• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제2권2호
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• pp.21-25
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• 1998

An algorithm for a solution of ordinary differential equations using a modified corrector in the Adams predictor-corrector method of order four is described. The Lagrange interpolation used in the corrector of the Adams method is replaced partially by the cubic spline interpolation satisfying the first derivative constraints at the two end points. By exhibiting three examples, we show that the proposed method is more effcient when the solution of a differential equation is highly oscillating.

• 한국해양학회지:바다
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• 제12권3호
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• pp.133-141
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• 2007

장파와 단파의 거동을 동시에 모의할 수 있는 확장형 Boussinesq 방정식에 대한 유한요소모형을 개발하였다. 3차 공간 미분항을 처리하기 위한 추가변수를 도입하고 Galerkin 가중잔차방법을 적용하여 모형을 수립하였으며, 시간적분방법으로 Adams-Bashforth-Moulton Predictor Corrector 기법을 적용하여 비물리적인 수치분산이나 수치소산 현상을 줄일 수 있도록 하였다. 이 개발된 모형을 검증하기 위해 고립파가 전파하는 문제에 적용을 하였다. 개발된 모형을 적용한 결과 이론해 또는 수리실험 결과에 매우 양호한 일치를 보였다.

• 한국전산응용수학회:학술대회논문집
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• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
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• pp.16.2-16
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• 2003

미분 방정식의 수치적 해를 나타내는 방법 중 예측자-수정자 방법(predictor-corrector method)으로 알려진 Adams-Bashford-Moulton 방법은 다단계 방법을 이용하기 때문에 일단계 방법에 비하여 훨씬 좋은 수치적인 결과를 보여주고 있다. 이제, 이 다단계 방법에 오차제어 변수를 첨가한 새로운 형태의 예측자-수정자 방법을 제시하고 안정적인 해를 구할 수 있는 오차 제어 변수의 범위를 확인한다. 또한, 새로운 형태의 예측자-수정자 방법이 기존의 방법에 비하여 미분 방정식의 해에 대한 오차를 줄일 수 있는 방법임을 수치적인 결과를 통하여 검증한다.

• 한국해안해양공학회지
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• 제13권4호
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• pp.296-308
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• 2001

Wei et al.의 완전비선형 Boussinesq방정식을 4차의 Adams predictorcorrector기법을 사용하여 차분하고 면 내부조파기법과 스폰지 경계충을 사용하였으며 쇄파구조를 추가하였다. 면 내부조파기법을 사용해 목적파를 잘 재현할 수 있었다. 비선형성이 부각되는 고립파의 천수실험을 통해 완전비선형 모형의 정화성을 확인할 수 있었고 해저평붕으로 인한 규칙파의 변형을 모의해 보았다. 쇄파 수치실험을 통해 적용된 쇄파구조의 특성을 확인해 보았고 수중천퇴에 대한 이차원 파랑전파 수치실험을 통해 비선형 모형의 중요성을 확인하였다.

• 대한기계학회논문집A
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• 제24권11호
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• pp.2804-2811
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• 2000

A Nordsick form opf the multirate integration scheme has been proposed for flexible multibody dynamic systems. It is assumed that vibrational modal coordinates in the equations of motion are treated as fast variables, whereas the relative joint coordinates are treated as slow variables. In the multirate integration, the fast variables are integrated with small step-size, and the slow variables are integrated with larger step-size. The proposed multirate integration method is based on the Adams-Bashforth-Moulton predictor-corrector method and implemented in the Nordsieck vector form. The Nordsieck form of multrate integration method provides effective step-size control and at the same time, inherits the efficiency from the Adams integration method. Simulations of a flexible gun and turret system of the military tank have been carried out to show the effectiveness and efficiency of the proposed method.

• International Journal of Naval Architecture and Ocean Engineering
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• 제8권4호
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• pp.320-329
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• 2016

An implicit method of solving the six degree-of-freedom rigid body motion equations based on the second order Adams-Bashforth-Moulten method was utilised as an improvement over the leapfrog scheme by making modifications to the rigid body motion solver libraries directly. The implementation will depend on predictor-corrector steps still residing within the hybrid Pressure Implicit with Splitting of Operators - Semi-Implicit Method for Pressure Linked Equations (PIMPLE) outer corrector loops to ensure strong coupling between fluid and motion. Aitken's under-relaxation is also introduced in this study to optimise the convergence rate and stability of the coupled solver. The resulting coupled solver ran on a free floating object tutorial test case when converged matches the original solver. It further allows a varying 70%-80% reduction in simulation times compared using a fixed under-relaxation to achieve the required stability.

• 대한기계학회논문집
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• 제18권1호
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• pp.12-23
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• 1994

This paper proposes an optimal design software for the open-chain dynamic systems whose governing equations are expressed as differential equation. In this software, an input module and an automatic creation module of the equation of motion are developed to contrive the user's convenience. To analyze the equation of motion of the dynamic systems, variable-order and variable-stepsize Adams-Bashforth-Moulton predictor-corrector method is used to improve the efficiency. For the optimization and the design sensitivity analysis, ALM(augmented lagrange multiplier)method and adjoint variable method are adopted respectively. An output module with which the user can compare and investigate the analysis and the optimization results through tables and graphs is also provided. The developed software is applied to three typical dynamic response optimization problems, and the results compare very well with those available in the literature, demonstrating its effectiveness.

• 한국해안해양공학회지
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• 제11권3호
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• pp.149-155
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• 1999

Nwogu의 확장형 Boussinesq 방정식에 쇄파모형을 추가하였다. 입사조건으로 내부조파기법을 사용하였고 경계에는 스폰지층을 사용하였다. 수치적분은 시간에 대해 4차의 Adams 기법을 사용하였고 공간에 대한 1계 미분은 4차의 차분식을 사용하므로써 모든 차분 오차가 분산항보다 작아지도록 하였다. 면내부조파기법을 이용하여 목적파를 잘 재현할 수 있었고 스폰지층에서 파를 감쇄시키므로써 경계에서 연산영역 내부로의 재반사를 억제할 수 있었다. 천수실험을 통해 수심 변화에 따른 파고와 파장의 변화를 살펴보았고 쇄파전후의 파고 변화는 실험치와 전반적으로 일치하였지만 쇄파후의 파고는 실험치보다 큰 값을 보여주었다.

• Ocean Systems Engineering
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• 제4권2호
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• pp.83-97
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• 2014

Wave propagation in a three-dimensional (3D) fully nonlinear numerical wave tank (NWT) is studied based on velocity potential theory. The governing Laplace equation with fully nonlinear boundary conditions on the moving free surface is solved using the indirect desingularized boundary integral equation method (DBIEM). The fourth-order predictor-corrector Adams-Bashforth-Moulton scheme (ABM4) and mixed Eulerian-Lagrangian (MEL) method are used for the time-stepping integration of the free surface boundary conditions. A smoothing algorithm, B-spline, is applied to eliminate the possible saw-tooth instabilities. The artificial wave speed employed in MTF (multi-transmitting formula) approach is investigated for fully nonlinear wave problem. The numerical results from incorporating the damping zone (DZ), MTF and MTF coupled DZ (MTF+DZ) methods as radiation condition are compared with analytical solution. An effective MTF+DZ method is finally adopted to simulate the 3D linear wave, second-order wave and irregular wave propagation. It is shown that the MTF+DZ method can be used for simulating fully nonlinear wave propagation very efficiently.

• Ocean Systems Engineering
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• 제1권4호
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• pp.355-372
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• 2011

Based on the fully nonlinear velocity potential theory, the liquid sloshing in a three dimensional tank under random excitation is studied. The governing Laplace equation with fully nonlinear boundary conditions on the moving free surface is solved using the indirect desingularized boundary integral equation method (DBIEM). The fourth-order predictor-corrector Adams-Bashforth-Moulton scheme (ABM4) and mixed Eulerian-Lagrangian (MEL) method are used for the time-stepping integration of the free surface boundary conditions. A smoothing scheme, B-spline curve, is applied to both the longitudinal and transverse directions of the tank to eliminate the possible saw-tooth instabilities. When the tank is undergoing one dimensional regular motion of small amplitude, the calculated results are found to be in very good agreement with linear analytical solution. In the simulation, the normal standing waves, travelling waves and bores are observed. The extensive calculation has been made for the tank undergoing specified random oscillation. The nonlinear effect of random sloshing wave is studied and the effect of peak frequency used for the generation of random oscillation is investigated. It is found that, even as the peak value of spectrum for oscillation becomes smaller, the maximum wave elevation on the side wall becomes bigger when the peak frequency is closer to the natural frequency.