• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.10 no.1
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• pp.21-29
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• 2006

The method to construct a surface from point data are widely known. But the way to make a surface from derivative data is not usually used since derivative data in engineering appears very often. In this paper, if more than one types of data among three possible data such as point data, first derivative data, second derivative data are given, we can construct a surface. If only first derivative data are given, we add a function value at the one point. If only second derivative data are given, we add a linear function.

• Interaction and multiscale mechanics
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• v.1 no.2
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• pp.251-278
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• 2008

In this study, we investigate the discontinuous-derivative treatment at the gas-liquid interface in underwater explosion (UNDEX) problems by using the Moving Least Squares-Smoothed Particle Hydrodynamics (MLS-SPH) method, which is known as one of the particle methods suitable for problems where large deformation and inhomogeneity occur in the whole domain. Because the numerical oscillation of pressure arises from derivative discontinuity in the UNDEX analysis using the standard SPH method, the MLS shape function with Discontinuous-derivative Basis Function (DBF) that is able to represent the derivative discontinuity of field function is utilized in the MLS-SPH formulation in order to suppress the nonphysical pressure oscillation. The effectiveness of the MLS-SPH with DBF is demonstrated in comparison with the standard SPH and conventional MLS-SPH though a shock tube problem and benchmark standard problems of UNDEX of a trinitrotoluene (TNT) charge.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.31-48
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• 2007

The paper deals with the solution of some fractional partial differential equations obtained by substituting modified Riemann-Liouville derivatives for the customary derivatives. This derivative is introduced to avoid using the so-called Caputo fractional derivative which, at the extreme, says that, if you want to get the first derivative of a function you must before have at hand its second derivative. Firstly, one gives a brief background on the fractional Taylor series of nondifferentiable functions and its consequence on the derivative chain rule. Then one considers linear fractional partial differential equations with constant coefficients, and one shows how, in some instances, one can obtain their solutions on bypassing the use of Fourier transform and/or Laplace transform. Later one develops a Lagrange method via characteristics for some linear fractional differential equations with nonconstant coefficients, and involving fractional derivatives of only one order. The key is the fractional Taylor series of non differentiable function $f(x+h)=E_{\alpha}(h^{\alpha}{D_x^{\alpha})f(x)$.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.6
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• pp.788-802
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• 1998

A numerical method using dual time stepping and preconditioning procedure for efficient computations of unsteady low speed compressible flow problems is developed. The time-derivative preconditioning method which is valid at low speed flow conditions cannot maintain temporal accuracy because of the modification of the time-derivative term in Navier-Stokes equations. The dual time stepping procedure is incorporated to enable the time accurate computations and this procedure introduces a pseudo-time derivative in addition to the physical time derivative. At a given physical time, an inner iteration can be carried out until a steady state in pseudo-time is achieved. This will effectively yield a time accurate solution. Computational capabilities of the above algorithm are demonstrated through computation of a variety of practical fluid flows and it is shown that the algorithms is efficient in the essentially incompressible flows and low Mach number compressible flows with heat source.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.913-921
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• 2010

The derivative influence measure is adapted to the Cholesky decomposition of a covariance matrix. Formulas for the derivative influence of observations on the Cholesky root and the inverse Cholesky root of a sample covariance matrix are derived. It is easy to implement this influence diagnostic method for practical use. A numerical example is given for illustration.

• Journal of Magnetics
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• v.22 no.1
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• pp.43-48
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• 2017

In order to detect the current flowing through concealed conductor, this paper proposes a new method based on derivative method. Firstly, this paper analyzes the main peak characteristic of the derivative function of magnetic field generated by a current-carrying conductor, and a relationship between the current flowing through the conductor and the main peak of the derivative function is obtained and applied to calculate the current. Then, the method is applied to detect the conductor current flowing through grounding grids of substations. Finally, the numerical experimental and field experiment verified the feasibility and accuracy of the method, and the computing results show that the method can effectively measure the conductor current of grounding grids with low error, and the error is within 5 %.

• YAKHAK HOEJI
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• v.30 no.4
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• pp.185-192
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• 1986

Authors developed the computer application program (language: APPLE SOFT BASIC) for derivative spectrophotometry. By means of this program, derivative of spectral absorbance with respect to wavelength is recorded versus wavelength. To try this program in connection with spectrophotometer system, the authors have done the simultaneous quantitation of pyridoxine center dot HCl and nicotinamide in the mixture, and the result was compared with that of absorbance method.

• Journal of the Korean earth science society
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• v.36 no.5
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• pp.437-446
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• 2015

Many edge detection methods, based on horizontal and vertical derivatives, have been introduced to provide us with intuitive information about the horizontal distribution of a subsurface anomalous body. Understanding the characteristics of each edge detection method is important for selecting an optimized method. In order to compare the characteristics of the individual methods, this study applied each method to synthetic magnetic data created using homogeneous prisms with different sizes, the numbers of bodies, and spacings between them. Seven edge detection methods were comprehensively and quantitatively analyzed: the total horizontal derivative (HD), the vertical derivative (VD), the 3D analytic signal (AS), the title derivative (TD), the theta map (TM), the horizontal derivative of tilt angle (HTD), and the normalized total horizontal derivative (NHD). HD and VD showed average good performance for a single-body model, but failed to detect multiple bodies. AS traced the edge for a single-body model comparatively well, but it was unable to detect an angulated corner and multiple bodies at the same time. TD and TM performed well in delineating the edges of shallower and larger bodies, but they showed relatively poor performance for deeper and smaller bodies. In contrast, they had a significant advantage in detecting the edges of multiple bodies. HTD showed poor performance in tracing close bodies since it was sensitive to an interference effect. NHD showed great performance under an appropriate window.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.299-306
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• 2006

Using a level set method and topological derivatives, a topological shape optimization method that is independent of an initial design is developed for linearly elastic structures. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in the level set function, which facilitates to handle complicated topological shape changes. The 'Hamilton-Jacobi (H-J)' equation and computationally robust numerical technique of 'up-wind scheme' lead the initial implicit boundary to an optimal one according to the normal velocity field while minimizing the objective function of compliance and satisfying the constraint of allowable volume. Based on the asymptotic regularization concept, the topological derivative is considered as the limit of shape derivative as the radius of hole approaches to zero. The required velocity field to update the H -J equation is determined from the descent direction of Lagrangian derived from optimality conditions. It turns out that the initial holes is not required to get the optimal result since the developed method can create holes whenever and wherever necessary using indicators obtained from the topological derivatives. It is demonstrated that the proper choice of control parameters for nucleation is crucial for efficient optimization process.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.3
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• pp.237-244
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• 2016

This paper presents a nonlinear Moving Least Squares(MLS) difference method for material nonlinearity problem. The MLS difference method, which employs strong formulation involving the fast derivative approximation, discretizes governing partial differential equation based on a node model. However, the conventional MLS difference method cannot explicitly handle constitutive equation since it solves solid mechanics problems by using the Navier's equation that unifies unknowns into one variable, displacement. In this study, a double derivative approximation is devised to treat the constitutive equation of inelastic material in the framework of strong formulation; in fact, it manipulates the first order derivative approximation two times. The equilibrium equation described by the divergence of stress tensor is directly discretized and is linearized by the Newton method; as a result, an iterative procedure is developed to find convergent solution. Stresses and internal variables are calculated and updated by the return mapping algorithm. Effectiveness and stability of the iterative procedure is improved by using algorithmic tangent modulus. The consistency of the double derivative approximation was shown by the reproducing property test. Also, accuracy and stability of the procedure were verified by analyzing inelastic beam under incremental tensile loading.