• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.299-318
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• 2023

This article devises an exponentially fitted method for the numerical solution of two parameter singularly perturbed parabolic boundary value problems. The proposed scheme is able to resolve the two lateral boundary layers of the solution. Error estimates show that the constructed scheme is parameter-uniformly convergent with a quadratic numerical rate of convergence. Some numerical test examples are taken from recently published articles to confirm the theoretical results and demonstrate a good performance of the current scheme.

• Atmosphere
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• v.30 no.4
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• pp.335-346
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• 2020

Three free parameters included in a cumulus parameterization are optimized by using micro-genetic algorithm for three precipitation cases occurred in the Korea Peninsula during the summer season in order to reduce biases in a regional model associated with the uncertainties of the parameters and thus to improve the predictability of precipitation. The first parameter is the one that determines the threshold in convective trigger condition. The second parameter is the one that determines boundary layer forcing in convective closure. Finally, the third parameter is the one used in calculating conversion parameter determining the fraction of condensate converted to convective precipitation. Optimized parameters reduce the occurrence of convections by suppressing the trigger of convection. The reduced convection occurrence decreases light precipitation but increases heavy precipitation. The sensitivity experiments are conducted to examine the effects of the optimized parameters on the predictability of precipitation. The predictability of precipitation is the best when the three optimized parameters are applied to the parameterization at the same time. The first parameter most dominantly affects the predictability of precipitation. Short-range forecasts for July 2018 are also conducted to statistically assess the precipitation predictability. It is found that the predictability of precipitation is consistently improved with the optimized parameters.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.34 no.2
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• pp.174-184
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• 1998

In order to accumulate fundamental. data for control of fishes’ behavior at the real fishing ground, the fitness of the numerical model for describing the behavior of fishes was examined by the marine fish. Mullet, Mugil cephalus were used as experimental fishes. The numerical model of fishes’ behavior presented in our earlier paper was modified on the vertical movement of fish school. For the comparision of parameters of the modified numerical model between mullet and rainbow trout, the estimated values of parameters were identified with dimension. The fitness of the modified numerical model was examined by the comparision between experiment and simulation on the several indexes represented by fishes’ swimming characteristics. The obtained result are summarized a follows : 1. The non-dimensional parameter a’ of propulsive force and kb’ of interactive force by the experiment without model net showed a similarity, but the non-dimensional parameter k sub(c’) of schooling force for rainbow trout was lager than one for mullet and the non-dimensional parameter k sub(w’) of repulsive force for mullet was lager than one for rainbow trout. 2. The non-dimensional parameter a’ and k sub(b’) for rainbow trout by the experiment with model net were a little lager than ones for mullet, but non-dimensional parameter k sub(c’) and k sub(w’) for mullet were lager than ones for rainbow trout. 3. The non-dimensional parameter k sub(c’) and k sub(b’) showed the largest and the smallest value among the non-dimensional parameters for rainbow trout and mullet, respectively. 4. The fitness of the modified numerical model was confirmed by means of the compulsion between experiment and simulation on the swimming trajectory of fishes, the mean distance of individual from wall, the mean swimming speed, the mean swimming depth and the mean distance between the nearest individuals. Especially, the similarity of mean swimming depth was improved by using the modified numerical model.

• Earthquakes and Structures
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• v.11 no.2
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• pp.297-313
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• 2016

A virtual parameter is introduced into the formulation of the previously published integration method to improve its stability properties. It seems that the numerical properties of this integration method are almost unaffected by this parameter except for the stability property. As a result, it can have second order accuracy, explicit formulation and controllable numerical dissipation in addition to the enhanced stability property. In fact, it can have unconditional stability for the system with the instantaneous degree of nonlinearity less than or equal to the specified value of the virtual parameter for the modes of interest for each time step.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.813-829
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• 2011

In this article, we present a numerical scheme for solving singularly perturbed (i.e. highest -order derivative term multiplied by small parameter) Burgers-Huxley equation with appropriate initial and boundary conditions. Most of the traditional methods fail to capture the effect of layer behavior when small parameter tends to zero. The presence of perturbation parameter and nonlinearity in the problem leads to severe difficulties in the solution approximation. To overcome such difficulties the present numerical scheme is constructed. In construction of the numerical scheme, the first step is the dicretization of the time variable using forward difference formula with constant step length. Then, the resulting non linear singularly perturbed semidiscrete problem is linearized using quasi-linearization process. Finally, differential quadrature method is used for space discretization. The error estimate and convergence of the numerical scheme is discussed. A set of numerical experiment is carried out in support of the developed scheme.

• Journal of Korean Tunnelling and Underground Space Association
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• v.19 no.5
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• pp.799-812
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• 2017

Backfill grouting and realistic convergence distribution were not properly considered in previous studies on 2D numerical analysis of a shield TBM tunnel. In this study, a modeling method was suggested to cope with this problem by considering a realistic convergence distribution and proper properties of backfill grouting. To this end, the influence of gap parameter and depth of rock cover on volume loss and composed of ground volume loss around tunnel excavation and surface volume loss were analyzed with a single layer of weathered soil. As a result, most of surface settlements were occurred immediately after excavation. Additional, as depth of rock cover and gap parameter increased, the influence range of surface settlement curves obtained from 2D numerical analyses became broader than a suggested theoretical equation. Therefore, it is inferred that gap parameter should be applied based on load distribution ratio and the property of backfill grouting properly considered for the estimation of the precise behavior of a shield TBM tunnel in 2D numerical analysis.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.9
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• pp.462-474
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• 2001

In this paper, Generalized Differential Quadrature Method is applied to the buckling analysis of built-up columns without or with stay plates. numerical analysis using GDQM is carried out for various boundary conditions(simply supported conditions, fixed conditions, fixed-simply supported conditions), dimensionless stiffness parameter and dimensionless inertia moment parameter. The accuracy and convergence of solutions are compared with exact solutions of Gjelsvik to validate the results of GDQM. Results obtained by this method are as follows. 91) This method can yield the accurate numerical solutions using few grid points. (2) The buckling load of built-up column increases as the dimensionless stiffness parameter decreases. (3) The effects of boundary conditions on the buckling load are not considerable as the dimensionless stiffness parameter increases. (4) The buckling load of built-up column increases due to the stay plate.

• 한국연소학회:학술대회논문집
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• 2003.05a
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• pp.57-62
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• 2003

A general procedure of obtaining reliable one-step kinetics model for hydrocarbon mixture from the fully detailed chemistry is described iin this study. One-step theoretical formulation of the induction parameter model IPM uses a theoretical reconstruction of the induction time database obtained from a detailed kinetics library. Non-dimensional induction time calculations is compared with that of detailed kinetics. The IPM was latter implemented to fluid dynamics code and applied for the numerical simulation of detonation wave propagation. The numerical results including the numerical smoked-foil record show the all the details of the detonation wave propagation characteristics at the cost around 1/100 of the detailed kinetics calculation.

• The Bulletin of The Korean Astronomical Society
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• v.46 no.1
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• pp.30.3-30.3
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• 2021

In order to generate the 3D structure of the 21-cm signal during the reionization, semi-numerical simulations based on Excursion set formalism are broadly used. However, semi-numerical simulations in the realization of the 3D structure are known to be the ionizing photon non-conserving by the structure of the Excursion set approach. Recently, explicit photon conserving algorithms for semi-numerical simulations introduced, but they are still too slow when forward modelling the 21-cm signal with high-dimensional parameter spaces. Here, we introduce a new method for approximately correcting photon non-conservation, which can be applied on-the-fly. This method is tailored towards the efficient simulation and Bayesian inference with high-dimensional parameter space. Then, we investigate how large an impact that photon non-conservation has on astrophysical parameter inference by performing an MCMC analysis. We find that the ionizing escape parameter is deviated from the fiducial value by 2 sigma when we infer astrophysical parameters without this correction.

• Computers and Concrete
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• v.34 no.3
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• pp.307-328
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• 2024

The concrete damage plasticity (CDP) model is widely used to simulate concrete behaviour using either implicit or explicit analysis methods. To effectively execute the models and resolve convergence issues in implicit analysis, activating the viscosity parameter of this material model is a common practice. Despite the frequent application of implicit analysis to analyse concrete structures with the CDP model, the viscosity parameter significantly varies among available models and lacks consistency. The adjustment of the viscosity parameter at the element/structural level disregards its indirect impact on the material. Therefore, the accuracy of the numerical model is confined to the validated range and might not hold true for other values, often explored in parametric studies subsequent to validations. To address these challenges and develop a unified numerical model for varied conditions, a quasi-static analysis using the explicit solver was conducted in this study. Fifteen thick flat plates tested under load control with different geometries and different eccentric loads were considered to verify the accuracy of the model. The study first investigated various concrete material behaviours under compression and tension as well as the concrete tensile strength to identify the most reliable models from previous methodologies. The study compared the results using both implicit and explicit analysis. It was found that, in implicit analysis, the viscosity parameter should be as low as 0.0001 to avoid affecting material properties. However, at the structural level, the optimum value may need adjustment between 0.00001 to 0.0001 with changing geometries and loading type. This observation raises concerns about further parametric study if the specific value of the viscosity parameter is used. Additionally, activating the viscosity parameter in load control simulations confirmed its inability to capture the peak load. Conversely, the unified explicit model accurately simulated the behaviour of the test specimens under varying geometries, load eccentricities, and column sizes. This study recommends restricting implicit solutions to the viscosity values proposed in this research. Alternatively, for highly nonlinear problems under load control simulation, explicit analysis stands as an effective approach, ensuring unified parameters across a wide range of applications without convergence problems.