CMES-Vol. 107, No. 6, 2015

Open Access

ARTICLE

A High-Order Accurate Wavelet Method for Solving Three-Dimensional Poisson Problems
Xiaojing Liu^1,2, Jizeng Wang¹, Youhe Zhou¹
CMES-Computer Modeling in Engineering & Sciences, Vol.107, No.6, pp. 433-446, 2015, DOI:10.3970/cmes.2015.107.433
Abstract Based on the approximation scheme for a L²-function defined on a three-dimensional bounded space by combining techniques of boundary extension and Coiflet-type wavelet expansion, a modified wavelet Galerkin method is proposed for solving three-dimensional Poisson problems with various boundary conditions. Such a wavelet-based solution procedure has been justified by solving five test examples. Numerical results demonstrate that the present wavelet method has an excellent numerical accuracy, a fast convergence rate, and a very good capability in handling complex boundary conditions. More >

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ARTICLE

The Accuracy of Mathematical Models in Simulator Distributed Computing
I. Kvasnica¹, P. Kvasnica²
CMES-Computer Modeling in Engineering & Sciences, Vol.107, No.6, pp. 447-462, 2015, DOI:10.3970/cmes.2015.107.447
Abstract The issue of simulation of decentralized mathematical models is discussed in the paper. The authors’ knowledge is based on a theory of design of decentralized computer control systems. Their knowledge is gained in the process of designing mathematical models that are simulated. A decomposed control system is required to meet the conditions of observation and control. The methodology of a multi-model design is based on main principles of object orientation such as abstraction, hierarchy, and modularity. Modelling on a parallel architecture has an impact on a simulator system. The system is defined by the equations More >

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ARTICLE

Kernel-Based Local Meshless Method for Solving Multi-DimensionalWave Equations in Irregular Domain
Marjan Uddin^1,2, Hazrat Ali¹, Amjad Ali¹
CMES-Computer Modeling in Engineering & Sciences, Vol.107, No.6, pp. 463-479, 2015, DOI:10.3970/cmes.2015.107.463
Abstract This work explores the application of kernel based local meshless method for solving multi-dimensional wave equations in irregular domain. The method is tested for various types of boundary conditions in irregular shaped domain. The method is capable of solving multi-dimension large scaled problems in complex shaped domain. More >

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ARTICLE

Meshless Local Petrov-Galerkin and RBFs Collocation Methods for Solving 2D Fractional Klein-Kramers Dynamics Equation on Irregular Domains
M. Dehghan¹, M. Abbaszadeh², A. Mohebbi³
CMES-Computer Modeling in Engineering & Sciences, Vol.107, No.6, pp. 481-516, 2015, DOI:10.3970/cmes.2015.107.481
Abstract In the current paper the two-dimensional time fractional Klein-Kramers equation which describes the subdiffusion in the presence of an external force field in phase space has been considered. The numerical solution of fractional Klein-Kramers equation is investigated. The proposed method is based on using finite difference scheme in time variable for obtaining a semi-discrete scheme. Also, to achieve a full discretization scheme, the Kansa's approach and meshless local Petrov-Galerkin technique are used to approximate the spatial derivatives. The meshless method has already proved successful in solving classic and fractional differential equations as well as for… More >

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