• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제18권1호
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• pp.61-74
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• 2014

This paper presents accurate and efficient numerical methods for calculating the sensitivities of two-asset European options, the Greeks. The Greeks are important financial instruments in management of economic value at risk due to changing market conditions. The option pricing model is based on the Black-Scholes partial differential equation. The model is discretized by using a finite difference method and resulting discrete equations are solved by means of an operator splitting method. For Delta, Gamma, and Theta, we investigate the effect of high-order discretizations. For Rho and Vega, we develop an accurate and robust automatic algorithm for finding an optimal value. A cash-or-nothing option is taken to demonstrate the performance of the proposed algorithm for calculating the Greeks. The results show that the new treatment gives automatic and robust calculations for the Greeks.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1999년도 추계 학술대회논문집
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• pp.17-22
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• 1999

Convergence characteristics and efficiency of three implicit approximate factorization schemes(ADI, DDADI and MAF) are examined using 2-Dimensional compressible upwind Navier-Stokes code. Second-order CSCM(Conservative Supra Characteristic Method) upwind flux difference splitting method with Fromm scheme is used for the right-hand side residual evaluation, while generally first-order upwind differencing is used for the implicit operator on the left-hand side. Convergence studies are performed using an example of the flow past a NACA0012 airfoil at steady transonic flow condition, i. e. Mach number 0.8 at $1.25^{\circ}$ angle of attack. The results were compared with other computational results in order to validate the current numerical analysis. The results from the implicit AF algorithms were compared well in low surface with the other computational results; however, not well in upper surface. It might be due to lack of the grid around the shock position. Because the algorithm minimizes the errors of the approximate decomposition, the improved convergence rate with MAF were observed.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2004년도 추계학술대회 논문집
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• pp.503-509
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• 2004

With modem computational fluid dynamics method (CFD), air-charging models of the air brake pipe system and auxiliary reservoir are built. Compared with one-dimension model, no empirical formula is introduced to solve branch pipe fields for two-dimension model. A modified operator-splitting method is presented to solve the coupled equations of pressure and velocity, and numerical simulation shows that it is very stable. Compare the numerical results with empirical data of heavy haul trains in home and abroad so as to prove the correctness of the theory and algorithm presented. This paper gives theoretic reference to the experiments of braking effects of heavy haul trains, and forms a basis for development of complete freight train air brake system simulation.

• 천문학회지
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• 제28권2호
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• pp.223-243
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• 1995

We describe the implementation of a multi-dimensional numerical code to solve the equations for idea! magnetohydrodynamics (MHD) in cylindrical geometry. It is based on an explicit finite difference scheme on an Eulerian grid, called the Total Variation Diminishing (TVD) scheme, which is a second-order-accurate extension of the Roe-type upwind scheme. Multiple spatial dimensions are treated through a Strang-type operator splitting. Curvature and source terms are included in a way to insure the formal accuracy of the code to be second order. The constraint of a divergence-free magnetic field is enforced exactly by adding a correction, which involves solving a Poisson equation. The Fourier Analysis and Cyclic Reduction (FACR) method is employed to solve it. Results from a set of tests show that the code handles flows in cylindrical geometry successfully and resolves strong shocks within two to four computational cells. The advantages and limitations of the code are discussed.

• Structural Engineering and Mechanics
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• 제3권2호
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• pp.185-192
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• 1995

A numerical algorithm for plane stress and shell elasto-plasticity is presented in this paper. The proposed strain decomposition (SD) algorithm is an elastic predictor/plastic corrector algorithm, and in the context of operator splitting, is a return mapping algorithm. However, it differs significantly from other return mapping algorithms in that only the necessary response functions are used without invoking their gradients, and the stress increment is updated only at the end of the time step. This makes the proposed SD algorithm more suitable for materials with complex yield surfaces and will guard against error accumulation during the time step. Comparative analyses of structural systems using the proposed strain decomposition (SD) algorithm and the iterative radial return (IRR) algorithm are presented. The results demonstrate the accuracy and usefulness of the proposed algorithm.

• Environmental Engineering Research
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• 제19권2호
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• pp.165-174
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• 2014

A model combining multi-dimensional discretized population balance equations with a computational fluid dynamics simulation (CFD-DPBE model) was developed and applied to simulate turbulent flocculation and sedimentation processes in sediment retention basins. Computation fluid dynamics and the discretized population balance equations were solved to generate steady state flow field data and simulate flocculation and sedimentation processes in a sequential manner. Up-to-date numerical algorithms, such as operator splitting and LeVeque flux-corrected upwind schemes, were applied to cope with the computational demands caused by complexity and nonlinearity of the population balance equations and the instability caused by advection-dominated transport. In a modeling and simulation study with a two-dimensional simplified pond system, applicability of the CFD-DPBE model was demonstrated by tracking mass balances and floc size evolutions and by examining particle/floc size and solid concentration distributions. Thus, the CFD-DPBE model may be used as a valuable simulation tool for natural and engineered flocculation and sedimentation systems as well as for flocculant-aided sediment retention ponds.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권4호
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• pp.329-341
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• 2021

In this study, we consider an efficient and accurate finite difference method for the four underlying asset equity-linked securities (ELS). The numerical method is based on the operator splitting method with non-uniform grids for the underlying assets. Even though the numerical scheme is implicit, we solve the system of discrete equations in explicit manner using the Thomas algorithm for the tri-diagonal matrix resulting from the system of discrete equations. Therefore, we can use a relatively large time step and the computation of the ELS option pricing is fast. We perform characteristic computational test. The numerical test confirm the usefulness of the proposed method for pricing the four underlying asset equity-linked securities.

• 대한전자공학회논문지SP
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• 제39권6호
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• pp.565-574
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• 2002

본 논문에서는 다중 표현(Multiple Description)과 비트율-왜곡 연산자(rate-distortion operator)를 이용하여 에러가 발생하기 쉬운 환경에서 사용될 수 있는 강인한 동영상 압축 알고리듬을 제안한다. 하나의 비디오 스트림을 두 개의 연관된 표현 (description)으로 나누기 위해 과잉 비트율-왜곡(redundancy rate-distortion : RRD) 기준을 사용하였다. 제안하는 방법은 새로 추가한 비트율-왜곡 연산자와 새로 제안된 최적화 방법을 통해 기존의 RRD 기반 방법들보다 최적화 성능을 향상시킬 수 있다. 또한 실질적인 에러 환경을 고려한 새로운 왜곡 측정법(distortion measure)을 정의하였다. 제안하는 다중 표현 동영상 압축기는 H.263 표준을 기반으로 하기 때문에 각각의 표현은 H.263 표준 디코더를 사용하여 독립적으로 디코딩 될 수 있다. 또한, 기존의 방법과는 달리 손실된 표현에 대한 복잡한 예측과정이 없어도 간단한 병합 과정을 통해 여러 개의 표현을 하나의 스트림으로 디코딩 할 수 있다. 모의 실험 결과, 제안하는 다중 표현 동영상 압축 방법은 기존의 다중 표현 분할(multiple description split) 방법보다 모든 비트율에서 더 좋은 성능을 보임을 알 수 있다.

• Earthquakes and Structures
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• 제8권6호
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• pp.1325-1348
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• 2015

Real-time hybrid testing (RTHT) involves virtual splitting of the structure into two parts: physical substructure that contains the key region of interest which is tested in a laboratory and numerical substructure that contains the remaining part of the structure in the form of a numerical model. This paper numerically assesses four step-by-step integration methods (Central difference method (CDM), Operator splitting method (OSM), Rosenbrock based method (RBM) and CR-integration method (CR)) which are widely used in RTHT. The methods have been assessed in terms of stability and accuracy for various realistic damping ratios of the physical substructure. The stability is assessed in terms of the spectral radii of the amplification matrix while the accuracy in terms of numerical damping and period distortion. In order to evaluate the performance of the methods, five carefully chosen examples have been studied - undamped SDOF, damped SDOF, instantaneous softening, instantaneous hardening and hysteretic system. The performance of the methods is measured in terms of a non-dimensional error index for displacement and velocity. Based on the error indices, it is observed that OSM and RBM are robust and performs fairly well in all the cases. CDM performed well for undamped SDOF system. CR method can be used for the system showing softening behaviour. The error indices indicate that accuracy of OSM is more than other method in case of hysteretic system. The accuracy of the results obtained through time integration methods for different damping ratios of the physical substructure is addressed in the present study. In the presence of a number of integration methods, it is preferable to have criteria for the selection of the time integration scheme. As such criteria are not available presently, this paper attempts to fill this gap by numerically assessing the four commonly used step-by-step methods.

• Smart Structures and Systems
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• 제14권6호
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• pp.1131-1150
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• 2014

One of the issues in extending the range of applicable problems of real-time hybrid simulation is the computation speed of the simulator when large-scale computational models with a large number of DOF are used. In this study, functionality of real-time dynamic simulation of MDOF systems is achieved by creating a logic circuit that performs the step-by-step numerical time integration of the equations of motion of the system. The designed logic circuit can be implemented to an FPGA-based system; FPGA (Field Programmable Gate Array) allows large-scale parallel computing by implementing a number of arithmetic operators within the device. The operator splitting method is used as the numerical time integration scheme. The logic circuit consists of blocks of circuits that perform numerical arithmetic operations that appear in the integration scheme, including addition and multiplication of floating-point numbers, registers to store the intermediate data, and data busses connecting these elements to transmit various information including the floating-point numerical data among them. Case study on several types of linear and nonlinear MDOF system models shows that use of resource sharing in logic synthesis is crucial for effective application of FPGA to real-time dynamic simulation of structural response with time step interval of 1 ms.