• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.297-311
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• 2015

We present a robust and accurate boundary condition for pricing financial options that is a hybrid combination of the payoff-consistent extrapolation and the Dirichlet boundary conditions. The payoff-consistent extrapolation is an extrapolation which is based on the payoff profile. We apply the new hybrid boundary condition to the multi-dimensional Black-Scholes equations with a high correlation. Correlation terms in mixed derivatives make it more difficult to get stable numerical solutions. However, the proposed new boundary treatments guarantee the stability of the numerical solution with high correlation. To verify the excellence of the new boundary condition, we have several numerical tests such as higher dimensional problem and exotic option with nonlinear payoff. The numerical results demonstrate the robustness and accuracy of the proposed numerical scheme.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.6
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• pp.685-692
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• 2003

A numerical simulation of flame propagation in a micro combustor was carried out. Combustor has a sub -millimeter depth cylindrical internal volume and axisymmetric one-dimensional was used to simplify the geometry. Semi-empirical heat transfer model was used to account for the heat loss to the walls during the flame propagation. A detailed chemical kinetics model of $H_2/Air$ with 10 species and 16 reaction steps was used to calculate the combustion. An operator-splitting PISO scheme that is non-iterative, time-dependent, and implicit was used to solve the system of transport equations. The computation was validated for adiabatic flame propagation and showed good agreement with existing results of adiabatic flame propagation. A full simulation including the heat loss model was carried out and results were compared with measurements made at corresponding test conditions. The heat loss that adds its significance at smaller value of combust or height obviously affected the flame propagation speed as final temperature of the burnt gas inside the combustor. Also, the distribution of gas properties such as temperature and species concentration showed wide variation inside the combustor, which affected the evaluation of total work available of the gases.

• Water for future
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• v.27 no.2
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• pp.155-166
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• 1994

Various Eulerian-Lagrangian numerical models for the one-dimensional longitudinal dispersion equation are studied comparatively. In the model studied, the transport equation is decoupled into two component parts by the operator-splitting approach ; one part governing adveciton and the other dispersion. The advection equation has been solved using the method of characteristics following fluid particles along the characteristic line and the results are interpolated onto an Eulerian grid on which the dispersion equation is solved by Crank-Nicholson type finite difference method. In solving the advection equation, various interpolation schemes are tested. Among those, Hermite interpolation polynomials are superior to Lagrange interpolation polynomials in reducing dissipation and dispersion errors in the simulation.

• Nuclear Engineering and Technology
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• v.54 no.8
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• pp.2828-2839
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• 2022

This study developed a safety assessment tool for geological disposal systems called APro, a systemically integrated modeling system based on modularizing and coupling the processes which need to be considered in a geological disposal system. Thermal, hydraulic, chemical, canister failure, radionuclide release and transport processes were considered in the current version of APro. Each of the unit processes in APro consists of a single Default Module, and several Alternative Modules which can increase the flexibility of the model. As an initial stage of developing the modularization concept and modeling interface, the Default Modules of each unit process were described, with one Alternative Module of chemical process. The computation part of APro is mainly a MATLAB workspace controlling COMSOL and PHREEQC, which are coupled by an operator splitting scheme. The APro model domain is a stylized geological disposal system employing the Swedish disposal concept (KBS-3 type), but the repository layout can be freely adjusted. In order to show the applicability of APro to the total system performance assessment of geological disposal system, some sample simulations were conducted. From the results, it was confirmed that coupling of the thermal and hydraulic processes and coupling of the canister failure and the radionuclide release processes were well reflected in APro. In addition, the technical connectivity between COMSOL and PHREEQC was also confirmed.

• Journal of the Korean Data and Information Science Society
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• v.28 no.6
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• pp.1229-1244
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• 2017

In recent years, as demand for data-based analytical methodologies increases in various fields, optimization methods have been developed to handle them. In particular, various constraints required for problems in statistics and machine learning can be solved by convex optimization. Alternating direction method of multipliers (ADMM) can effectively deal with linear constraints, and it can be effectively used as a parallel optimization algorithm. ADMM is an approximation algorithm that solves complex original problems by dividing and combining the partial problems that are easier to optimize than original problems. It is useful for optimizing non-smooth or composite objective functions. It is widely used in statistical and machine learning because it can systematically construct algorithms based on dual theory and proximal operator. In this paper, we will examine applications of ADMM algorithm in various fields related to statistics, and focus on two major points: (1) splitting strategy of objective function, and (2) role of the proximal operator in explaining the Lagrangian method and its dual problem. In this case, we introduce methodologies that utilize regularization. Simulation results are presented to demonstrate effectiveness of the lasso.

• Water for future
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• v.28 no.5
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• pp.151-162
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• 1995

A two-dimensional stream tube dispersion model is developed to simulate accurately transverse dispersion processes of pollutants in natural channels. Two distinct features of the stream tube dispersion model derived herein are that it employs the transverse cumulative discharge as an independent variable replacing the transverse distance and that it is developed in a natural coordinate system which follows the general direction of the channel flow. In the model studied, Eulerian-Lagrangian method is used to solve the stream tube dispersion equation. The stream tube dispersion equation is decoupled into two components by the operator-splitting approach; one is governing advection and the other is governing dispersion. The advection equation has been solved using the method of characteristics and the results are interpolated onto Eulerian grid on which the dispersion equation is solved by centered difference method. In solving the advection equation, cubic spline interpolating polynomials is used. In the present study, the results of the application of this model to a natural channel are compared with a steady-state flow measurements. Simulation results are in good accordance with measured data.

• Journal of the Korean Society of Hazard Mitigation
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• v.7 no.3
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• pp.69-78
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• 2007

In this study, a time-dependent aspect of an embankment failure is considered to simulate a flood inundation map and calculate overtopping discharge induced by an embankment failure. A numerical model has been developed by solving the two dimensional nonlinear shallow water equations with a finite volume method on unstructured grids. To analyze a Riemann problem, the HLLC approximate Riemann solver and the Weighted Averaged Flux method are employed by using a TVD limiter and the source term treatment is also employed by using the operator splitting method. Firstly, the numerical model is applied to a dam break problem and a sloping seawall. Obtained numerical results show good agreements with experimental data. Secondly, the model is applied to a flow induced by an embankment failure by assuming that the width and elevation of embankment are varied with time-dependent functions. As a result of the comparison with each numerical overtopping discharge, established flood inundation discharges in the previous studies are overestimated than the result of the present numerical model.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.17 no.2
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• pp.227-234
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• 2019

A user-friendly modeling interface is developed for a process-based total system performance assessment framework (APro) specialized for a generic geological disposal system for high-level radioactive waste. The APro modeling interface is constructed using MATLAB, and the operator splitting scheme is used to combine COMSOL for simulation of multiphysics and PHREEQC for the calculation of geochemical reactions. As APro limits the modeling domain to the generic disposal system, the degree of freedom of the model is low. In contrast, the user-friendliness of the model is improved. Thermal, hydraulic, mechanical and chemical processes considered in the disposal system are modularized, and users can select one of multiple modules: "Default process" and multi "Alternative process". APro mainly consists of an input data part and calculation execution part. The input data are prepared in a single EXCEL file with a given format, and the calculation part is coded using MATLAB. The final results of the calculation are created as an independent COMSOL file for further analysis.

• Tuberculosis and Respiratory Diseases
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• v.86 no.3
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• pp.203-215
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• 2023

Background: Surgical resection is the standard treatment for early-stage lung cancer. Since postoperative lung function is related to mortality, predicted postoperative lung function is used to determine the treatment modality. The aim of this study was to evaluate the predictive performance of linear regression and machine learning models. Methods: We extracted data from the Clinical Data Warehouse and developed three sets: set I, the linear regression model; set II, machine learning models omitting the missing data: and set III, machine learning models imputing the missing data. Six machine learning models, the least absolute shrinkage and selection operator (LASSO), Ridge regression, ElasticNet, Random Forest, eXtreme gradient boosting (XGBoost), and the light gradient boosting machine (LightGBM) were implemented. The forced expiratory volume in 1 second measured 6 months after surgery was defined as the outcome. Five-fold cross-validation was performed for hyperparameter tuning of the machine learning models. The dataset was split into training and test datasets at a 70:30 ratio. Implementation was done after dataset splitting in set III. Predictive performance was evaluated by R² and mean squared error (MSE) in the three sets. Results: A total of 1,487 patients were included in sets I and III and 896 patients were included in set II. In set I, the R² value was 0.27 and in set II, LightGBM was the best model with the highest R² value of 0.5 and the lowest MSE of 154.95. In set III, LightGBM was the best model with the highest R² value of 0.56 and the lowest MSE of 174.07. Conclusion: The LightGBM model showed the best performance in predicting postoperative lung function.