• Title/Summary/Keyword: Gauss-Seidel method

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Topology optimization of multiphase elastic plates with Reissner-Mindlin plate theory

  • Banh, Thanh T.;Lee, Dongkyu;Lee, Jaehong;Kang, Joowon;Shin, Soomi
    • Smart Structures and Systems
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    • v.22 no.3
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    • pp.249-257
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    • 2018
  • This study contributes to evaluate multiphase topology optimization design of plate-like elastic structures with constant thickness and Reissner-Mindlin plate theory. Stiffness and adjoint sensitivity formulations linked to Reissner-Mindlin plate potential energy of bending and shear are derived in terms of multiphase design variables. Multiphase optimization problem is solved through alternative active-phase algorithm with Gauss-Seidel version as an optimization model of optimality criteria. Numerical examples verify efficiency and diversity of the present topology optimization method of Reissner-Mindlin elastic plates depending on multiphase and Poisson's ratio.

Design and Performance Analysis of the H/V-bus Parallel Computer (H/V-버스 병렬컴퓨터의 설계 및 성능 분석)

  • 김종현
    • Journal of the Korea Society for Simulation
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    • v.3 no.1
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    • pp.29-42
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    • 1994
  • The architecture of a MIMD-type parallel computer system is specified: a simulator is developed to support design and evaluation of systems based on the architecture: and conducted with the simulator to evaluate system performance. The horizontal/vertical-bus(H/V-bus) system architecture provides an NxN array of processing elements which communicate with each other through a network of N horizontal buses and N vertical buses. The simulator, written in SLAM II and FORTRAN, is designed to provide high-resolution in simulating the IPC mechanism. Parameters provide the user with independent control of system size, PE speed and IPC mechanism speed. Results generated by the simulator include execution times, PE utilizations, queue lengths, and other data. The simulator is used to study system performance when a partial differential equation is solved by parallel Gauss-Seidel method. For comparisons, the benchmark is also executed on a single-bus system simulator that is derived from the H/V-bus system simulator. The benchmark is also solved on a single PE to obtain data for computing speedups. An extensive analysis of results is presented.

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NUMERICAL SIMULATION OF THE INTERFERENCE EFFECT OF EXTERNAL STORES AND TAIL WING SURFACES OF A GENERIC FIGHTER AIRCRAFT (전투기 형상의 외부 장착물과 꼬리 날개 공력 간섭에 대한 수치적 연구)

  • Kim, M.J.;Kwon, O.J.;Kim, J.H.
    • 한국전산유체공학회:학술대회논문집
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    • 2007.10a
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    • pp.149-156
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    • 2007
  • A three-dimensional inviscid flow solver has been developed based on unstructured meshes for the simulation of steady and unsteady flowfields around a generic fighter aircraft and for the investigation of the aerodynamic interference between the external stores and the tail surfaces. The flow solver is based on a vertex-centered finite-volume method and an implicit point Gauss-Seidel relaxation scheme. To validate the flow solver, calculations were made for a steady flow and the computed results were compared with experimental data. An unsteady time-accurate computation of the generic fighter aircraft with external stores at transonic flight conditions showed that the external stores cause undesirable vibration on the horizontal tail surface due to the mutual interference between their wake and the horizontal tail surface. It was shown that downward deflection of the trailing edge flap significantly reduces the undesirable interference effect.

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Computation of 3-Dimensional Unseady Flows Using an Parallel Unstructured Mesh (병렬화된 비정렬 격자계를 이용한 3차원 비정상 유동 계산)

  • Kim Joo Sung;Kwon Oh Joon
    • Proceedings of the KSME Conference
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    • 2002.08a
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    • pp.59-62
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    • 2002
  • In the present study, solution algorithms for the computation of unsteady flows on an unstructured mesh are presented. Dual time stepping is incorporated to achieve the 2-nd order temporal accuracy while reducing the linearization and the factorization errors associated with a linear solver. Hence, any time step can be used by only considering physical phenomena. Gauss-Seidel scheme is used to solve linear system of equations. Rigid motion and spring analogy method fur moving mesh are all considered and compared. Special treatments of spring analogy for high aspect ratio cells are presented. Finally, numerical results for oscillating wing are compared with experimental data.

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Computation of 3-Dimensional Unsteady Viscous Plows Using an Parallel Unstructured Mesh (병렬화된 비정렬 격자계를 이용한 3차원 비정상 점성 유동 계산 기법 개발)

  • Kim J.S.;Kwon O.J.
    • 한국전산유체공학회:학술대회논문집
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    • 2003.08a
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    • pp.18-24
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    • 2003
  • In the present study, solution algorithms for the connotation of unsteady flows on an unstructured mesh me presented Dual time stepping is incorporated to achieve the 2-nd order temporal accuracy while reducing the linearization and the factorization errors associated with a linear solver. Hence, any time step can be used by only considering physical phenomena. Gauss-Seidel scheme is used to solve linear system of equations. Rigid motion and suing analogy method for moving mesh are all considered and compared. Special treatments of suing analogy for high aspect ratio cells are presented. Finally, numerical results for oscillating ing are compared with experimental data.

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Topology optimization for thin plate on elastic foundations by using multi-material

  • Banh, Thien Thanh;Shin, Soomi;Lee, Dongkyu
    • Steel and Composite Structures
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    • v.27 no.2
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    • pp.177-184
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    • 2018
  • This study contributes to evaluate multiphase topology optimization design of plate-like structures on elastic foundations by using classic plate theory. Multi-material optimal topology and shape are produced as an alternative to provide reasonable material assignments based on stress distributions. Multi-material topology optimization problem is solved through an alternative active-phase algorithm with Gauss-Seidel version as an optimization model of optimality criteria. Stiffness and adjoint sensitivity formulations linked to thin plate potential strain energy are derived in terms of multiphase design variables and Winkler-Pasternak parameters considering elastic foundation to apply to the current topology optimization. Numerical examples verify efficiency and diversity of the present topology optimization method of elastic thin plates depending on multiple materials and Winkler-Pasternak parameters with the same amount of volume fraction and total structural volume.

Parameterized Modeling of Spatially Varying PSF for Lens Aberration and Defocus

  • Wang, Chao;Chen, Juan;Jia, Hongguang;Shi, Baosong;Zhu, Ruifei;Wei, Qun;Yu, Linyao;Ge, Mingda
    • Journal of the Optical Society of Korea
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    • v.19 no.2
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    • pp.136-143
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    • 2015
  • Image deblurring by a deconvolution method requires accurate knowledge of the blur kernel. Existing point spread function (PSF) models in the literature corresponding to lens aberrations and defocus are either parameterized and spatially invariant or spatially varying but discretely defined. In this paper, a parameterized model is developed and presented for a PSF which is spatially varying due to lens aberrations and defocus in an imaging system. The model is established from the Seidel third-order aberration coefficient and the Hu moment. A skew normal Gauss model is selected for parameterized PSF geometry structure. The accuracy of the model is demonstrated with simulations and measurements for a defocused infrared camera and a single spherical lens digital camera. Compared with optical software Code V, the visual results of two optical systems validate our analysis and proposed method in size, shape and direction. Quantitative evaluation results reveal the excellent accuracy of the blur kernel model.

Curvature Radius of Equivalent Lens Obtained by Recursive Numerical Solving of Gaussian Equations (재귀적 수치 계산법을 이용한 등가 렌즈의 곡률 계산)

  • Lee, Kyu Haeng
    • Korean Journal of Optics and Photonics
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    • v.33 no.6
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    • pp.275-286
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    • 2022
  • As a first step in the optical design process, we derive a recursive numerical calculation method that can give a solution to the Gaussian equation that the paraxial rays satisfy. Given the refractive power, the angle of incidence to the first principal plane of the lens, the angle of exit to the second principal plane of the lens, and the distance between the principal planes, the radii of curvature of the front and back surfaces of a lens can be obtained by applying the recursive numerical calculation method proposed in this paper according to the thickness of the lens. If a module consists of two or more lenses, the thickness and radius of curvature of each lens can be similarly determined after selecting the distance between the principal planes of the lens under the condition of the design specification while increasing the number of lenses one by one.

Diffusion synthetic acceleration with the fine mesh rebalance of the subcell balance method with tetrahedral meshes for SN transport calculations

  • Muhammad, Habib;Hong, Ser Gi
    • Nuclear Engineering and Technology
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    • v.52 no.3
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    • pp.485-498
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    • 2020
  • A diffusion synthetic acceleration (DSA) technique for the SN transport equation discretized with the linear discontinuous expansion method with subcell balance (LDEM-SCB) on unstructured tetrahedral meshes is presented. The LDEM-SCB scheme solves the transport equation with the discrete ordinates method by using the subcell balances and linear discontinuous expansion of the flux. Discretized DSA equations are derived by consistently discretizing the continuous diffusion equation with the LDEM-SCB method, however, the discretized diffusion equations are not fully consistent with the discretized transport equations. In addition, a fine mesh rebalance (FMR) method is devised to accelerate the discretized diffusion equation coupled with the preconditioned conjugate gradient (CG) method. The DSA method is applied to various test problems to show its effectiveness in speeding up the iterative convergence of the transport equation. The results show that the DSA method gives small spectral radii for the tetrahedral meshes having various minimum aspect ratios even in highly scattering dominant mediums for the homogeneous test problems. The numerical tests for the homogeneous and heterogeneous problems show that DSA with FMR (with preconditioned CG) gives significantly higher speedups and robustness than the one with the Gauss-Seidel-like iteration.

A New Concept of Power Flow Analysis

  • Kim, Hyung-Chul;Samann, Nader;Shin, Dong-Geun;Ko, Byeong-Hun;Jang, Gil-Soo;Cha, Jun-Min
    • Journal of Electrical Engineering and Technology
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    • v.2 no.3
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    • pp.312-319
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    • 2007
  • The solution of the power flow is one of the most important problems in electrical power systems. These traditional methods such as Gauss-Seidel method and Newton-Raphson (NR) method have had drawbacks up to now such as initial values, abnormal operating solutions and divergences in heavy loads. In order to overcome theses problems, the power flow solution incorporating genetic algorithm (GA) is introduced in this paper. General operator of genetic algorithm, arithmetic crossover, and non-uniform mutation operator of GA are suggested to solve the power flow problem. While abnormal solution cannot be obtained by a NR method, multiple power flow solution can be obtained by a GA method. With a heavy load, both normal solution and abnormal solution can be obtained by a proposed method. In this paper, a floating number representation instead of the binary number representation is introduced for accuracy. Simulation results have been compared with traditional methods.