• 한국전산유체공학회:학술대회논문집
• /
• 2006.05a
• /
• pp.372-375
• /
• 2006

• Wind and Structures
• /
• v.12 no.1
• /
• pp.1-19
• /
• 2009

In this paper, the airflow around an ideal thin plate (hereafter referred to as ITP) with various ratios of central slot is simulated by using the finite-difference-method (FDM)-based Arbitrary-Lagrangian-Eulerian descriptions for the rigid oscillating body. The numerical procedure employs the second-order projection scheme to decouple the governing equations, and the multigrid algorithm with three levels to improve the computational efficiency in evaluating of the pressure equation. The present CFD method is validated through comparing the computed flutter derivatives of the ITP without slot to Theodorsen analytical solutions. Then, the unsteady aerodynamics of the ITP with and without central slot is investigated. It is found that even a smaller ratio of central slot of the ITP has notable effects on pressure distributions of the downstream section, and the pressure distributions on the downstream section will further be significantly affected by the slot ratio and the reduced wind speeds. Continuous increase of $A_2^*$ with the increase of central slot may be the key feature of the slotted ITP. Finally, flutter analyses based on the flutter derivatives of the slotted ITP are performed, and moreover, flutter instabilities of a scaled sectional model of a twin-deck bridge with various ratios of deck slot are investigated. The results confirm that the central slot is effective to improve bridge flutter stabilities, and that the flutter critical wind speeds increase with the increase of slot ratio.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.23 no.2
• /
• pp.65-92
• /
• 2019

We survey a recently developed immersed finite element method (IFEM) for the interface problems. The IFEM uses structured grids such as uniform grids, even if the interface is a smooth curve. Instead of fitting the curved interface, the bases are modified so that they satisfy the jump conditions along the interface. The early versions of IFEM [1, 2] were suboptimal in convergence order [3]. Later, the consistency terms were added to the bilinear forms [4, 5], thus the scheme became optimal and the error estimates were proven. For elasticity problems with interfaces, we modify the Crouzeix-Raviart based element to satisfy the traction conditions along the interface [6], but the consistency terms are not needed. To satisfy the Korn's inequality, we add the stabilizing terms to the bilinear form. The optimal error estimate was shown for a triangular grid. Lastly, we describe the multigrid algorithms for the discretized system arising from IFEM. The prolongation operators are designed so that the prolongated function satisfy the flux continuity condition along the interface. The W-cycle convergence was proved, and the number of V-cycle is independent of the mesh size.

• Proceedings of the Korea Water Resources Association Conference
• /
• 1995.05a
• /
• pp.67-72
• /
• 1995

• Communications of the Korean Mathematical Society
• /
• v.15 no.1
• /
• pp.143-153
• /
• 2000

In [8], Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated linear systems. In this work, we propose the block diagonal preconditioners. The preconditioned conjugate residual method is robust in that the convergence is uniform as the parameter, v, goes to $\sfrac{1}{2}$. Computational experiments are included.

• Communications of the Korean Mathematical Society
• /
• v.24 no.4
• /
• pp.617-628
• /
• 2009

We present an efficient and accurate finite-difference method for computing Black-Scholes partial differential equations with multiunderlying assets. We directly solve Black-Scholes equations without transformations of variables. We provide computational results showing the performance of the method for two underlying asset option pricing problems.

• Tribology and Lubricants
• /
• v.23 no.5
• /
• pp.187-194
• /
• 2007

The profile of the roller in the axial direction is the main design factor in order to increase endurance life against the contact fatigue due to the stress concentration along the edge of the roller. Even under the elas-tohydrodynamic lubrication (ehl) conditions, the stress concentration along the edge of the roller greatly worsens the fatigue life both for the roller and contacting body. In this study, roller contacts of finite axial length are studied for the film thickness and pressure of ehl. For the real contact behaviors under the ehl conditions, multigrid and multi-level method is applied so that much higher loading conditions can be investigated. Several axial profiles of roller are investigated to verify how both ehl film and pressure are generated and some of them are recommended for the ehl contact condition.

• Computers and Concrete
• /
• v.29 no.2
• /
• pp.93-105
• /
• 2022

The degrees of freedom (DOFs) of high-rise structures increase rapidly due to the need for refined analysis, which poses a challenge toward a computationally efficient method for numerical analysis of high-rise structures using the finite element method (FEM). This paper presented an efficient iterative method, an algebraic multigrid (AMG) with a Jacobi overrelaxation smoother preconditioned conjugate gradient method (AMG-CG) used for solving large-scale structural system equations running on heterogeneous platforms with parallel accelerator graphics processing units (GPUs) enabled. Furthermore, an AMG-CG FEM application framework was established for the numerical analysis of high-rise structures. In the proposed method, the coarsening method, the optimal relaxation coefficient of the JOR smoother, the smoothing times, and the solution method for the coarsest grid of an AMG preconditioner were investigated via several numerical benchmarks of high-rise structures. The accuracy and the efficiency of the proposed FEM application framework were compared using the mature software Abaqus, and there were speedups of up to 18.4x when using an NVIDIA K40C GPU hosted in a workstation. The results demonstrated that the proposed method could improve the computational efficiency of solving structural system equations, and the AMG-CG FEM application framework was inherently suitable for numerical analysis of high-rise structures.

• 한국전산유체공학회:학술대회논문집
• /
• 1999.05a
• /
• pp.23-28
• /
• 1999

A mutigrid convergence acceleration technique is presented for computing hypersonic inviscid and viscous flows in equilibrium state. The governing equations are solved using an explicit Runge-Kutta method. Curve fitting data in NASA Reference Publication 1181, 1260 are used to calculate equilibrium properties. In order to ensure stability, damped prolongation and modified implicit residual smoothing are proposed. Blunt body test cases are presented to demonstrate the robustness and the efficiency in performance of the proposed methods

• Geophysics and Geophysical Exploration
• /
• v.11 no.1
• /
• pp.60-67
• /
• 2008

In this paper we consider an application of the method of electromagnetic (EM) migration to the interpretation of a typical marine controlled-source (MCSEM) survey consisting of a set of sea-bottom receivers and a moving electrical bipole transmitter. Three-dimensional interpretation of MCSEM data is a very challenging problem because of the enormous number of computations required in the case of the multi-transmitter and multi-receiver data acquisition systems used in these surveys. At the same time, we demonstrate that the MCSEM surveys with their dense system of transmitters and receivers are extremely well suited for application of the migration method. In order to speed up the computation of the migration field, we apply a fast form of integral equation (IE) solution based on the multigrid quasi-linear (MGQL) approximation which we have developed. The principles of migration imaging formulated in this paper are tested on a typical model of a sea-bottom petroleum reservoir.