a sum operator, the existence and uniqueness of positive solution for a class of boundary value problem of nonlinear fractional differential equation is studied. An iterative scheme is constructed to approximate it. Finally, an example is given to illustrate the main result.

Keywords: Fractional differential equation, Boundary value problem, Positive solution, Existence and uniqueness, Fixed point theorem of a sum operator.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1484

Authors: Ahmet Faruk Akyuz, Hasan Sakir Bilge

Abstract:

Depth estimation using stereo images is a challenging problem in computer vision. Many different studies have been carried out to solve this problem. With advancing machine learning, tackling this problem is often done with neural network-based solutions. The images used in these studies are mostly in the visible spectrum. However, the need to use the Infrared (IR) spectrum for depth estimation has emerged because it gives better results than visible spectra in some conditions. At this point, we recommend using thermal-thermal (IR) image pairs for depth estimation. In this study, we used two well-known networks (PSMNet, FADNet) with minor modifications to demonstrate the viability of this idea.

Keywords: thermal stereo matching, depth estimation, deep neural networks, CNN

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 695

Authors: Kokiat Aodsup, Thanatchai Kulworawanichpong

Abstract:

This paper describes a finite-difference time-domainFDTD) method to analyze lightning surge propagation in electric transmission lines. Numerical computation of solving the Telegraphist-s equations is determined and investigated its effectiveness. A source of lightning surge wave on power transmission lines is modeled by using Heidler-s surge model. The proposed method was tested against medium-voltage power transmission lines in comparison with the solution obtained by using lattice diagram. As a result, the calculation showed that the method is one of accurate methods to analyze transient lightning wave in power transmission lines.

Keywords: Traveling wave, Lightning surge, Bewley lattice diagram, Telegraphist's equations, Finite-difference time-domain (FDTD) method,

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5331

Authors: Zhang Tianci, Ding Meng, Zuo Hongfu, Zeng Lina, Sun Zejun

Abstract:

Automation of airport operations can greatly improve ground movement efficiency. In this paper, we study the speed profile design problem for advanced airport ground movement control and guidance. The problem is constrained by the surface four-dimensional trajectory generated in taxi planning. A decomposed approach of two stages is presented to solve this problem efficiently. In the first stage, speeds are allocated at control points, which ensure smooth speed profiles can be found later. In the second stage, detailed speed profiles of each taxi interval are generated according to the allocated control point speeds with the objective of minimizing the overall fuel consumption. We present a swarm intelligence based algorithm for the first-stage problem and a discrete variable driven enumeration method for the second-stage problem, since it only has a small set of discrete variables. Experimental results demonstrate the presented methodology performs well on real world speed profile design problems.

Keywords: Airport ground movement, fuel consumption, particle swarm optimization, smoothness, speed profile design.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1941

Authors: S. G. Ponnambalam, Low Seng Kiat

Abstract:

In this paper, a particle swarm optimization (PSO) algorithm is proposed to solve machine loading problem in flexible manufacturing system (FMS), with bicriterion objectives of minimizing system unbalance and maximizing system throughput in the occurrence of technological constraints such as available machining time and tool slots. A mathematical model is used to select machines, assign operations and the required tools. The performance of the PSO is tested by using 10 sample dataset and the results are compared with the heuristics reported in the literature. The results support that the proposed PSO is comparable with the algorithms reported in the literature.

Keywords: Machine loading problem, FMS, Particle Swarm Optimization.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2121

Authors: Hayedeh Ahrabian, Comfar Badamchi, Abbass Nowzari-Dalini

Abstract:

In this paper, two versions of an iterative loopless algorithm for the classical towers of Hanoi problem with O(1) storage complexity and O(2n) time complexity are presented. Based on this algorithm the number of different moves in each of pegs with its direction is formulated.

Keywords: Loopless algorithm, Binary tree, Towers of Hanoi.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4838

Authors: Siddhartha Chauhan, Nitin Kumar Kotania

Abstract:

Traditional Wireless Sensor Networks (WSNs) generally use static sinks to collect data from the sensor nodes via multiple forwarding. Therefore, network suffers with some problems like long message relay time, bottle neck problem which reduces the performance of the network.

Many approaches have been proposed to prevent this problem with the help of mobile sink to collect the data from the sensor nodes, but these approaches still suffer from the buffer overflow problem due to limited memory size of sensor nodes. This paper proposes an energy efficient scheme for data gathering which overcomes the buffer overflow problem. The proposed scheme creates virtual grid structure of heterogeneous nodes. Scheme has been designed for sensor nodes having variable sensing rate. Every node finds out its buffer overflow time and on the basis of this cluster heads are elected. A controlled traversing approach is used by the proposed scheme in order to transmit data to sink. The effectiveness of the proposed scheme is verified by simulation.

Keywords: Buffer overflow problem, Mobile sink, Virtual grid, Wireless sensor networks.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1826

Authors: Yongzhong Wu, Ping Ji

Abstract:

This paper proposes a genetic algorithm based on a new replacement strategy to solve the quadratic assignment problems, which are NP-hard. The new replacement strategy aims to improve the performance of the genetic algorithm through well balancing the convergence of the searching process and the diversity of the population. In order to test the performance of the algorithm, the instances in QAPLIB, a quadratic assignment problem library, are tried and the results are compared with those reported in the literature. The performance of the genetic algorithm is promising. The significance is that this genetic algorithm is generic. It does not rely on problem-specific genetic operators, and may be easily applied to various types of combinatorial problems.

Keywords: Quadratic assignment problem, Genetic algorithm, Replacement strategy, QAPLIB.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2749

Authors: Gopi Ram, Durbadal Mandal, Rajib Kar, Sakti Prasad Ghoshal

Abstract:

A design problem of non-uniform circular antenna arrays for maximum reduction of both the side lobe level (SLL) and first null beam width (FNBW) is dealt with. This problem is modeled as a simple optimization problem. The method of Firefly algorithm (FFA) is used to determine an optimal set of current excitation weights and antenna inter-element separations that provide radiation pattern with maximum SLL reduction and much improvement on FNBW as well. Circular array antenna laid on x-y plane is assumed. FFA is applied on circular arrays of 8-, 10-, and 12- elements. Various simulation results are presented and hence performances of side lobe and FNBW are analyzed. Experimental results show considerable reductions of both the SLL and FNBW with respect to those of the uniform case and some standard algorithms GA, PSO and SA applied to the same problem.

Keywords: Circular arrays, First null beam width, Side lobe level, FFA.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3176

Authors: Chuanyun Gu, Shouming Zhong

Abstract:

In this paper, the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problem is concerned by a fixed point theorem of a sum operator. Our results can not only guarantee the existence and uniqueness of positive solution, but also be applied to construct an iterative scheme for approximating it. Finally, the example is given to illustrate the main result.

Keywords: Fractional differential equation, Boundary value problem, Positive solution, Existence and uniqueness, Fixed point theorem of a sum operator

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1491

Authors: Adam Galuszka, Krzysztof Skrzypczyk, Damian Bereska, Marcin Pacholczyk

Abstract:

In this paper an average number of re-handlings analysis is proposed to solve the problem of finding bays configuration in small container terminal in Gliwice, Poland. Rehandlings in this terminal can be performed only by reachstackers. The goal of the heuristic is to plan the reachstacter moves in the terminal, assuming that the target containers are reached and the number of re-handings is minimized. The real situation requires also to take into account the model of the problem environment uncertainty caused by the fact that many containers are not delivered to the terminal on time, or can not be sent on scheduled time. To enable this, the heuristic uses some assumptions to simplify problem analysis.

Keywords: Container Terminal, Re-handling operations, Computational efficiency, WiMax.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2631

Authors: Somkiat Lerkvaranyu, Yoshikazu Miyanaga

Abstract:

In this paper, a new technique of signal detection has been proposed for detecting the orthogonal frequency-division multiplexing (OFDM) signal in the presence of nonlinear distortion.There are several advantages of OFDM communications system.However, one of the existing problems is remain considered as the nonlinear distortion generated by high-power-amplifier at the transmitter end due to the large dynamic range of an OFDM signal. The proposed method is the maximum likelihood detection with the symbol estimation. When the training data are available, the neural network has been used to learn the characteristic of received signal and to estimate the new positions of the transmitted symbol which are provided to the maximum likelihood detector. Resulting in the system performance, the nonlinear distortions of a traveling wave tube amplifier with OFDM signal are considered in this paper.Simulation results of the bit-error-rate performance are obtained with 16-QAM OFDM systems.

Keywords: OFDM, TWTA, nonlinear distortion, detection.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1679

Authors: Maatoug Hassine, Mourad Hrizi

Abstract:

In this paper, we consider a geometric inverse source problem for the heat equation with Dirichlet and Neumann boundary data. We will reconstruct the exact form of the unknown source term from additional boundary conditions. Our motivation is to detect the location, the size and the shape of source support. We present a one-shot algorithm based on the Kohn-Vogelius formulation and the topological gradient method. The geometric inverse source problem is formulated as a topology optimization one. A topological sensitivity analysis is derived from a source function. Then, we present a non-iterative numerical method for the geometric reconstruction of the source term with unknown support using a level curve of the topological gradient. Finally, we give several examples to show the viability of our presented method.

Keywords: Geometric inverse source problem, heat equation, topological sensitivity, topological optimization, Kohn-Vogelius formulation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1119

Authors: Nabil M. Hewahi, Motaz K. Saad

Abstract:

In large datasets, identifying exceptional or rare cases with respect to a group of similar cases is considered very significant problem. The traditional problem (Outlier Mining) is to find exception or rare cases in a dataset irrespective of the class label of these cases, they are considered rare events with respect to the whole dataset. In this research, we pose the problem that is Class Outliers Mining and a method to find out those outliers. The general definition of this problem is “given a set of observations with class labels, find those that arouse suspicions, taking into account the class labels". We introduce a novel definition of Outlier that is Class Outlier, and propose the Class Outlier Factor (COF) which measures the degree of being a Class Outlier for a data object. Our work includes a proposal of a new algorithm towards mining of the Class Outliers, presenting experimental results applied on various domains of real world datasets and finally a comparison study with other related methods is performed.

Keywords: Class Outliers, Distance-Based Approach, Outliers Mining.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3388

Authors: Xiaofei Hu, Zhiyu Cai, Weian Yao

Abstract:

V-notch problem under dynamic loading condition is considered in this paper. In the time domain, the precise time domain expanding algorithm is employed, in which a self-adaptive technique is carried out to improve computing accuracy. By expanding variables in each time interval, the recursive finite element formulas are derived. In the space domain, a Symplectic Analytical Singular Element (SASE) for V-notch problem is constructed addressing the stress singularity of the notch tip. Combining with the conventional finite elements, the proposed SASE can be used to solve the dynamic stress intensity factors (DSIFs) in a simple way. Numerical results show that the proposed SASE for V-notch problem subjected to dynamic loading condition is effective and efficient.

Keywords: V-notch, dynamic stress intensity factor, finite element method, precise time domain expanding algorithm.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1332

Authors: Songtao Chang, Yongji Wang, Lei Liu, Dangjun Zhao

Abstract:

Reentry trajectory optimization is a multi-constraints optimal control problem which is hard to solve. To tackle it, we proposed a new algorithm named CDEN(Constrained Differential Evolution Newton-Raphson Algorithm) based on Differential Evolution( DE) and Newton-Raphson.We transform the infinite dimensional optimal control problem to parameter optimization which is finite dimensional by discretize control parameter. In order to simplify the problem, we figure out the control parameter-s scope by process constraints. To handle constraints, we proposed a parameterless constraints handle process. Through comprehensive analyze the problem, we use a new algorithm integrated by DE and Newton-Raphson to solve it. It is validated by a reentry vehicle X-33, simulation results indicated that the algorithm is effective and robust.

Keywords: reentry vehicle, trajectory optimization, constraint optimal, differential evolution.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1735

Authors: S. Khanpour, A. Movaghar

Abstract:

The one of best robust search technique on large scale search area is heuristic and meta heuristic approaches. Especially in issue that the exploitation of combinatorial status in the large scale search area prevents the solution of the problem via classical calculating methods, so such problems is NP-complete. in this research, the problem of winner determination in combinatorial auctions have been formulated and by assessing older heuristic functions, we solve the problem by using of genetic algorithm and would show that this new method would result in better performance in comparison to other heuristic function such as simulated annealing greedy approach.

Keywords: Bids, genetic algorithm, heuristic, metaheuristic, simulated annealing greedy.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1790

Authors: Carol B. Collins, M. H. N Tabrizi

Abstract:

The purposes of this paper are to (1) promote excellence in computer science by suggesting a cohesive innovative approach to fill well documented deficiencies in current computer science education, (2) justify (using the authors' and others anecdotal evidence from both the classroom and the real world) why this approach holds great potential to successfully eliminate the deficiencies, (3) invite other professionals to join the authors in proof of concept research. The authors' experiences, though anecdotal, strongly suggest that a new approach involving visual modeling technologies should allow computer science programs to retain a greater percentage of prospective and declared majors as students become more engaged learners, more successful problem-solvers, and better prepared as programmers. In addition, the graduates of such computer science programs will make greater contributions to the profession as skilled problem-solvers. Instead of wearily rememorizing code as they move to the next course, students will have the problem-solving skills to think and work in more sophisticated and creative ways.

Keywords: Algorithms, CASE, UML, Problem-solving.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1616

Authors: Abida Harbi

Abstract:

We provide a maximum norm analysis of a finite element Schwarz alternating method for a nonlinear elliptic boundary value problem of the form -Δu = f(u), on two overlapping sub domains with non matching grids. We consider a domain which is the union of two overlapping sub domains where each sub domain has its own independently generated grid. The two meshes being mutually independent on the overlap region, a triangle belonging to one triangulation does not necessarily belong to the other one. Under a Lipschitz assumption on the nonlinearity, we establish, on each sub domain, an optimal L∞ error estimate between the discrete Schwarz sequence and the exact solution of the boundary value problem.

Keywords: Error estimates, Finite elements, Nonlinear PDEs, Schwarz method.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2756