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Papers by Hossein Hosseinzade

Mathematical and Computer Modelling, 2012

The boundary element method (BEM) is a popular method of solving linear partial differential equa... more The boundary element method (BEM) is a popular method of solving linear partial differential equations, and it can be applied in many areas of engineering and science including fluid mechanics, acoustics, electromagnetics. The circular arc element (CAE) method is a scheme to discretize the boundary of problems arising in the BEM. In Dehghan and Hosseinzadeh (2011) [10] the order of the convergence of CAE discretization was obtained for the 2D Laplace equation. The current work extends the formulation developed in Dehghan and Hosseinzadeh (2011) [10] to convert CAE to a robust discretization method. In the present paper the upper bound of the CAE's discretization error is determined theoretically for the 2D Laplace equation. Also we present a new method based on the complex space C to obtain CAE's boundary integrals without facing singularity and near singularity. Since there is no efficient approach to treat the near singular integrals of CAE in the BEM literature, the new scheme presented in this paper enhances the CAE discretization significantly. Several test problems are given and the numerical simulations are obtained which confirm the theoretical results.

Engineering Analysis with Boundary Elements, 2011

The boundary element method (BEM) is a popular technique to solve engineering problems. We compar... more The boundary element method (BEM) is a popular technique to solve engineering problems. We compare the circular arc elements (CAE) discretization to both linear and quadratic discretizations. The main aim of this paper is to determine analytical expressions for the ...

Computers & Mathematics with Applications, 2013

A numerical method is presented in this article to deal with the drawback of boundary elements me... more A numerical method is presented in this article to deal with the drawback of boundary elements method (BEM) at corner points. The use of continuous elements instead of the discontinuous ones has been recommended in the BEM literature widely because of the simplicity and accuracy. However the continuous elements lead to certain difficulties for problems where their domains contain corners. In this paper the finite difference method (FDM) has been applied to obtain some constraints for boundary points near the corners to deal with this drawback. Because of its simplicity and capability, the new scheme is applicable on BEM problems for all geometries, all governing equations and general boundary conditions, easily. Since the Dirichlet boundary condition is more critical than the other ones, we will focus on it in the numerical implementation. The numerical results show that the new treatment improves the accuracy of BEM significantly.

Applied Mathematics and Computation, 2010

The solution of Poisson's equation is essential for many branches of science and engineering such... more The solution of Poisson's equation is essential for many branches of science and engineering such as fluid-mechanics, geosciences, and electrostatics. Solution of two-dimensional Poisson's equations is carried out by BEM based on Galerkin Vector Method in which the integrals that appear in the boundary element method are expressed by analytical integration. In this paper, the Galerkin vector method is developed for more general case than presented in the previous works. The integrals are computed for constant and linear elements in BEM. By employing analytical integration in BEM computation, the numerical schemes and coordinate transformations can be avoided. The presented method can also be used for the multiple domain case. The results of the analytical integration are employed in BEM code and the obtained analytical expression will be applied to several examples where the exact solution exists. The produced results are in good agreement with the exact solution.

Applied Mathematical Modelling, 2012

Applied Mathematical Modelling, 2013

ABSTRACT In this article the constant and the continuous linear boundary elements methods (BEMs) ... more ABSTRACT In this article the constant and the continuous linear boundary elements methods (BEMs) are given to obtain the numerical solution of the coupled equations in velocity and induced magnetic field for the steady magneto-hydrodynamic (MHD) flow through a pipe of rectangular and circular sections having arbitrary conducting walls. In recent decades, the MHD problem has been solved using some variations of BEM for some special boundary conditions at moderate Hartmann numbers up to 300. In this paper we develop this technique for a general boundary condition (arbitrary wall conductivity) at Hartmann numbers up to 105105 by applying some new ideas. Numerical examples show the behavior of velocity and induced magnetic field across the sections. Results are also compared with the exact values and the results of some other numerical methods.

Computers & Mathematics with Applications, 2011

The boundary element method (BEM) is a popular method to solve various problems in engineering an... more The boundary element method (BEM) is a popular method to solve various problems in engineering and physics and has been used widely in the last two decades. In high-order discretization the boundary elements are interpolated with some polynomial functions. These polynomials are employed to provide higher degrees of continuity for the geometry of boundary elements, and also they are used as interpolation functions for the variables located on the boundary elements. The main aim of this paper is to improve the accuracy of the high-order discretization in the two-dimensional BEM. In the high-order discretization, both the geometry and the variables of the boundary elements are interpolated with the polynomial function P m , where m denotes the degree of the polynomial. In the current paper we will prove that if the geometry of the boundary elements is interpolated with the polynomial function P m+1 instead of P m , the accuracy of the results increases significantly. The analytical results presented in this work show that employing the new approach, the order of convergence increases from O(L 0) m to O(L 0) m+1 without using more CPU time where L 0 is the length of the longest boundary element. The theoretical results are also confirmed by some numerical experiments.

Finite difference method (FDM) Corner points 2D elliptic equations Continuous and discontinuous b... more Finite difference method (FDM) Corner points 2D elliptic equations Continuous and discontinuous boundary elements Singular value decomposition (SVD)

In this article the constant and the continuous linear boundary elements methods (BEMs) are given... more In this article the constant and the continuous linear boundary elements methods (BEMs) are given to obtain the numerical solution of the coupled equations in velocity and induced magnetic field for the steady magneto-hydrodynamic (MHD) flow through a pipe of rectangular and circular sections having arbitrary conducting walls. In recent decades, the MHD problem has been solved using some variations of BEM for some special boundary conditions at moderate Hartmann numbers up to 300. In this paper we develop this technique for a general boundary condition (arbitrary wall conductivity) at Hartmann numbers up to 10 5 by applying some new ideas. Numerical examples show the behavior of velocity and induced magnetic field across the sections. Results are also compared with the exact values and the results of some other numerical methods. Please cite this article in press as: H. Hosseinzadeh et al., The boundary elements method for magneto-hydrodynamic (MHD) channel flows at high Hartmann numbers, Appl. Math. Modell. (2012), http://dx.

Boundary elements method (BEM) Multiple reciprocity method (MRM) Dual reciprocity method (DRM) 2D... more Boundary elements method (BEM) Multiple reciprocity method (MRM) Dual reciprocity method (DRM) 2D potential problems Singular and near singular integrals The complex space C a b s t r a c t

Boundary element method (BEM) Circular arc element (CAE) Error analysis Singular and near singula... more Boundary element method (BEM) Circular arc element (CAE) Error analysis Singular and near singular boundary integrals Laplace equation a b s t r a c t

Books by Hossein Hosseinzade