• Title/Summary/Keyword: Implicit method

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Reduction of Computing Time through FDM using Implicit Method and Latent Heat Treatment in Solidification Analysis (FDM에 의한 응고해석시 계산시간 단축을 위한 음적해법의 적용과 잠열처리방법)

  • Kim, Tae-Gyu;Choi, Jung-Kil;Hong, Jun-Pyo;Lee, Zin-Hyoung
    • Journal of Korea Foundry Society
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    • v.13 no.4
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    • pp.323-332
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    • 1993
  • An implicit finite difference formulation with three methods of latent heat treatment, such as equivalent specific heat method, temperature recovery method and enthalpy method, was applied to solidification analysis. The Neumann problem was solved to compare the numerical results with the exact solution. The implicit solutions with the equivalent specific heat method and the temperature recovery method were comparatively consistent with the Neumann exact solution for smaller time steps, but its error increased with increasing time step, especially in predicting the solidification beginning time. Although the computing time to solve energy equation using temperature recovery method was shorter than using enthalpy method, the method of releasing latent heat is not realistic and causes error. The implicit formulation of phase change problem requires enthalpy method to treat the release of latent heat reasonably. We have modified the enthalpy formulation in such a way that the enthalpy gradient term is not needed, and as a result of this modification, the computation stability and the computing time were improved.

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The Semi-Implicit Numerical Scheme for Transient Two-Phase Flows on Unstructured Grids (과도 다차원 2상 유동 해석을 위한 비정렬 격자계에서의 Semi-Implicit 수치 해법 개발)

  • Cho, H.K.;Park, I.K.;Yoon, H.Y.;Kim, J.;Jeong, J.J.
    • Journal of Energy Engineering
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    • v.17 no.4
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    • pp.218-226
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    • 2008
  • A component-scale two-phase analysis code has been developed for a realistic simulation of two-phase flow transients in a light water nuclear reactor component. In the code, a two-fluid three-field model is adopted and the governing equations are solved on an unstructured mesh. For the numerical solution scheme, the semi-implicit method used in the RELAP5 code was selected, which has been proved to be very stable and accurate for most of practical applications. However, some modifications were needed for its application to an unstructured non-staggered grid. This paper presents the modified semi-implicit numerical method for unstructured grid and the preliminary results of the calculations.

Implicit guidance using linear tangent pitch program (선형 탄젠트 피치 프로그램을 이용하는 Implicit 유도)

  • 진재현;탁민제
    • 제어로봇시스템학회:학술대회논문집
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    • 1992.10a
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    • pp.686-691
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    • 1992
  • Implicit guidance algorithm can deal with the trajectory error rapidly, but it has to save much data. If, however, the control variable is represented by a specific function form, a few parameters will suffice to define the control variable. In this paper, we study the method of updating the parameters of the control function for the reduction of trajectory errors. The method proposed here does not require much memory for guidance.

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2-D Consolidation Numerical Analysis of Multi_Layered Soils (II) (다층 지반의 2차원 압밀 수치해석 II)

  • 류권일;김팔규;구기욱;남상규
    • Proceedings of the Korean Geotechical Society Conference
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    • 2000.11a
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    • pp.665-672
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    • 2000
  • The problems of discontinuous layer interface are very important in the algorithm and programming for the analysis of multi-layered consolidation using a numerical analysis, finite difference method(F.D,M.). Better results can be obtained by the process for discontinuous layer interface, since it can help consolidation analysis to model the actual ground Explicit method is simple for analysis algorithm and convenient for use except for applying the operator Crank-Nicolson method represents implicit method, which have different analysis method according to weighting factor. This method uses different algorithm according to dimension. And, this paper uses alternative direction implicit method. The purpose of this paper provides an efficient computer algorithm based on numerical analysis using finite difference method which account for multi-layered soils with confined aquifer to determine the degree of consolidation and excess pore pressures relative to time and positions more realistically.

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A Study on Shifted Multi-Z-Buffers Anti-Aliasing for 3D Implicit Surface Rendering (3차원 임플리시트 곡면 렌더링을 위한 시프트(shifted) 멀티 Z-버퍼 앤티 앨리어싱 연구)

  • Park Hwa Jin;Kim Hak Ran
    • Journal of Korea Multimedia Society
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    • v.8 no.2
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    • pp.249-257
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    • 2005
  • This paper aims at reducing aliasing in pixel-based rendering for 3D implicit surfaces by shifted multi Z-buffers. The voxelized implicit surfaces with high resolution take so much time in generating high Quality image without aliasing. So in rendering a voxelized implicit surfaces, a new antialiasing method which can generate a high quality image at a lower resolution is required. Therefore, this paper suggests that a method which get various sampling values by shifting several z-buffers in each voxel and average them, The advantages are effective memory, simple calculation and easy convergence with various filters. But, the increase of number of z-buffer also increase the consuming time rapidly. Therefore, the research for representing the relation the degree of image quality with the consumption of time as a number is required.

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AN IMPROVED IMPLICIT EULER METHOD FOR SOLVING INITIAL VALUE PROBLEMS

  • YUN, BEONG IN
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.26 no.3
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    • pp.138-155
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    • 2022
  • To solve the initial value problem we present a new single-step implicit method based on the Euler method. We prove that the proposed method has convergence order 2. In practice, numerical results of the proposed method for some selected examples show an error tendency similar to the second-order Taylor method. It can also be found that this method is useful for stiff initial value problems, even when a small number of nodes are used. In addition, we extend the proposed method by using weighted averages with a parameter and show that its convergence order becomes 2 for the parameter near $\frac{1}{2}$. Moreover, it can be seen that the extended method with properly selected values of the parameter improves the approximation error more significantly.

A COMPARISON STUDY OF EXPLICIT AND IMPLICIT NUMERICAL METHODS FOR THE EQUITY-LINKED SECURITIES

  • YOO, MINHYUN;JEONG, DARAE;SEO, SEUNGSUK;KIM, JUNSEOK
    • Honam Mathematical Journal
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    • v.37 no.4
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    • pp.441-455
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    • 2015
  • In this paper, we perform a comparison study of explicit and implicit numerical methods for the equity-linked securities (ELS). The option prices of the two-asset ELS are typically computed using an implicit finite diffrence method because an explicit finite diffrence scheme has a restriction for time steps. Nowadays, the three-asset ELS is getting popularity in the real world financial market. In practical applications of the finite diffrence methods in computational finance, we typically use relatively large space steps and small time steps. Therefore, we can use an accurate and effient explicit finite diffrence method because the implementation is simple and the computation is fast. The computational results demonstrate that if we use a large space step, then the explicit scheme is better than the implicit one. On the other hand, if the space step size is small, then the implicit scheme is more effient than the explicit one.

An Imprevement of the Approximate-Factorization Scheme and Its Application to the Analysis of Incompressible Viscous Flows (근사인자화법의 개량과 비압축성 유동해석에의 응용)

  • 신병록
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.19 no.8
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    • pp.1950-1963
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    • 1995
  • A modification of the approximate-factorization method is made to accelerate the convergency rate and to take sufficiently large Courant number without loss of accuracy. And a stable implicit finite-difference scheme for solving the incompressible Navier-Stokes equations employed above modified method is developed. In the present implicit scheme, the volume fluxes with contravariant velocity components and the pressure formulation in curvilinear coordinates is adopted. In order to satisfy the continuity condition completely and to remove spurious errors for the pressure, the Navier-Stokes equations are solved by a modified SMAC scheme using a staggered gird. The upstream-difference scheme such as the QUICK scheme is also employed to the right hand side. The implicit scheme is unconditionally stable and satisfies a diagonally dominant condition for scalar diagonal linear systems of implicit operator on the left hand side. Numerical results for some test calculations of the two-dimensional flow in a square cavity and over a backward-facing step are obtained using both usual approximate-factorization method and the modified one, and compared with each other. It is shown that the present scheme allows a sufficiently large Courant number of O(10$^{2}$) and reduces the computing time.

Automatic NURBS Surface Generation from Unorganized Point Cloud Data (임의의 점 군 데이터로부터 NURBS 곡면의 자동생성)

  • Yoo, Dong-Jin
    • Journal of the Korean Society for Precision Engineering
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    • v.23 no.9 s.186
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    • pp.200-207
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    • 2006
  • In this paper a new approach which combines implicit surface scheme and NURBS surface interpolation method is proposed in order to generate a complete surface model from unorganized point cloud data. In the method a base surface was generated by creating smooth implicit surface from the input point cloud data through which the actual surface would pass. The implicit surface was defined by a combination of shape functions including quadratic polynomial function, cubic polynomial functions and radial basis function using adaptive domain decomposition method. In this paper voxel data which can be extracted easily from the base implicit surface were used in order to generate rectangular net with good quality using the normal projection and smoothing scheme. After generating the interior points and tangential vectors in each rectangular region considering the required accuracy, the NURBS surface were constructed by interpolating the rectangular array of points using boundary tangential vectors which assure C$^1$ continuity between rectangular patches. The validity and effectiveness of this new approach was demonstrated by performing numerical experiments for the various types of point cloud data.

Comparison of Semi-Implicit Integration Schemes for Rate-Dependent Plasticity (점소성 구성식의 적분에 미치는 선형화 방법의 영향)

  • Yoon, Sam-Son;Lee, Soon-Bok
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.27 no.11
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    • pp.1907-1916
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    • 2003
  • During decades, there has been much progress in understanding of the inelastic behavior of the materials and numerous inelastic constitutive equations have been developed. The complexity of these constitutive equations generally requires a stable and accurate numerical method. To obtain the increment of state variable, its evolution laws are linearized by several approximation methods, such as general midpoint rule(GMR) or general trapezoidal rule(GTR). In this investigation, semi-implicit integration schemes using GTR and GMR were developed and implemented into ABAQUS by means of UMAT subroutine. The comparison of integration schemes was conducted on the simple tension case, and simple shear case and nonproportional loading case. The fully implicit integration(FI) was the most stable but amplified the truncation error when the nonlinearity of state variable is strong. The semi-implicit integration using GTR gave the most accurate results at tension and shear problem. The numerical solutions with refined time increment were always placed between results of GTR and those of FI. GTR integration with adjusting midpoint parameter can be recommended as the best integration method for viscoplastic equation considering nonlinear kinematic hardening.