• Journal of computational fluids engineering
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• v.13 no.3
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• pp.69-78
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• 2008

The high-order numerical method based on the adaptive mesh refinement(AMR) on the quadrilateral unstructured grids has been developed in this paper. This adaptive-grid method, originally developed with MUSCL-TVD scheme, is now extended to the WENO (weighted essentially no-oscillatory) scheme with the Runge-Kutta time integration of fifth order in spatial and temporal accuracy. The multidimensional interpolation was studied in the preliminary research, which allows us to maintain the same order of accuracy for the computation of numerical flux between two adjacent cells of different levels. Some standard benchmark tests are done to validate this method for checking the overall capacity and efficiency of the present adaptive-grid technique.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.4
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• pp.295-306
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• 2013

In this paper, we consider the adaptive multigrid method for solving the Black-Scholes equation to improve the efficiency of the option pricing. Adaptive meshing is generally regarded as an indispensable tool because of reduction of the computational costs. The Black-Scholes equation is discretized using a Crank-Nicolson scheme on block-structured adaptively refined rectangular meshes. And the resulting discrete equations are solved by a fast solver such as a multigrid method. Numerical simulations are performed to confirm the efficiency of the adaptive multigrid technique. In particular, through the comparison of computational results on adaptively refined mesh and uniform mesh, we show that adaptively refined mesh solver is superior to a standard method.

• 한국전산유체공학회:학술대회논문집
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• 2006.10a
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• pp.24-25
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• 2006

An unstructured mesh method has been developed for the simulation of steady and time-accurate flows around helicopter rotors. A dynamic and quasi-unsteady solution-adaptive mesh refinement technique was adopted for the enhancement of the solution accuracy in the local region of interest involving highly vortical flows. Applications were made to the 2-D blade-vortex interaction aerodynamics and the 3-D rotor blades in hover. The interaction between the rotor and the airframe in forward flight was investigated by introducing an overset mesh technique.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1993.04a
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• pp.3-10
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• 1993

A new three-dimensional transition solid elements was presented for the automated three-dimensional adaptive h-refinement where the steep stress gradient exists. To be consistent with 8-node solid element with nonconforming modes in accuracy, these transition elements were improved through the addition of the associated nonconforming modes. Numerical examples show that the performance of the element and the applicability to 3D adaptations are satisfactory.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.3
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• pp.265-272
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• 2007

The finite element linear buckling analysis of folded plate structures using adaptive h-refinement methods is presented in this paper. The variable-node flat shell element used in this study possesses the drilling D.O.F. which, in addition to improvement of the element behavior, permits an easy connection to other elements with six degrees of freedom per node. The Box-typed structures can be analyzed using these developed flat shell elements. By introducing the variable-node elements some difficulties associated with connecting the different layer patterns, which are common in the adaptive h-refinement on quadrilateral mesh, can be overcome. To obtain better stress field for the error estimation, the super-convergent patch recovery is used. The convergent buckling modes and the critical loads associated with these modes can be obtained.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.9
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• pp.1849-1858
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• 2002

An h-adaptive scheme of first-order least-squares meshfree method is presented. A posteriori error estimates, which can be readily computed from the residual, are also presented. For elliptic problem the error indicators are further improved by applying the Aubin-Nitsche method. In the proposed refinement scheme, Voronoi cells are utilized to insert nodes at appropriate positions. Through numerical examples, it is demonstrated that the error indicators reveal good correlations with the actual errors and the adaptive first-order least-squares meshfree method is effectively applied to the localized problems such as the shock formation in fluid dynamics.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.1
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• pp.224-241
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• 2015

Multiview plus depth (MVD) videos are widely used in free-viewpoint TV systems. The best-known technique to determine depth information is based on stereo vision. In this paper, we propose a novel local stereo matching algorithm which is radiometric invariant. The key idea is to use a combined matching cost of intensity and gradient based similarity measure. In addition, we realize an adaptive cost aggregation scheme by constructing an adaptive support window for each pixel, which can solve the boundary and low texture problems. In the disparity refinement process, we propose a four-step post-processing technique to handle outliers and occlusions. Moreover, we conduct stereo reconstruction tests to verify the performance of the algorithm more intuitively. Experimental results show that the proposed method is effective and robust against local radiometric distortion. It has an average error of 5.93% on the Middlebury benchmark and is compatible to the state-of-art local methods.

• 한국전산유체공학회:학술대회논문집
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• 2011.05a
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• pp.294-301
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• 2011

A two-dimensional hybrid flaw solver has been developed for the accurate and efficient simulation of steady and unsteady flaw fields. The flow solver was cast to accommodate two different topologies of computational meshes. Triangular meshes are adopted in the near-body region such that complex geometric configurations can be easily modeled, while adaptive Cartesian meshes are, utilized in the off-body region to resolve the flaw more accurately with less numerical dissipation by adopting a spatially high-order accurate scheme and solution-adaptive mesh refinement technique. A chimera mesh technique has been employed to link the two flow regimes adopting each mesh topology. Validations were made for the unsteady inviscid vol1ex convection am the unsteady turbulent flaws over an NACA0012 airfoil, and the results were compared with experimental and other computational results.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.335-349
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• 2003

Almost all business are affected by the weather so that weather derivatives has been traded to hedge weather risk. Since the weather itself is not an asset with a market price, some analysts believe that the Black-Scholes equation could not be used appropriately to price weather derivative options. But some weather derivatives can be considered as an Asian option, we revisit the Black-scholes model. Numerical solution of the Black-Scholes equation has a significant error at the money option or around the money option, it is necessary to adopt adaptive mesh near to the strike value. Here we propose a numerical method with an adaptive grid refinement.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.9
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• pp.149-157
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• 2004

This paper presents a new method for hi-objective optimization. Ordinary weighted sum method is easy to implement, but it has two significant drawbacks: (1) the solution distribution by the weighted sum method is not uniform, and (2) the method cannot determine any solutions that reside in non-convex regions of a Pareto front. The proposed adaptive weighted sum method does not solve a multiobjective optimization in a predetermined way, but it focuses on the regions that need more refinement by imposing additional inequality constraints. It is demonstrated that the adaptive weighted sum method produces uniformly distributed solutions and finds solutions on non-convex regions. Two numerical examples and a simple structural problem are presented to verify the performance of the proposed method.