• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 1998년도 가을 학술발표회 논문집
• /
• pp.431-438
• /
• 1998

An efficient solution method is presented to solve the eigenvalue problem arising in tile dynamic analysis of non-proportionally damped structural systems with multiple or close eigenvalues. The proposed method is obtained by applying the modified Newton-Raphson technique and the orthonormal condition of the eigenvectors to the quadratic eigenvalue problem. Even if the shift value is an eigenvalue of the system, the proposed method guarantees nonsingularity, which is analytically proved. The initial values of the proposed method can be taken as the intermediate results of iteration methods or results of approximate methods. Two numerical examples are also presented to demonstrate the effectiveness of the proposed method and the results are compared with those of the well-known subspace iteration method and the Lanczos method.

• 전산구조공학
• /
• 제10권2호
• /
• pp.139-148
• /
• 1997

A finite element method is programmed to analyse the nonlinear behavior of axisymmetric structures. The lst order Mindlin shell theory which takes into account the transversal shear deformation is used to formulate a conical two node element with six degrees of freedom. To evade the shear locking phenomenon which arises in Mindlin type element when the effect of shear deformation tends to zero, the reduced integration of one point Gauss Quadrature at the center of element is employed. This method is the Updated Lagrangian formulation which refers the variables to the state of the most recent iteration. The solution is searched by Newton-Raphson iteration method. The tangent matrix of this method is obtained by a finite difference method by perturbating the degrees of freedom with small values. For the moment this program is limited to the analyses of non-linear elastic problems. For structures which could have elastic stability problem, the calculation is controled by displacement.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제3권2호
• /
• pp.1-4
• /
• 1999

The Helmholtz equation is very important in physics and engineering. However, solution of the Helmholtz equation is in general known as a very difficult phenomenon. For if the ${\omega}$ is negative, the FDM discretized linear system becomes indefinite, whose solution by iterative method requires a very clever preconditioner. In this paper we assume that ${\omega}$ is nonnegative, and determine the optimal ${\rho}$ parameter for the three dimensional ADI iteration for the Helmholtz equation. The ADI(Alternating Direction Implicit) method is also getting new attentions due to the fact that it is very suitable to the vector/parallel computers, for example, as a preconditioner to the Krylov subspace methods. However, classical ADI was developed for two dimensions, and for three dimensions it is known that its convergence behaviour is quite different from that in two dimensions. So far, in three dimensions the so-called Douglas-Rachford form of ADI was developed. It is known to converge for a relatively wide range of ${\rho}$ values but its convergence is very slow. In this paper we determine the necessary conditions of the ${\rho}$ parameter for the convergence and optimal ${\rho}$ for the three dimensional ADI iteration of the Peaceman-Rachford form for the real Helmholtz equation with nonnegative ${\omega}$. Also, we conducted some experiments which is in close agreement with our theory. This straightforward extension of Peaceman-rachford ADI into three dimensions will be useful as an iterative solver itself or as a preconditioner to the the Krylov subspace methods, such as CG(Conjugate Gradient) method or GMRES(m).

• Journal of Electrical Engineering and Technology
• /
• 제11권1호
• /
• pp.1-8
• /
• 2016

It is well known that the behavior of PV curves is similar to a quadratic function. This is used in some papers to approximate PV curves and calculate the maximum-loading point by minimum number of power flow runs. This paper also based on quadratic approximation of the PV curves is aimed at completing previous works so that the computational efforts are reduced and the accuracy is maintained. To do this, an iterative method based on a quadratic function with two constant coefficients, instead of the three ones, is used. This simplifies the calculation of the quadratic function. In each iteration, to prevent the calculations from diverging, the equations are solved on the assumption that voltage magnitude at a selected load bus is known and the loading factor is unknown instead. The voltage magnitude except in the first iteration is selected equal to the one at the nose point of the latest approximated PV curve. A method is presented to put the mentioned voltage in the first iteration as close as possible to the collapse point voltage. This reduces the number of iterations needed to determine the maximum-loading point. This method is tested on four IEEE test systems.

• 한국인터넷방송통신학회논문지
• /
• 제12권4호
• /
• pp.119-130
• /
• 2012

최근 들어 소프트웨어 시스템은 점차적으로 복잡해지고 있으며, 고객(customer)은 보다 빠른 개발을 요구하고 있다. 전통적인(traditional) 순차적 접근법 (Sequential Approach)으로는 이러한 압력에 효과적으로 대처할 수 없어 대안으로 반복적 접근법 (Iterative Approach)이 적용되고 있다. 대표적인 반복적 접근법으로는 래쇼날의 단일화된 프로세스 (Rational Unified Process, RUP)가 있다. 그러나 RUP의 표준화된 수행방법은 단계, 반복과 활동들을 모두 순차적으로 수행하는 형태이다. 그 결과, 하나의 반복에서 수행된 하나의 활동은 다음 반복의 해당 활동이 수행될 때까지 기다려야 하는 인력낭비 현상이 발생한다. RUP를 수행하는 방법으로는 선형 접근법, 순차적 접근법, 중첩된 반복 접근법과 Time-boxed 반복 접근법이 제안되었다. 그러나 이들 방법은 인력낭비 현상 또는 적용시 프로젝트 관리의 어려움이라는 문제점을 갖고 있다. 본 논문은 활동들을 동시에 수행하는 방법을 제안하였다. 동시개발 접근법은 인력 낭비 현상을 방지할 수 있으며, 프로젝트 관리의 어려움도 해결할 수 있는 장점을 갖고 있다.

• Structural Engineering and Mechanics
• /
• 제62권1호
• /
• pp.85-95
• /
• 2017

This paper presents an explicit analytical iteration method for form-finding analysis of suspension bridges. By extending the conventional analytical form-finding method predicated on the elastic catenary theory, two nonlinear governing equations are derived for calculating the accurate unstrained lengths of the entire cable systems both the main cable and the hangers. And for the gradient-based iteration method, the derivation of explicit calculation for the Jacobian matrix while solving the nonlinear governing equation enhances the computational efficiency. The results from sensitivity analysis show well performance of the explicit Jacobian matrix compared with the traditional finite difference method. According to two numerical examples of long span suspension bridges studied, the proposed method is also compared with those reported approaches or the fundamental criterions in suspension bridge structural analysis, which eventually confirms the accuracy and efficiency of the proposed approach.

• Journal of applied mathematics & informatics
• /
• 제36권1_2호
• /
• pp.135-154
• /
• 2018

In this paper, an almost second order overlapping Schwarz method for singularly perturbed third order convection-diffusion type problem is constructed. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region we use the combination of classical finite difference scheme and central finite difference scheme on a uniform mesh while on the non-layer region we use the midpoint difference scheme on a uniform mesh. It is shown that the numerical approximations which converge in the maximum norm to the exact solution. We proved that, when appropriate subdomains are used, the method produces convergence of second order. Furthermore, it is shown that, two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantages of this method used with the proposed scheme are it reduce iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.

• Journal of applied mathematics & informatics
• /
• 제36권3_4호
• /
• pp.181-203
• /
• 2018

In this paper, we have constructed an overlapping Schwarz method for singularly perturbed second order convection-diffusion equations. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region we use the central finite difference scheme on a uniform mesh while on the non-layer region we use the mid-point difference scheme on a uniform mesh. It is shown that the numerical approximations which converge in the maximum norm to the exact solution. When appropriate subdomains are used, the numerical approximations generated from the method are shown to be first order convergent. Furthermore it is shown that, two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantages of this method used with the proposed scheme is it reduces iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.

• Journal of applied mathematics & informatics
• /
• 제27권5_6호
• /
• pp.1343-1359
• /
• 2009

In this paper, we implement a relatively new analytical technique by combining the traditional variational iteration method and the decomposition method which is called as the variational decomposition method (VDM) for solving the sixth-order boundary value problems. The proposed technique is in fact the modification of variatioanal iteration method by coupling it with the so-called Adomian's polynomials. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Comparisons are made to verify the reliability and accuracy of the proposed algorithm. Several examples are given to check the efficiency of the proposed algorithm. We have also considered an example where the VDM is not reliable.

• Journal of electromagnetic engineering and science
• /
• 제2권2호
• /
• pp.81-86
• /
• 2002

This paper presents the full wave analysis of microwave circuits with nonlinear device using the finite difference time domain method. The equivalent current source is used to model nonlinear device and all the electric field components at the nonlinear device are updated by FDTD algorithm. The currents and voltages of nonlinear device are calculated by the state equations and iteration method. To validate the proposed method, the S-parameters of NEC NE72089 MESFET in various conditions are analyzed and the results are compared with those of the ADS. The proposed method is applied to the analysis of a microwave amplifier, which includes NEC NE72089 MESFET. The analysis results obtained by the present method show good agreement with those of the ADS.