• Nuclear Engineering and Technology
• /
• v.49 no.6
• /
• pp.1135-1142
• /
• 2017

The applicability of the algebraic collapsing acceleration (ACA) technique to the method of characteristics (MOC) in cases with scattering anisotropy and/or linear sources was investigated. Previously, the ACA was proven successful in cases with isotropic scattering and uniform (step) sources. A presentation is first made of the MOC implementation, available in the DRAGON5 code. Two categories of schemes are available for integrating the propagation equations: (1) the first category is based on exact integration and leads to the classical step characteristics (SC) and linear discontinuous characteristics (LDC) schemes and (2) the second category leads to diamond differencing schemes of various orders in space. The acceleration of these MOC schemes using a combination of the generalized minimal residual [GMRES(m)] method preconditioned with the ACA technique was focused on. Numerical results are provided for a two-dimensional (2D) eight-symmetry pressurized water reactor (PWR) assembly mockup in the context of the DRAGON5 code.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
• /
• v.12 no.7
• /
• pp.1076-1085
• /
• 2001

In this paper, the FMM(Fast Multipole Method) combined with GMRES(Generalized Minimal RESidual Method) matrix solver is used to extract the parasitic impedance for complicated 3-D structures in uniform dielectric materials which limit the use of MoM(Method of Moment) due to its large computation time and memory requirement. This algorithm is a fast multipole-accelerated method based on quasistatic analysis and is very efficient for computing impedance between conductors. This paper proved the accuracy and efficiency of the FMM by comparing with MoM in simple examples. Finally the parasitic impedance of FC-PGA(Flip Chip Pin Grid Array) Package pins has been extracted by this algorithm and we have considered the possibility of the EMI/EMC problem caused by the signal interference.

• Journal of the Society of Naval Architects of Korea
• /
• v.37 no.1
• /
• pp.67-81
• /
• 2000

An accurate and efficient numerical method for two-dimensional nonlinear radiation problem has been developed. The wave motion due to a moving body is described by the assumption of ideal fluid flow, and the governing Laplace equation can be effectively solved by the higher-order boundary element method with the help of the GMRES (Generalized Minimal RESidual) algorithm. The intersection or corner problem is resolved by utilizing the so-called discontinuous elements. The implicit trapezoidal rule is used in updating solutions at new time steps by considering stability and accuracy. Traveling waves caused by the oscillating body are absorbed downstream by the damping zone technique. It is demonstrated that the present method for time marching and radiation condition works efficiently for nonlinear radiation problem. To avoid the numerical instability enhanced by the local gathering of grid points, the regriding technique is employed so that all the grids on the free surface may be distributed with an equal distance. This makes it possible to reduce time interval and improve numerical stability. Special attention is paid to the local flow around the body during time integration. The nonlinear radiation force is calculated by the "acceleration potential technique". Present results show good agreement with other numerical computations and experiments.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.25 no.3
• /
• pp.322-329
• /
• 2001

A study of the shock wave turbulent boundary layer interaction is presented. The focus of the study is the interactions of the shock waves with the turbulent boundary layer on the falt plate. Three examples are investigated. The computations are performed, using mixed explicit-implicit generalized Galerkin finite element method. The linear equations at each time step are solved by a preconditioned GMRES algorithm. Numerical results indicate that the implicit scheme converges to the asymptotic steady state much faster than the explicit counterpart. The computed surface pressures and skin friction coefficients display good agreement with experimental data. The flowfield manifests a complex shock wave system and a pair of counter-rotating vortices.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2000.11a
• /
• pp.484-488
• /
• 2000

병렬 컴퓨터를 사용하는 경우 하드웨어만으로 모든 것이 해결되지 않으며 병렬처리 기법의 도입이 불가피하다. 효과를 극대화하기 위하여서는 각 병렬 컴퓨터의 하드웨어적인 특징을 극대화할 수 있는 병렬 알고리즘과 병렬 프로그램 등 소프트웨어 개발이 필수적이다. GMRES(Generalized Minimal residual) 방법은 아주 큰 대칭 또는 비대칭 선형시스템의 해를 구하는 반복법 중의 하나로 일반적으로 많이 사용되고 있다. 서로 직교인 벡터를 하나씩 구하는 대신에 선형인 s개의 벡터를 구하고 각 그룹간에는 직교가 되게하는 s-step GMRES 알고리즘은 병렬적 성질을 더 많이 가지고 있다. 이 병렬 알고리즘의 전반부는 이미 개발된 s-step Arnoldi 알고리즘을 이용할 수 있다. s-step GMRES 알고리즘은 message passing 병렬 시스템에서 모든 프로세서들 사이의 자료 교환 시간을 줄임으로써 기존의 GMRES 방법에 비해 훨씬 더 병렬성을 증가시킨다. 본 논문에서는 초병렬 시스템(MPP)인 Cray T3E에서 많은 프로세서를 이용할 경우 개발된 s-step 알고리즘이 기존의 알고리즘에 비하여 얼마나 더 효과적으로 빨리 수행될 수 있는지 분석한다.

• 한국전산유체공학회:학술대회논문집
• /
• 1998.05a
• /
• pp.43-48
• /
• 1998

The development of unsteady three-dimensional incompressible viscous solver based on unsteady physical curvilinear coordinate system is presented. A 12-point finite analytic scheme based on local uniform grid spacing is extended for nonuniform grid spacing. The formulation of a condition is suggested to avoid the oscillation of the series summations produced by the application of the method of separation of variables. SIMPLER and pressure Poisson equation techniques are used for solving a velocity-pressure coupled problem. The matrix is solved using the Generalized Minimal RESidual (GMRES) method to enhance the convergence rate of unsteady flow solver and the Kinematic boundary condition of a free surface flow. It is demonstrated that the numerical solutions of these equations are less mesh sensitive.

• 한국방재학회:학술대회논문집
• /
• 2010.02a
• /
• pp.52.2-52.2
• /
• 2010

본 연구에서는 자유수면의 계산을 위해 동수압을 해석하는 수치모형을 제시하였다. 동수압과 자유수면을 고려하기 위해, 비점성 Navier-Stokes 방정식을 3단계로 나누어 해석하였다. 제1단계에서는 동수압과 자유수면을 전번 시간단계에서 계산된 값으로 대입하여 차분하였으며 이 차분식은 NGMRES(Newton-Generalized Minimal Residual) 방법을 이용해 음해적으로 해석되었다. 이때 계산된 유속장은 연속방정식을 고려하지 않았으므로 각 계산격자에서 질량보존법칙을 만족하지 않을 수도 있다. 제2단계에서 유속과 동수압 보정항으로 이루어진 식을 연속방정식에 대입하여 얻어지는 타원형 방정식인 동수압-포와송 방정식을 해석하므로 여기서 얻어지는 유속은 질량보존법칙을 만족하게 된다. 마지막 3 단계에서는 자유수면과 최종 유속을 계산하였다. 새로 개발된 수치모형을 검증하기위해 정사각형 탱크에서 수면의 자유 진동 문제에 적용한 결과 수치해는 해석해와 잘 일치하였다.

• Journal of Ship and Ocean Technology
• /
• v.8 no.3
• /
• pp.8-17
• /
• 2004

A numerical method is developed for computing the free surface flows around a transom stern of a ship at a high Froude number. At high speed, the flow may be detached from the flat transom stern. In the limit of the high Froude number, the problem becomes a planning problem. In the present study, we make the finite-element computations for a transom stern flows around a wedge-shaped floating ship. The numerical method is based on the Hamilton's principle. The problem is formulated as an initial value problem with nonlinear free surface conditions. In the numerical procedures, the domain was discretized into a set of finite elements and the numerical quadrature was used for the functional equation. The time integrations of the nonlinear free surface condition are made iteratively at each time step. A set of large algebraic equations is solved by GMRES(Generalized Minimal RESidual, Saad and Schultz 1986) method which is proven very efficient. The computed results are compared with previous numerical results obtained by others.

• Journal of electromagnetic engineering and science
• /
• v.19 no.1
• /
• pp.6-12
• /
• 2019

An IE-FFT algorithm is implemented and applied to the electromagnetic (EM) solution of perfect electric conducting (PEC) scattering problems. The solution of the method of moments (MoM), based on the magnetic field integral equation (MFIE), is obtained for PEC objects with closed surfaces. The IE-FFT algorithm uses a uniform Cartesian grid to apply a global fast Fourier transform (FFT), which leads to significantly reduce memory requirement and speed up CPU with an iterative solver. The IE-FFT algorithm utilizes two discretizations, one for the unknown induced surface current on the planar triangular patches of 3D arbitrary geometries and the other on a uniform Cartesian grid for interpolating the free-space Green's function. The uniform interpolation of the Green's functions allows for a global FFT for far-field interaction terms, and the near-field interaction terms should be adequately corrected. A 3D block-Toeplitz structure for the Lagrangian interpolation of the Green's function is proposed. The MFIE formulation with the IE-FFT algorithm, without the help of a preconditioner, is converged in certain iterations with a generalized minimal residual (GMRES) method. The complexity of the IE-FFT is found to be approximately $O(N^{1.5})$and $O(N^{1.5}logN)$ for memory requirements and CPU time, respectively.

• Journal of the Society of Naval Architects of Korea
• /
• v.46 no.6
• /
• pp.587-594
• /
• 2009

In the paper the effect of a stern-plate attached to a ship was taken into account. The relationship between the trim angle of a ship and the wave-resistance coefficient induced by the a stern-plate was studied using the potential flow analysis method. Numerical algorithm was described using the panel method and the vortex lattice method(VLM) to simulate the flow phenomena around a ship. The non-linearity of the free surface boundary conditions were considered using the iterative method and the IGE-GMRES(Incomplete Gaussian Elimination-The Generalized Minimal RESidual) algorithm was adopted to solve the linear equation at each iterative step. Numerical calculations were carried out to investigate the validity of the adopted algorithm using KCS(KRISO 3600 TEU Container) hull. Possible cases for attachment of the plate were checked. The results showed that the numerical algorithm could be physically appropriate.