• 대한조선학회논문집
• /
• 제32권1호
• /
• pp.58-69
• /
• 1995

본 논문에서는 이상유체모델에서의 비선형 자유표면파의 발생, 전파 및 상호간섭에 대한 비정상 문제의 수치해법을 개발하였다. 본 수치해법은 매 시간 스텝에서 비선형 축차해법을 이용한 음함수적(implicit)방법이다. 속도장함수를 구하기 위하여 경계접합좌표계를 도입한 유한차분법을 이용하였다. 본 수치해법의 유효성과 효율성의 검증을 위하여 타원형 유체의 변형과 바닥의 일부분이 올라옴으로서 발생하는 자유표면파의 생성에 대한 두 가지 계산결과를 보여준다.

• 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).

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제20권1호
• /
• pp.51-57
• /
• 2013

In this paper, we introduce asymptotically quasi-$f-g$-nonexpansive mappings in convex normed vector spaces and consider approximating common fixed points of a sequence of asymptotically quasi-$f-g$-nonexpansive mappings in convex normed vector spaces.

• Kyungpook Mathematical Journal
• /
• 제52권3호
• /
• pp.327-346
• /
• 2012

In this paper, we present a simple explicit type numerical method for discretizations in time for solving one dimensional Burgers' equations. The proposed method does not need an iteration process that may be required in most implicit methods and have good convergence and efficiency in computational sense compared to other known numerical methods. For evidences, several numerical demonstrations are also provided.

• 소성∙가공
• /
• 제12권8호
• /
• pp.710-717
• /
• 2003

The implicit, finite element analysis program for analyzing the springback in the warm forming process of aluminum alloy sheets was developed. For the description of planar anisotropy in warm forming temperatures, Barlat's yield function is employed, and the power law type constitutive equation is used in terms of working temperatures for the depiction of work hardening in high temperatures. Also, Jetture's 4-node shell elements are introduced for reflecting the mechanical behavior of aluminum alloy sheet and the non-steady heat balance equations are solved for considering heat gain and loss during the forming process. For the springback evaluation, Newton-Raphson iteration method is introduced for overcoming the geometric nonlinearlity problem. In order to verify the validity of the FEM program developed, the stretching bending and springback processes are simulated. Though springback analysis results are slightly bigger than experimental ones, they have the same trend of the decreasing springback as the forming temperature increases.

• 한국소성가공학회:학술대회논문집
• /
• 한국소성가공학회 2003년도 제4회 박판성형 심포지엄
• /
• pp.13-20
• /
• 2003

The implicit, finite element analysis program for analyzing the springback in the warm forming process of aluminum alloy sheets was developed. For the description of planar anisotropy in warm forming temperatures, Barlat's yield function is employed, and the power law type constitutive equation is used in terms of working temperatures fur the depiction of work hardening in high temperatures. Also, Jetture's 4-node shell elements are introduced for reflecting the mechanical behavior of aluminum alloy sheet and the non-steady heat balance equations are solved for considering heat gain and loss during the forming process. For the springback evaluation, Newton-Raphson iteration method is introduced for overcoming the geometric nonlinearlity problem. In order to verify the validity of the FEM program developed, the stretching bending and springback processes are simulated. Though springback analysis results are slightly bigger than experimental ones, they have the same trend of the decreasing springback as the forming temperature increases.

• 한국지반공학회논문집
• /
• 제22권9호
• /
• pp.45-59
• /
• 2006

탄소성 구성방정식은 주로 미분방적식(rate equation)으로 이루어져 있기 때문에 유한요소법 등을 이용한 지반구조물 해석시 미분방정식들에 대한 수치적분을 수행할 수 있는 방법이 필요하다. 구조물의 거동을 해석할시 미분방정식들을 위한 적분방법은 해석결과의 정확성과 유한요소법 모델링의 안전성에 큰 영향을 미치고 있다. 본 논문에서는 최근에 개발되어 사용되고 있는 흙에 관한 구성모델인 "Two-surface soil plasticity model (Manzari and Dafalias 1997)"을 Implicit return-mapping 수치적분방법을 이용하여 실행하는 과정을 제시한다. 본 연구에서 사용된 수치적분방법은 Closest-Point-Projection Method(CPPM) 방법으로 탄성 예측자-소성 교정자(elastic predictor-plastic corrector) 개념을 Implicit Backward Euler방법으로 체계화 시킨 알고리듬이다. 본 연구에서 수행한 "Two-surface soil plasticity model"은 조립토의 비선형거동을 해석하며, Bounding surface 개념 및 비선형 등방경화와 이동경화법칙을 사용하는 모델이다. 본 연구는 CPPM 방법이 정확하고 안정되며 유용한 수치적분을 수행할 수 있는 알고리듬이라는 것을 제시한다. 또한, CPPM 알고리듬은 구성방정식의 해를 반복적으로 해석하는 동안 "Consistent tangent operator $d{\sigma}/d{\varepsilon}$"를 제공하므로, 비선형 유한요소 해석이 2차(quadratic convergence rate)의 수렴 조건을 만족하는데 기여한다는 것을 보여준다.

• 한국게임학회 논문지
• /
• 제18권5호
• /
• pp.123-132
• /
• 2018

실시간 그래픽스 응용에서 연체의 움직임을 효율적으로 생성하기 위해 다양한 방법이 제안되었다. 연체 구성 요소들의 위상을 유지하기 위해서는 서로를 묶는 힘이 존재할 수밖에 없으며, 이는 강직도(stiffness)로서 수치적분의 시간간격의 크기를 제한하고 효율성을 떨어트린다. 이를 해결하기 위해 시간간격을 늘릴 수 있는 암시적 적분이 제안되었지만, 대규모 행렬이 포함된 선형시스템을 풀어야 해서 계산복잡도가 크게 높아진다. 이 문제를 개선한 근사 기법들은 댐핑 효과의 증가와 정확성의 손실을 초래할 수밖에 없다. 본 논문에서는 선형시스템을 풀지 않고도 안정성은 크게 높이기 위해 조화진동에 근거하여 스프링 힘을 적분하고, 이를 근사 암시적 기법과 결합하여 안정성을 극대화 하는 방법을 제안한다. 이 기법은 GPU를 통한 병렬화가 용이하여 거대한 규모를 가진 연체 객체의 움직임을 실시간에 생성할 수 있다.

• 한국전산유체공학회지
• /
• 제13권4호
• /
• pp.33-38
• /
• 2008

For study on the unsteady blockage effect, flows around a rotationally oscillating circular cylinder with relatively low forcing frequency in closed test-section wind tunnels have been numerically investigated by solving compressible Navier-Stokes equations. The numerical scheme is based on a node-based finite-volume method with the Roe's flux-difference splitting and an implicit time-integration method coupled with dual time-step sub-iteration. The computed results of the oscillating cylinder in the test section showed that the fluctuations of lift and drag are augmented by the blockage effects. The drag further increases because of low base pressure. The pressure on the test section wall shows the harmonics having the oscillating and the shedding frequencies contained in the blockage effect.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2005년도 춘계학술대회논문집
• /
• pp.662-667
• /
• 2005

Nonlinear dynamics of active piezolaminated plates are investigated with respect to the thermopiezoelastic behaviors. For largely deformed structures with small strain, the incremental total Lagrangian formulation is presented based on the virtual work principles. A multi field layer wise finite shell element is proposed for assuring high accuracy and non-linearity of displacement, electric and thermal fields. For dynamic consideration of thermopiezoelastic snap through phenomena, the implicit Newmark's scheme with the Newton-Raphson iteration is implemented for the transient response of various piezolaminated models with symmetric or eccentric active layers. The bifurcate thermal buckling of symmetric structural models is first investigated and the characteristics of piezoelectric active responses are studied for finding snap through piezoelectric potentials and the load path tracking map. The thermoelastic stable and unstable postbuckling, thermopiezoelastic snap through phenomena with several attractors are proved using the nonlinear time responses for various initial conditions and damping loss factors. Present results show that thermopiezoelastic snap through phenomena can result in the difficulty of buckling and postbuckling control of intelligent structures.