• Title/Summary/Keyword: Implicit method

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A NEWTON-IMPLICIT ITERATIVE METHOD FOR NONLINEAR INVERSE PROBLEMS

  • Meng, Zehong;Zhao, Zhenyu
    • Journal of applied mathematics & informatics
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    • v.29 no.3_4
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    • pp.909-920
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    • 2011
  • A regularized Newton method for nonlinear ill-posed problems is considered. In each Newton step an implicit iterative method with an appropriate stopping rule is proposed and analyzed. Under certain assumptions on the nonlinear operator, the convergence of the algorithm is proved and the algorithm is stable if the discrepancy principle is used to terminate the outer iteration. Numerical experiment shows the effectiveness of the method.

A Study on Filling Holes of the Polygon Model using Implicit Surface Scheme (음함수 곡면기법을 이용한 폴리곤 모델의 홀메움에 관한 연구)

  • Yoo Dong-Jin
    • Journal of the Korean Society for Precision Engineering
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    • v.22 no.3 s.168
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    • pp.107-114
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    • 2005
  • A new approach which combines implicit surface scheme and point projection method is presented in order to fill the arbitrarily shaped holes in the polygon model. In the method a trimmed surface which has an outer boundary curve is generated by using the implicit surface scheme and normal projection of point onto the base surface. The base surface is constructed by creating smooth implicit surface from the incomplete polygon model through which the surface should pass. In this paper an implicit surface is defined by a radial basis function, a continuous scalar-valued function over the domain $R^3$. The base surface is the set of all points at which this scalar function takes on the value zero and is created by placing zero-valued constraints at the vertices of the polygon model. In order to show the validity of the present study, various hole fillings are carried out for the complex polygon model of arbitrary topology.

Development of Optimized Compact Finite Difference Schemes (최적화된 집적 유한 차분법을 위한 내재적 시간전진 기법의 개발)

  • Park N. S.;Kim J. W.;Lee D. J.
    • 한국전산유체공학회:학술대회논문집
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    • 1998.11a
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    • pp.7-12
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    • 1998
  • Optimized high-order compact(OHOC) schemes were proposed, which have high spatial order of truncation and resolution to simulate the aeroacoustic problems due to unsteady compressible flows. Generally, numerical schemes are categorized explicit or implicit by time-marching method. In this research, OHOC differences which were developed with explicit time-marching method is used to have implicit formulation and the implicit OHOC differences result in block hepta-diagonal matrix. This paper presents the comparisons between the explicit and implicit OHOC schemes with a second order accuracy of time in the 1-d linear wave convection problem, and between the explicit OHOC scheme of 4th-order accuracy in time and the implicit OHOC scheme of 1st-order accuracy in tine for the 1-d nonlinear wave convection problem. With these comparisons, the characteristics of implicit OHOC scheme are shown in the point of CFL number.

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DEVELOPMENT OF A HIGH-ORDER IMPLICIT DISCONTINUOUS GALERKIN METHOD FOR SOLVING COMPRESSIBLE NAVIER-STOKES EQUATIONS (압축성 Navier-Stokes 방정식 해를 위한 고차 정확도 내재적 불연속 갤러킨 기법의 개발)

  • Choi, J.H.;Lee, H.D.;Kwon, O.J.
    • Journal of computational fluids engineering
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    • v.16 no.4
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    • pp.72-83
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    • 2011
  • A high-order discontinuous Galerkin method for the two-dimensional compressible Navier-Stokes equations was developed on unstructured triangular meshes. For this purpose, the BR2 methd(the second Bassi and Rebay discretization) was adopted for space discretization and an implicit Euler backward method was used for time integration. Numerical tests were conducted to estimate the convergence order of the numerical solutions of the Poiseuille flow for which analytic solutions are available for comparison. Also, the flows around a flat plate, a 2-D circular cylinder, and an NACA0012 airfoil were numerically simulated. The numerical results showed that the present implicit discontinuous Galerkin method is an efficient method to obtain very accurate numerical solutions of the compressible Navier-Stokes equations on unstructured meshes.

A Preconditioned Time Method for Efficient Calculation of Reactive Flow (예조건화 시간차분을 통한 화학반응유동의 효율적 계산)

  • Kim, Seong-Lyong;Jeung, In-Seuck;Choi, Jeong-Yeol
    • 한국연소학회:학술대회논문집
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    • 1999.10a
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    • pp.219-230
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    • 1999
  • The Equations of Chemical kinetics are very stiff, which forces the use of an implicit scheme. The problem of implicit scheme, however, is that the jacobian must be solved at each time step. In this paper, we examined the methodology that can be stable without full chemical jacobian, This method is derived by applying the different time steps to the chemical source term. And the lower triangular chemical jacobian is derived. This is called the preconditioned time differencing method and represents partial implicit method. We show that this method is more stable in chemical kinetics than the full implicit method and that this is more efficient in supersonic combustion problem than the full jacobian method with same accuracy.

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Study on the Numerical Analysis of Nuclear Reactor Kinetics Equations (원자로 동특성 방정식의 수치해석에 관한 연구)

  • Jae Choon Yang
    • Nuclear Engineering and Technology
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    • v.15 no.2
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    • pp.98-109
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    • 1983
  • A two-step alternating direction explicit method is developed to solve the space-dependent reactor kinetics equations in two space dimensions. As a special case in the general class of alternating direction implicit methods, this method is analysed for accuracy and stability. To test the validity of this method it is compared with the implicit-difference method used in the TWIGL program. It is shown that the two methods are closely related. The time dependent neutron fluxes of the pressurized water reactor (PWR), during control rod insertion, and, of the CANDU-PHW reactor, in case of postulated loss of coolant accident, are obtained from the numerical calculation results.

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Automatic Generation of the Input Data for Rapid Prototyping from Unorganized Point Cloud Data (임의의 점 군 데이터로부터 쾌속조형을 위한 입력데이터의 자동생성)

  • Yoo, Dong-Jin
    • Journal of the Korean Society for Precision Engineering
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    • v.24 no.11
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    • pp.144-153
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    • 2007
  • In order to generate the input data for rapid prototyping, a new approach which is based on the implicit surface interpolation method is presented. In the method a surface is reconstructed by creating smooth implicit surface from unorganized cloud of points through which the surface should pass. In the method an implicit surface is defined by the adaptive local shape functions including quadratic polynomial function, cubic polynomial function and RBF(Radial Basis Function). By the reconstruction of a surface, various types of error in raw STL file including degenerated triangles, undesirable holes with complex shapes and overlaps between triangles can be eliminated automatically. In order to get the slicing data for rapid prototyping an efficient intersection algorithm between implicit surface and plane is developed. For the direct usage for rapid prototyping, a robust transformation algorithm for the generation of complete STL data of solid type is also suggested.

An Implicit Integration Method for Joint Coordinate Subsystem Synthesis Method (조인트 좌표계를 이용한 부분시스템 합성방법의 내재적 적분기법)

  • Jo, Jun-Youn;Kim, Myoung-Ho;Kim, Sung-Soo
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.36 no.4
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    • pp.437-442
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    • 2012
  • To analyze a multibody system, this paper proposes an implicit numerical integration method for joint coordinates subsystem synthesis method. To verify the proposed method, a multibody model for an unmanned robot vehicle, which consists of six identical independent suspension systems, is developed. The symbolic method is applied to compute the system Jacobian matrix for the implicit integration method. The proposed method is also verified by performing rough terrain run-over simulation in comparison with the conventional implicit integration method. In addition, to evaluate the efficiency of the proposed method, the CPU time obtained by using this method is compared with that obtained by using the conventional implicit method.

A Study on Filling Holes of Large Polygon Model using Implicit Surface Scheme and Domain Decomposition Method (음함수 곡면기법과 영역 분할법을 이용한 대형 폴리곤 모델의 홀 메움에 관한 연구)

  • Yoo Dong-Jin
    • Journal of the Korean Society for Precision Engineering
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    • v.23 no.1 s.178
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    • pp.174-184
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    • 2006
  • In order to fill the holes with complex shapes in the large polygon model, a new approach which is based on the implicit surface interpolation method combined with domain decomposition method is presented. In the present study, a surface is constructed by creating smooth implicit surface from the incomplete polygon model through which the surface should pass. In the method an implicit surface is defined by a radial basis function, a continuous scalar-valued function over the domain $R^3$ The generated surface is the set of all points at which this scalar function takes on the value zero and is created by placing zero-valued constraints at the vertices of the polygon model. In this paper the well-known domain decomposition method is used in order to treat the large polygon model. The global domain of interest is divided into smaller domains where the problem can be solved locally. LU decomposition method is used to solve a set of small local problems and their local solutions are combined together using the weighting coefficients to obtain a global solution. In order to show the validity of the present study, various hole fillings are carried out fur the large and complex polygon model of arbitrary topology.

Improvement of 3-Dimensional Finite-Difference Beam Propagation Method by Combining the Implicit and the Explicit methods (Implicit와 explicit 방법의 결합에 의한 3차원 유한차분 빔전파 방법의 개선)

  • Kim, Hyun-Jun;O, Beom-Hoan;Park, Se-Geun;Lee, El-Hang;Lee, Seung-Gol
    • Korean Journal of Optics and Photonics
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    • v.15 no.6
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    • pp.555-562
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    • 2004
  • We propose a hybrid method combining the implicit with the explicit methods in order to reduce the calculation time and improve the convergence problem of the 3-dimensional finite-difference beam propagation method. The numerical simulation of a directional coupler is carried out by the proposed method. It is found from the simulation results that the calculation speed of our method is 10 times faster than that of direct solving techniques.