• 한국전산유체공학회:학술대회논문집
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• 2001.05a
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• pp.189-194
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• 2001

In this paper, non-reacting and reacting flowfields were computed using a preconditioned Navier-Stokes solver. The preconditioning technique of Merkle et al. and TVD scheme or Chakravarthy and Osher was employed and the results obtained using developed code have a good agreement with the previous results and experimental data. The preconditioned Wavier-Stokes equation set with low Reynolds number $\kappa-\epsilon$ equation and species continuity equations, are discretized with strongly implicit manner and time integrated with LU-SSOR scheme. For the purpose of treating unsteady problem the duel-time stepping scheme was employed. For the validation of the code in incompressible flow regime, steady driven square cavity flow was considered and calculation result shows reasonably good agreement with the result of incompressible code. Shock wave/boundary layer interaction problem was considered to show the shock capturing performance of preconditioned-TVD scheme. To validate unsteady flow, acoustic oscillation problem was calculated, and supersonic premix flame of $H_2$-air reaction problem which is calculated with turbulence model, 9-species/18-reaction step reaction model, shows reasonable agreement with the previous results. As a result, the preconditioning method has an advantage to calculate incompressible and compressible flow through one code and preconditioned solver easily developed from standard compressible code with minor efforts. But additional computational time and computer memory is required due to preconditioning matrix.

• Structural Engineering and Mechanics
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• v.23 no.6
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• pp.675-689
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• 2006

In structural analysis of tall buildings the traditional primary loading analysis approach that assumes all the loads are simultaneously applied to the fully built structure has been shown to be unsuitable by many researches. The construction sequential analysis that reflects the fact of the level-by-level construction of tall buildings can provide more reliable results and has been used more and more. However, too much computational cost has prevented the construction sequential analysis from its application in CAD/CAE software for building structures, since such an approach needs to deal with systematic changing of resultant stiffness matrices following level-by-level construction. This paper firstly analyzes the characteristics of assembling and triangular factorization of the stiffness matrix in the finite element model of the construction sequential analysis, then presents a fast construction sequential analysis strategy and a corresponding step-by-step active column solver by means of improving the existing skyline solver. The new strategy avoids considerably repeated calculation by only working on the latest appended and modified part of resultant stiffness matrices in each construction level. Without any simplification, the strategy guarantees accuracy while efficiency is greatly enhanced. The numerical tests show that the proposed strategy can be implemented with high efficiency in practical engineering design.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.824-830
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• 2003

The Power Flow Finite Element Method(PFFEM) offers very promising results in predicting the vibration responses of system structures, and the first PFFEM software, PFADS has been developed in Seoul National University for the vibration predictions and analysis of coupled system structures in medium-to-high frequency ranges. PFFEM is numerical method which solves energy governing equation using finite element technique for complicated structures where the exact solutions are not available. Through the upgrades, the current version PFADS R3 could cover the general beam and plate structures including various kinds of beam-plate rigid joints, spring-damper connection and rigid body connection within beam and plate in addition. This software is composed of three parts; translator, model converter and solver. The translator makes its own FE-model from bulk data of commercial FE software, and the model converter is used to convert FE-model to PFFE-model automatically. The solver calculates vibrational energy density and intensity for PFFE-model by solving global matrix equations of PFFEM. For the applications of PFADS R3, two vehicle models and a container model are examined with respect to major parameters, and reliable results are obtained.

• Journal of Ship and Ocean Technology
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• v.8 no.4
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• pp.26-33
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• 2004

PFFEM software, PFADS has been developed for the vibration predictions and analysis of coupled system structures in medium-to-high frequency ranges. PFFEM is numerical method which solves energy governing equation using finite element technique for complicated structures where the exact solutions are not available. Through the upgrades, present PFADS R3 could cover the general beam and plate structures including various kinds of beam-plate rigid joints and other joint systems such as spring-damper junction and rigid bar connection. This software is composed of 3 parts; translator, model converter and solver. The translator makes its own FE-model from bulk data of commercial FE software, and the model converter is used to convert FE-model to PFFE-model automatically. The solver calculates vibrational energy density and intensity for PFFE-model by solving global matrix equations of PFFEM. For the applications of real transportation systems, a container ship model has been examined with respect to major parameters, and reliable results have been obtained.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.1
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• pp.85-100
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• 2001

In this paper we propose a block-type parallel preconditioner for solving large sparse nonsymmetric linear systems, which we expect to be scalable. It is Multi-Color Block SOR preconditioner, combined with direct sparse matrix solver. For the Laplacian matrix the SOR method is known to have a nondeteriorating rate of convergence when used with Multi-Color ordering. Since most of the time is spent on the diagonal inversion, which is done on each processor, we expect it to be a good scalable preconditioner. Finally, due to the blocking effect, it will be effective for ill-conditioned problems. We compared it with four other preconditioners, which are ILU(0)-wavefront ordering, ILU(0)-Multi-Color ordering, SPAI(SParse Approximate Inverse), and SSOR preconditioner. Experiments were conducted for the Finite Difference discretizations of two problems with various meshsizes varying up to 1024 x 1024, and for an ill-conditioned matrix from the shell problem from the Harwell-Boeing collection. CRAY-T3E with 128 nodes was used. MPI library was used for interprocess communications. The results show that Multi-Color Block SOR and ILU(0) with Multi-Color ordering give the best performances for the finite difference matrices and for the shell problem only the Multi-Color Block SOR converges.

• Structural Engineering and Mechanics
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• v.45 no.1
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• pp.95-110
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• 2013

In the recent decade, practical of wavelet technique is being utilized in various domain of science. Particularly, engineers are interested to the wavelet solution method in the time series analysis. Fundamentally, seismic responses of structures against time history loading such as an earthquake, illustrates optimum capability of systems. In this paper, a procedure using particularly discrete Haar wavelet basis functions is introduced, to solve dynamic equation of motion. In the proposed approach, a straightforward formulation in a fluent manner is derived from the approximation of the displacements. For this purpose, Haar operational matrix is derived and applied in the dynamic analysis. It's free-scaled matrix converts differential equation of motion to the algebraic equations. It is shown that accuracy of dynamic responses relies on, access of load in the first step, before piecewise analysis added to the technique of equation solver in the last step for large scale of wavelet. To demonstrate the effectiveness of this scheme, improved formulations are extended to the linear and nonlinear structural dynamic analysis. The validity and effectiveness of the developed method is verified with three examples. The results were compared with those from the numerical methods such as Duhamel integration, Runge-Kutta and Wilson-${\theta}$ method.

• Proceeding of EDISON Challenge
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• 2016.03a
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• pp.195-202
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• 2016

In this paper, crack detection method using eigen value analysis is presented. Three methods are used: theoretical analysis, finite element method with the cracked beam elements and finite element method with three dimensional continuum elements. Finite element formulation of the cracked beam element is introduced. Additional term about stress intensity factor based on fracture mechanics theory is added to flexibility matrix of original beam to model the crack. As using calculated stiffness matrix of cracked beam element and mass matrix, natural frequencies are calculated by eigen value analysis. In the case of using continuum elements, the natural frequencies could be calculated by using EDISON CASAD solver. Several cases of crack are simulated to obtain natural frequencies corresponding the crack. The surface of natural frequency is plotted as changing with crack location and depth. Inverse analysis method is used to find crack location and depth from the natural frequencies of experimental data, which are referred by another papers. Predicted results are similar with the true crack location and depth.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.48 no.1
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• pp.90-100
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• 2011

We present a parallel bi-conjugate gradient (Bi-CG) matrix solver for large scale Bio-FET simulations based on recent graphics processing units (GPUs) which can realize a large-scale parallel processing with very low cost. The proposed method is focused on solving the Poisson equation in a parallel way, which requires massive computational resources in not only semiconductor simulation, but also other various fields including computational fluid dynamics and heat transfer simulations. As a result, our solver is around 30 times faster than those with traditional methods based on single core CPU systems in solving the Possion equation in a 3D FDM (Finite Difference Method) scheme. The proposed method is implemented and tested based on NVIDIA's CUDA (Compute Unified Device Architecture) environment which enables general purpose parallel processing in GPUs. Unlike other similar GPU-based approaches which apply usually 32-bit single-precision floating point arithmetics, we use 64-bit double-precision operations for better convergence. Applications on the CUDA platform are rather easy to implement but very hard to get optimized performances. In this regard, we also discuss the optimization strategy of the proposed method.

• Journal of the Institute of Electronics and Information Engineers
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• v.54 no.4
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• pp.91-98
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• 2017

Electrical impedance tomography is a nondestructive imaging technique to reconstruct unknown conductivity distribution based on applied current data and measured voltage data through an array of electrodes attached on the periphery of a domain. In this paper, an inverse method based on truncated singular value decomposition is proposed to solve the inverse problem with the generalized Tikhonov regularization and to reconstruct the conductivity distribution. In order to reduce the inverse computational time, truncated singular value decomposition is applied to the inverse term after the generalized regularization matrix is taken out from the inverse matrix term. Numerical experiments and phantom experiments have been performed to verify the performance of the proposed method.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.9 s.240
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• pp.1049-1056
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• 2005

A conservative pressure-based finite-volume numerical method has been developed for computing flow and heat transfer by using an unstructured grid system. The method admits arbitrary convex polyhedra. Care is taken in the discretization and solution procedures to avoid formulations that are cell-shape-specific. A collocated variable arrangement formulation is developed, i.e. all dependent variables such as pressure and velocity are stored at cell centers. Gradients required for the evaluation of diffusion fluxes and for second-order-accurate convective operators are found by a novel second-order accurate spatial discretization. Momentum interpolation is used to prevent pressure checkerboarding and the SIMPLE algorithm is used for pressure-velocity coupling. The resulting set of coupled nonlinear algebraic equations is solved by employing a segregated approach, leading to a decoupled set of linear algebraic equations fer each dependent variable, with a sparse diagonally dominant coefficient matrix. These equations are solved by an iterative preconditioned conjugate gradient solver which retains the sparsity of the coefficient matrix, thus achieving a very efficient use of computer resources.