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THE FRACTIONAL STEP METHOD FOR COUPLED STOKES EQUATIONS USING SPECTRAL ELEMENT
Xiang Fan PIAO,Sang Dong KIM 한국산업응용수학회 2009 한국산업응용수학회 학술대회 논문집 Vol.2009 No.5
This work deals with the numerical solution of coupled stokes equations,which obtained from the optimal control problem subject to Stokes equations.The fractional step method for this problem is developed.We using PCG(Precondition Conjugate Gradient Method) solve serval linear systems,which are obtained from the fractional step method for coupled stokes equations. For this solver,we using a finite element method precondition operator.Finally,the numerical results on a test problem show that this method is correct and feasible.
A New Time Stepping Method for Solving One Dimensional Burgers' Equations
Piao, Xiang Fan,Kim, Sang-Dong,Kim, Phil-Su,Kim, Do-Hyung Department of Mathematics 2012 Kyungpook mathematical journal Vol.52 No.3
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.
A second order backward semi-Lagrangian scheme for guiding center problems
Xiang Fan Piao,Jae-Min Kwon,Dokkyun Yi,Sang Dong Kim,Philsu Kim 한국산업응용수학회 2013 한국산업응용수학회 학술대회 논문집 Vol.8 No.1
In this study, we develop a class of backward semi-Lagrangian finite difference methods for solving nonlinear guiding center models. A key problem in the time discretization is to find the starting point of the characteristic curves arriving at each grid point, which is a highly nonlinear problem with a self-consistency imposed by the Poisson equation. The proposed method is based on the error correction method recently developed by the au-thors. For the error correction method, we introduce a modified Euler’s polygon and solve the induced asymptotically linear differential equation with the mid-point quadrature rule to get the error correction term. It is proved that the proposed method is iteration free and has the convergence order 3 in space and 2 in time. In particular, it is shown that the proposed method has a good performance in computational cost together with a superior mass conservation and a similar conservation in the total kinetic energy compared to the conventional second-order iteration methods.
Design and Development of Large Electric Curtain Control System for Time Controlled
Shuo Cheng(정석),Yong Taek Chung(정용택),Xiang Fan Piao(박상범) 한국기계가공학회 2019 한국기계가공학회지 Vol.18 No.3
The purpose of this paper is to design a curtain control system for centralized management of large curtains, which includes curtain structure, electric curtain controller, communication system, user interface and remote control. Curtain structure is designed to avoid using limit switch. The system is based on microprocessor, determined the stop position and complete running time of electric curtain through time control, and achieved remote control of curtain opening and closing through wired and wireless communication modes. By establishment of a mathematical model to calculate the inertia compensation time of the electric curtain, the electric curtain can be stopped ahead of time, and the curtain can be completely closed by the inertia. The result of test experiment of 32 electric curtain controllers shows the communication success rate reached 100%.
Jun Cheng Zhao(조준성),Shuo Cheng(정석),Xiang Fan Piao(박상범) 한국기계가공학회 2020 한국기계가공학회지 Vol.19 No.1
The emergence of the flow-through cell (FTC) method has made up for the limitations of previous dissolution test methods, but the high cost of the FTC dissolution devices have seriously hindered the progression of research and application of the FTC. This new design uses a peristaltic pump to simulate the sinusoidal flow rate of a piston pump. The flow profile of each peristaltic pump was sinusoidal with a pulsation of 120 ± 1 pulses per minute, and the flow rate ranged from 1.0 - 36.0 mL/min. The flow control of each channel was adjusted independently so the flow errors of the seven channels were close to 2%. The structure of the system was simplified, and the cost was reduced through manual sampling and immersing the FTC in a water bath. The dissolution rate of the theophylline and aminophylline films was determined, and good experimental results were obtained.
FIRST-ORDER SYSTEM LEAST-SQUARES METHOD FOR THE OPTIMAL CONTROL BY THE STOKES EQUATIONS
Sang Dong KIM,Hyung-Chun LEE,Soorok RYU,Xiang Fan PIAO 한국산업응용수학회 2007 한국산업응용수학회 학술대회 논문집 Vol.2 No.1
We consider the approximate solution of optimal control problem governed by the Stokes equations. For the constrained optimization problem, Lagrange multiplier method is used. We employ a least-squares functional developed in [3] for the two-and three-dimensional first order optimality systems, by introducing a velocity flux variable and associated curl and trace equations. With the provided H²-regularity of that system, ellipticity in an H¹ product norm is established. This yields optimal discretization error estimates for finite element spaces in a product H¹ norm. The resulting matrix becomes symmetric and positive definite. For numerical tests, we apply V-cycle multigrid methods to the total discrete algebraic system.