• 한국전산유체공학회:학술대회논문집
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• 2010.05a
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• pp.115-121
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• 2010

Cavitating flow is widely shown in many engineering systems, such as marine propellers, pump impellers, nozzles, injectors, torpedoes, etc. The present work focuses on the numerical analysis of the multiphase flow around the underwater vehicle which was launched from a submarine. The governing equation is the Navier-Stokes equation with a homogeneous mixture mode. The multiphase flow solver uses an implicit preconditioning scheme in curvilinear coordinate. For the code validation, the results from the present work are compared with the existing experimental and numerical results, and a reasonably good agrements are obtained. The multiphase flow around an underwater vehicle is simulated which includes submarine wake effects.

• 한국전산유체공학회:학술대회논문집
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• 1998.05a
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• pp.35-42
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• 1998

Time marching algorithms applied to compressible Navier-Stokes equation have a convergence problem at low Mach number. It is mainly due to the eigenvalue stiffness and pressure singularity as Mach number approaches to zero. Among the several methods to overcome the shortcomings of time marching scheme, time derivative preconditioning method have been used successfully. In this numerical analysis, we adopted a preconditioner of K.H. Chen and developed a two-dimensional, axisymmetric Navier-Stokes program. The steady state driven cavity flow and backward facing step flow problems were computed to confirm the accuracy and the robustness of preconditioned algorithm for low Mach number flows. And the transonic and supersonic flows insice the JPL axisymmetric nozzle internal flow is exampled to investigate the effects of preconditioning at high Mach number flow regime. Test results showed excellent agreement with the experimental data.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.2
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• pp.171-188
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• 2015

In this paper, the efficient column-wise/row-wise lattice reduction (LR) updating and downdating methods are developed and their complexities are analyzed. The well-known LLL algorithm, developed by Lenstra, Lenstra, and Lov${\acute{a}}$sz, is considered as a LR method. When the column or the row is appended/deleted in the given lattice basis matrix H, the proposed updating and downdating methods modify the preconditioning matrix that is primarily computed for the LR with H and provide the initial parameters to reduce the updated lattice basis matrix efficiently. Since the modified preconditioning matrix keeps the information of the original reduced lattice bases, the redundant computational complexities can be eliminated when reducing the lattice by using the proposed methods. In addition, the rounding error analysis of the proposed methods is studied. The numerical results demonstrate that the proposed methods drastically reduce the computational load without any performance loss in terms of the condition number of the reduced lattice basis matrix.

• Journal of Chest Surgery
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• v.34 no.11
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• pp.823-830
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• 2001

Background: Paraplegia is a serious complication of thoracic or thoracoabdominal aortic operations, which is related to ischemic injury of the spinal cord induced by low perfusion pressure during cross clamping of the aorta. Ischemic preconditioning of heart or brain with reversible sublethal ischemic injury induces resistance to subsequent lethal ischemia. The aim of this study is to investigate whether ischemic tolerance could be induced by the preconditioning of the spinal cord using swine model. Material and Method: The animals were randomly assigned to three groups: sham group(n=3), control group(n=6) and pre-conditioning group(n=8). In the sham group, we performed the left thoracotomy only without any ischemic injury. In the preconditioning group, the swine received reversible spinal cord ischemic injury by aortic clamping for 20 minutes, whereas control group had no previous aortic cross- clamping. Forty-eight hours later, the aorta was clamped for 30 minutes in both groups. Neurological examination was done 24 hours later, then the animals were euthanized for histopathology and malonedialdehyde(MDA) spectrophotometry assay of the spinal cord. Result: Statistically significant difference in neurological outcome was observed between the control and preconditioning groups at 24 hours after ischemic injury. The incidence of paraplegia and severe paresis was 100% in the control group, and 62.5% in the preconditing group(p=0.028). There was no statistically significant difference in histopathology and MDA assay of the ischemic spinal cord between these two groups with borderline statistical difference in MDA assay(p=0.0745). Conclusion: In the present swine study, ischemic preconditioning could induce tolerance against 30 minute ischemic insult of the spinal cord, although the animals did not completely recover(stand-up or walk). We expect that combining this preconditioning with other currently existing protection methods might lead to a synergistic effect, which warrants further investigation.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.495-501
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• 1996

There is currently a regain of interest in ADI (Alternating Direction Implicit) method as a preconditioner for iterative Method for solving large sparse linear systems, because of its suitability for parallel computation. However the classical ADI is not applicable to FE(Finite Element) matrices. In this paper wer propose a Block-ADI method, which is applicable to Finite Element metrices. The new approach is a combination of classical ADI method and domain decompositi on. Also, we provide a partial proof of the convergence based on the results from the regular splittings, in case the discretization metrix is symmetric positive definite.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.435-443
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• 2007

Computing the interior spectrum of large sparse generalized eigenvalue problems $Ax\;=\;{\lambda}Bx$, where A and b are large sparse and SPD(Symmetric Positive Definite), is often required in areas such as structural mechanics and quantum chemistry, to name a few. Recently, CG-type methods have been found useful and hence, very amenable to parallel computation for very large problems. Also, as in the case of linear systems proper choice of preconditioning is known to accelerate the rate of convergence. After the smallest eigenpair is found we use the orthogonal deflation technique to find the next m-1 eigenvalues, which is also suitable for parallelization. This offers advantages over Jacobi-Davidson methods with partial shifts, which requires re-computation of preconditioner matrx with new shifts. We consider as preconditioners Incomplete LU(ILU)(0) in two variants, ever-relaxation(SOR), and Point-symmetric SOR(SSOR). We set m to be 5. We conducted our experiments on matrices from discretizations of partial differential equations by finite difference method. The generated matrices has dimensions up to 4 million and total number of processors are 32. MPI(Message Passing Interface) library was used for interprocessor communications. Our results show that in general the Multi-Color ILU(0) gives the best performance.

• 한국전산유체공학회:학술대회논문집
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• 2001.10a
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• pp.1-9
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• 2001

In this paper, some numerical methods recently developed for gas-liquid two-phase flows are reviewed. And then, a preconditioning method to solve cavitating flow by the author is introduced. This method employs a finite-difference Runge-Kutta method combined with MUSCL TVD scheme, and a homogeneous equilibrium cavitation model. So that it permits to treat simply the whole gas-liquid two-phase flow field including wave propagation, large density changes and incompressible flow characteristic at low Mach number. Finally, numerical results such as detailed observations of the unsteady cavity flows, a sheet cavitation break-off phenomena and some data related to performance characteristics of hydrofoils are shown.

• Journal of Chest Surgery
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• v.34 no.11
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• pp.809-822
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• 2001

Background: Ischemic preconditioning(IP) is known to be effective in the protection of myocardial necrosis, arrhythmia, and the restoration of the myocardial function in the ischemia-reperfusion state of the heart. However the exact mechanism is not clearly understood. The purpose of this study was to elucidate the trigger mechanism 7f IP on the restoration of the myocardial function after ischemia-reperfusion. Material and Method: By connecting a Langendorff perfusion apparatus with an isolated heart of a rat, the normal temperature of the heart was maintained. The experiment was conducted in seven groups, which were divided according to the preconditioning stimuli and blockage methods Group I(n=10) was a group without IP, Group II(n=10) a group of three-minute IP, Group III(n=10) a group of PEIP, Group IV(n=10) a group of clonidine IP, Group V(n=10) a group of If after reserpine, Group Vl(n=10) a group of PE & prazosin IP, and Group Vll(n=10) a group of clonidine & yohimbine IP. Hemodynamic parameters of DP, LVEDP, $\pm$dP/dT and the changes of perfusion in the coronary artery were evaluated. Result: Developed pressure and +dP/dT changed per unit time. After 20 minutes of reperfusion, those of Group II and III were 63.1$\pm$3.7%, 64.8$\pm$4.6% and 64.5$\pm$4.6%, 63.8$\pm$4.4%, which improved more significantly than those of Group I(P<0.05), However, there were no significant differences between the Groups V and Vl, and Group I. Conclusion: The Brief ischemic preconditioning and pharmacological preconditioning using $\alpha$-receptor sympatho-mimetics have protecting effects on the restoration of myocardial function after reperfusion. And the protecting effect of preconditioning seems to be related to sympathetic neurotransmitters and to the selective action of the $\alpha$$_1$-adrenergic receptor.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.35-38
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• 2002

The convergence acceleration methods for the compressible Wavier-Stokes equations are studied ,which are multigrid method and implicit preconditioned multistage time stepping method. In this paper, the performance of implicit preconditioning methods are studied for the full-coarsening multigrid methods on the high Reynolds number compressible flow computations. The effect of numerical flux on the convergence are investigated for the inviscid and viscous calculations.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.127-137
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• 2005

The objective of numerical analysis is to devise and analyze efficient algorithms or numerical methods for equations arising in mathematical modeling for science and engineering. In this article, we present some recent topics in computational mathematics, specially in the finite element method and overview the development of the mixed finite element method in the context of second order elliptic and parabolic problems. Multiscale methods such as MsFEM, HMM, and VMsM are included.