• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.81-93
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• 2013

We consider a distributed optimal flux control problem: finding the potential of which gradient approximates the target vector field under an elliptic constraint. Introducing the Lagrange multiplier and a change of variables the Euler-Lagrange equation turns into a coupled equation of an elliptic equation and a reaction diffusion equation. The change of variables reduces iteration steps dramatically when the Gauss-Seidel iteration is considered as a solution method. For the elliptic equation solver we consider the Cell Boundary Element (CBE) method, which is the finite element type flux preserving methods.

• 한국전산유체공학회:학술대회논문집
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• 2001.05a
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• pp.38-44
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• 2001

An efficient Gauss-Seidel time integration scheme is developed for solving the Euler and Navier-Stokes equations on unstructured meshes. Roe's FDS is used for the explicit residual computations and van Leer's FVS for evaluating implicit flux Jacobian. To reduce the memory requirement to a minimum level, off-diagonal flux Jacobian contributions are repeatedly calculated during the Gauss-Seidel sub-iteration process. Computational results based on the present scheme show that approximately $15\%$ of CPU time reduction is achieved while maintaining the memory requirement level to $50-60\%$ of the original Gauss-Seidel scheme.

• Proceedings of the ESK Conference
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• 1997.10a
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• pp.463-467
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• 1997

인간에게 운동감을 적절히 제시해주기 위하여는 Newton에 의한 운동의 세가지 법칙뿐만 아니라 EInstein의 상대성이론이 첨가되어야 한다. 즉, Newton운동의 제1법칙에 의하여 피실험자가 외력을 받지 않으면 등속운동 또는 정지상태를 계속 유지하게 되어 자신이 등속좌표계에 고정되어있기 때문에 시각적 인 정보가 없으면 어떠한 운동감도 못 느낀다. 이때 피실험자에게 정지해있는 기준좌표계에 대하여 등속 으로 움직이는 것을 인식시켜주기 위하여 피실험자에 대한 기준좌표계의 상대속도를 시각정보로 제공해 주어야 한다. 또한 Newton운동의 제2법칙에 의하여 똑같은 힘이 외력으로 작용하더라도 피실험자의 질량과 가속도는 서로 반비례하므로 화면이동속도변화를 피실험자의 질량에 반비례하도록 제시해 주어야 한다(김 정흠, 1982). 본 연구에서는 이러한 개념에 근거하여, 체중이 다른 여섯 피실험자들로 구성된 시스템에 대해서 각 피실험자에게 서로 다른 변위를 주고자할 때, 여섯가지 외력에 요구되는 작용시간을 Jacobi Iteration 방법과 Gauss-Seidel Iteration 방법으로 구하는 알고리즘을 제시하였다(D.V. Griffiths and I.M. Smith, 1991).

• Nuclear Engineering and Technology
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• v.54 no.2
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• pp.532-545
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• 2022

In-depth convergence analyses for neutronics/thermal-hydraulics (T/H) coupled calculations are performed to investigate the performance of nonlinear methods based on the Fixed-Point Iteration (FPI). A simplified neutronics-T/H coupled system consisting of a single fuel pin is derived to provide a testbed. The xenon equilibrium model is considered to investigate its impact during the nonlinear iteration. A problem set is organized to have a thousand different fuel temperature coefficients (FTC) and moderator temperature coefficients (MTC). The problem set is solved by the Jacobi and Gauss-Seidel (G-S) type FPI. The relaxation scheme and the Anderson acceleration are applied to improve the convergence rate of FPI. The performances of solution schemes are evaluated by comparing the number of iterations and the error reduction behavior. From those numerical investigations, it is demonstrated that the number of FPIs is increased as the feedback is stronger regardless of its sign. In addition, the Jacobi type FPIs generally shows a slower convergence rate than the G-S type FPI. It also turns out that the xenon equilibrium model can cause numerical instability for certain conditions. Lastly, it is figured out that the Anderson acceleration can effectively improve the convergence behaviors of FPI, compared to the conventional relaxation scheme.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.25 no.5
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• pp.601-606
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• 2014

The IPO(Iterative Physical Optics) method repeatedly applies the well-known PO(Physical Optics) approximation to calculate the scattered field by a large object. Thus, the IPO method can consider the multiple scattering in the object, which is ignored for the PO approximation. This kind of iteration can improve the final accuracy of the induced current on the scatterer, which can result in the enhancement of the accuracy of the RCS(Radar Cross Section) of the scatterer. Since the IPO method can not exactly but approximately solve the required integral equation, however, the convergence of the IPO solution can not be guaranteed. Hence, we apply the famous techniques used in the inversion of a matrix to the IPO method, which include Jacobi, Gauss-Seidel, SOR(Successive Over Relaxation) and Richardson methods. The proposed IPO methods can efficiently calculate the RCS of a large scatterer, and are numerically verified.

• Membrane Journal
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• v.22 no.6
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• pp.470-480
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• 2012

In this study, for a linear tubular membrane with constant diameter the mass balance considering permeate velocity of the each unit length was established. On this basis, mathematical modelling of flows in a pipe was solved using nonlinear second order differential equations as well as steady-state equation. Since this equation is nonlinear, Gauss-Seidel method or another iteration method were used to solve the differential equations. Simulation algorithm for numerical solutions was presented. Also since the permeate flow is varied as operating condition, the solution of equations at each conditions using numerical integrations such as Simpson's rules was used. In order to analyze and compare simulation results, we have performed experiments using a hollow fiber membrane with almost identical tubular membrane. Comparison of theoretical and experimental results, pressure drop, flow rate, and permeate flow in a hollow fiber membrane, were illustrated.

• Journal of Biosystems Engineering
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• v.23 no.1
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• pp.21-30
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• 1998

A theoretical model was developed to evaluate the effects of soil and airflow characteristics on the soil-air heat exchanger performances. The model, which includes three-dimensional transient energy and mass equilibrium-equation, was solved by using a computer program that uses Finite Difference Methods and Gauss-Seidel iteration computation. Energy gains, heat exchange efficiencies, and outlet air temperature are presented including the effects of soil moisture content, soil conductivity, soil thermal diffusivity, and soil initial temperature. Also, data related to the effects of airflow rate and inlet air temperature on the thermal performance of the system are presented. The results indicated that energy gains depend on soil conductivity, soil thermal diffusivity, and soil initial temperature. Heat exchange efficiencies relied on air mass flow rate and soil moisture content.

• KIEAE Journal
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• v.5 no.1
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• pp.27-33
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• 2005

Global efforts have made to reduce energy consumption and $CO_2$ gas emission. One of the weakest parts for energy loss through the whole building components is building envelopes. Lots of technologies to increase the thermal performance of building envelopes have been introduced in recent year. Transparent Insulation Wall(TIW) is a new technology for building insulation and has been function both solar transmittance and thermal insulation. A mathematical model of a Transparent Insulation Wall equipped with south wall was proposed in order to predict thermal performance under varying climates(summer and winter). Unsteady state heat transfer equations were set up using an energy balance equation and solved using Gauss-Seidel iteration solution procedure. The thermal performance of the TIW determined from a wall surface and air layer temperature, non-airconditioned room temperature and air conditioning load. As a result, this numerical study shows that the TIW is effective in an air conditioning load reduction. Further experimental study is required to establish complete TIW system.

• Journal of Biosystems Engineering
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• v.22 no.4
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• pp.459-468
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• 1997

To optimize the design and operation of a soil- air heat exchanger system, the effects of variables characterizing system design and operation on the performance of the system were analyzed by a theoretical model which included the three-dimensional transient heat conduction equation. The solution of the theoretical model was acquired by a computer program that uses Finite Difference Methods and Gauss-Seidel iteration computation, in which the time discretization scheme was an implicit difference appoximation. The computer program was validated first by comparison of the results for different grid sizes. Air outlet temperature, energy gain, and heat exchange efficiency of the system were analyzed based upon the tube diameter, tube length, tube thickness, and tube thermal diffusivity.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.10a
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• pp.266-273
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• 1995

An efficient dynamic analysis method is developed f3r building structures subjected to ground home loadings. The soil medium is modeled using the finite elements and infinite elements. Then, the dynamic stiffness of the soil medium is calculated at the interfacial nodes between the soil and the building foundation. The equivalent subway loading at the interfacial nodes are obtained from the wave propagation analysis of the subway loading through the soil medium. The dynamic response of the building Is computed using the mode superposition method equipped with gauss-seidel iteration technique. The analysis is carried out by the frequency domain and the time domain methods.