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 shown below. An important part… More >

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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 several other engineering and physical… More >

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