• Journal of applied mathematics & informatics
• /
• v.6 no.1
• /
• pp.163-174
• /
• 1999

The purpose of this paper is to obtain the solution of Fredholm-Volterra integral equation with singular kernel in the space $L_2(-1, 1)\times C(0,T), 0 \leq t \leq T< \infty$, under certain conditions,. The numerical method is used to solve the Fredholm integral equation of the second kind with weak singular kernel using the Toeplitz matrices. Also the error estimate is computed and some numerical examples are computed using the MathCad package.

• Proceedings of the KSME Conference
• /
• 2001.11a
• /
• pp.341-348
• /
• 2001

A Mixed Volume and Boundary Integral Equation Method is applied for the effective analysis of plane elastostatic problems in unbounded solids containing general anisotropic inclusions and voids or isotropic inclusions. It should be noted that this newly developed numerical method does not require the Green's function for anisotropic inclusions to solve this class of problems since only Green's function for the unbounded isotropic matrix is involved in their formulation for the analysis. This new method can also be applied to general two-dimensional elastodynamic and elastostatic problems with arbitrary shapes and number of anisotropic inclusions and voids or isotropic inclusions. Through the analysis of plane elastostatic problems in unbounded isotropic matrix with orthotropic inclusions and voids or isotropic inclusions, it will be established that this new method is very accurate and effective for solving plane elastic problems in unbounded solids containing general anisotropic inclusions and voids or isotropic inclusions.

• Journal of the Korean Society of Safety
• /
• v.14 no.1
• /
• pp.10-18
• /
• 1999

An integral equation representation of cracks was presented, which differs from well-known "dislocation layer" representation. In this new representation, the integral equation representation of cracks was developed and coupled to the direct boundary-element method for treatment of cracks in finite plane bodies. The method was developed for in-plane(mode I and II) loadings only. In this paper, the method is formulated and applied to various crack problems involving multiple and branch cracks in finite region. The results are compared to exact solutions where available and the method is shown to be very accurate despite of its simplicity.implicity.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.32 no.12
• /
• pp.1072-1087
• /
• 2008

A mixed volume and boundary integral equation method (Mixed VIEM-BIEM) is used to calculate the plane elastostatic field in an isotropic elastic half-plane containing an isotropic or anisotropic inclusion and a void subject to remote loading parallel to the traction-free boundary. A detailed analysis of stress field at the interface between the isotropic matrix and the isotropic or orthotropic inclusion is carried out for different values of the distance between the center of the inclusion and the traction-free surface boundary in an isotropic elastic half-plane containing three different geometries of an isotropic or orthotropic inclusion and a void. The method is shown to be very accurate and effective for investigating the local stresses in an isotropic elastic half-plane containing multiple isotropic or anisotropic inclusions and multiple voids.

• The Transactions of the Korean Institute of Electrical Engineers C
• /
• v.52 no.4
• /
• pp.185-191
• /
• 2003

In this Paper, we propose an accurate and stable solution of the transient electromagnetic response from three-dimensional arbitrarily shaped conducting objects by using a time domain magnetic field integral equation. This method does not utilize the conventional marching-on in time (MOT) solution. Instead we solve the time domain integral equation by expressing the transient behavior of the induced current in terms of temporal expansion functions with decaying exponential functions and Laguerre·polynomials. Since these temporal expansion functions converge to zero as time progresses, the transient response of the induced current does not have a late time oscillation and converges to zero unconditionally. To show the validity of the proposed method, we solve a time domain magnetic field integral equation for three closed conducting objects and compare the results of Mie solution and the inverse discrete Fourier transform (IDFT) of the solution obtained in the frequency domain.

• Journal of applied mathematics & informatics
• /
• v.29 no.1_2
• /
• pp.23-37
• /
• 2011

In this paper, we use a modified Tikhonov regularization method to solve the Fredholm integral equation of the first kind. Under the assumption that measured data are contaminated with deterministic errors, we give two error estimates. The convergence rates can be obtained under the suitable choices of regularization parameters and the number of measured points. Some numerical experiments show that the proposed method is effective and stable.

• Journal of applied mathematics & informatics
• /
• v.9 no.1
• /
• pp.261-275
• /
• 2002

Besides asymptotic method, the method of orthogonal polynomials has been used to obtain the solution of the Fredholm integral equation. The principal (singular) part of the kerne1 which corresponds to the selected domain of parameter variation is isolated. The unknown and known functions are expanded in a Chebyshev polynomial and an infinite a1gebraic system is obtained.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.2 no.2
• /
• pp.67-80
• /
• 1998

In this paper the linear algebraic system obtained from a singular integral equation with variable coeffcients by a quadrature-collocation method is considered. We study this underdetermined system by means of the Moore Penrose generalized inverse. Convergence in compact subsets of [-1, 1] can be shown under some assumptions on the coeffcients of the equation.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.9 no.1
• /
• pp.111-123
• /
• 2005

Here, the Fredholm integral equation with Hilbert kernel is solved numerically, using two different methods. Also the error, in each case, is estimated.

• Computational Structural Engineering
• /
• v.10 no.2
• /
• pp.213-223
• /
• 1997

Calculation of elastic wave fields has important applications in a variety of engineering fields including NDE (Non-destructive evaluation). Scattering problems have been investigated by numerous authors with different solution schemes. For simple geometries of the scatterers (e.g., cylinders or spheres), the analysis of steady-state elastic wave scattering has been carried out using analytical techniques. For arbitrary geometries and multiple inclusions, numerical methods have been developed. Special finite element methods, e.g., the infinite element method and a hybrid method called the Global-Local finite element method have also been developed for this purpose. Recently, the boundary integral equation method has been used successfully to solve scattering problems. In this paper, a volume integral equation method (VIEM) is proposed as a new numerical solution scheme for the solution of general elasto-dynamic problems in unbounded solids containing multiple inclusions and voids or cracks. A boundary integral equation method (BIEM) is also presented for elastic wave scattering problems. The relative advantage of the volume and boundary integral equation methods for solving scattering problems is discussed.