• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.215-222
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• 2000

A multigrid algorithm is developed for solving the one- dimensional initial boundary value problem. The numerical solutions of linear and nonlinear Burgers; equation for various initial conditions are studied. The stability conditions are derived by Von -Neumann analysis . Numerical results are presented.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.1
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• pp.10-17
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• 1985

A new method is suggested for the solution of plane elasticity problems. With use of the dislocation model in the crack problems, the basic scheme of this method is to find equilibrium Burgers vectors of dislocations which are distributed along the boundary of the first fundamental boundary value problems. The stress distribution in the region can be found by superposition of the contributions of each dislocation. The method is applied to three cases with known analytical solutions, and to a V-notched specimen under uniaxial tension. The numerical results are compared with other available solutions. This method is effective and simple in its use, compared with other numerical methods. The method also provides very accurate solutions in the region except near the boundary where the discretization error is significant. The extrapolation method is suggested for the stresses in the boundary region. Extensive application are also suggested for a general estimate of the computational efficiency of the method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.415-429
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• 2002

Various modeling techniques for ultrasonic wave propagation and scattering problems in finite solid media are presented. Elastodynamic boundary value problems in inhomogeneous multi-layered plate-like structures are set up for modal analysis of guided wave propagation and numerically solved to obtain dispersion curves which show propagation characteristics of guided waves. As a powerful modeling tool to overcome such numerical difficulties in wave scattering problems as the geometrical complexity and mode conversion, the Boundary Element Method(BEM) is introduced and is combined with the normal mode expansion technique to develop the hybrid BEM, an efficient technique for modeling multi-mode conversion of guided wave scattering problems.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.365-383
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• 2001

We consider path integrals, more precisely projective systems of Fresnel distributions, associated with Sturm-Liouville boundary value problems.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1057-1069
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• 2008

We consider singularly perturbed Boundary Value Problems (BVPs) for third and fourth order Ordinary Differential Equations(ODEs) of convection-diffusion type with discontinuous source term and a small positive parameter multiplying the highest derivative. Because of the type of Boundary Conditions(BCs) imposed on these equations these problems can be transformed into weakly coupled systems. In this system, the first equation does not have the small parameter but the second contains it. In this paper a computational method named as 'An asymptotic finite element method' for solving these systems is presented. In this method we first find an zero order asymptotic approximation to the solution and then the system is decoupled by replacing the first component of the solution by this approximation in the second equation. Then the second equation is independently solved by a fitted mesh Finite Element Method (FEM). Numerical experiments support our theoritical results.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.235-244
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• 2012

In this paper, we solve the three-dimensional biharmonic equation with Dirichlet boundary conditions of second kind using the full multigrid (FMG) algorithm. We derive a finite difference approximations for the biharmonic equation on a 18 point compact stencil. The unknown solution and its second derivatives are carried as unknowns at grid points. In the multigrid methods, we use a fourth order interpolation to producing a new intermediate unknown functions values on a finer grid, and the full weighting restriction operators to calculating the residuals at coarse grid points. A set of test problems gives excellent results.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1991.04a
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• pp.8-14
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• 1991

The finite element technique incorporating infinite elements is applied to analyzing the general three dimensional wave-structure interaction problems within the limits of linear wave theory. The hydrodynamic farces are assumed to be inertially dominated, and viscous effects are neglected. In order to analyze the corresponding boundary value problems efficiently, two types of elements are developed. One is the infinite element for modeling the radiation condition at infinity, and the other is the fictitious bottom boundary element for the case of deep water. To validate those elements, numerical analyses are performed for several floating structures. Comparisons with the results from culler available solution methods show that the present method incorporating tile infinite and the fictitious bottom boundary elements gives good results.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.191-200
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• 2011

This paper deals with second order differential equations with different deviated arguments ${\alpha}$(t) and ${\beta}$(t, ${\mu}$(t)). We investigate the existence of solutions of such problems with nonlinear mixed boundary conditions. To obtain corresponding results we apply the monotone iterative technique and the lower-upper solutions method. Two examples demonstrate the application of our results.

• Steel and Composite Structures
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• v.2 no.2
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• pp.99-112
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• 2002

The differential quadrature method (DQM) is a numerical technique of rather recent origin, which by its continually increasing applications in different problems of engineering, is a competing alternative to the conventional numerical techniques for the solution of initial and boundary value problems. The work of this paper concerns the application of the DQM in the area of the buckling of multi layered orthotropic composite plates with various boundary conditions the buckling of multi layered composite plates with constant and variable thickness under axial compressive static loading is considered. The effects of fiber orientation and boundary conditions on static behavior of composite plates are presented. The comparison of results from the present method and those obtained from NISA II software shows the accuracy and reliability of this method.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.5
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• pp.413-420
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• 2012

In this study, the Kernel integration scheme for 2D linear elastic direct boundary element method has been discussed on the basis of subparametric element. Usually, the isoparametric based boundary element uses same polynomial order in the both basis function and mapping function. On the other hand, the order of mapping function is lower than the order of basis function to define displacement field when the subparametric concept is used. While the logarithmic numerical integration is generally used to calculate Kernel integration as well as Cauchy principal value approach, new formulation has been derived to improve the accuracy of numerical solution by algebraic modification. The subparametric based direct boundary element has been applied to 2D elliptical partial differential equation, especially for plane stress/strain problems, to demonstrate whether the proposed algebraic expression for integration of singular Kernel function is robust and accurate. The problems including cantilever beam and square plate with a cutout have been tested since those are typical examples of simple connected and multi connected region cases. It is noted that the number of DOFs has been drastically reduced to keep same degree of accuracy in comparison with the conventional isoparametric based BEM. It is expected that the subparametric based BEM associated with singular Kernel function integration scheme may be extended to not only subparametric high order boundary element but also subparametric high order dual boundary element.