• Communications of the Korean Mathematical Society
• /
• v.9 no.2
• /
• pp.449-465
• /
• 1994

The two common numerical methods to approximate the solution of partial differential equations are the finite element method and the finite difference method. They both lead to solving large sparse linear systems. For many applications, it is not unusal that the order of matrix is greater than 10, 000. For this kind of problem, a direct method such as Gaussian elimination can not be used because of the prohibitive cost. To this end, many iterative methods with modest cost have been studied and proposed by numerical analysts.(omitted)

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.28 no.10
• /
• pp.1590-1597
• /
• 2004

Three methods of design sensitivity analysis for structures such as numerical method, analytical method and semi-analytical method have been developed for the last three decades. Although analytical design sensitivity analysis can provide very exact result, it is difficult to implement into practical design problems. Therefore, numerical method such as finite difference method is widely used to simply obtain the design sensitivity in most cases. The numerical differentiation is sufficiently accurate and reliable fur most linear problems. However, it turns out that the numerical differentiation is inefficient and inaccurate in nonlinear design sensitivity analysis because its computational cost depends on the number of design variables and large numerical errors can be included. Thus the semi-analytical method is more suitable for complicated design problems. Moreover, semi-analytical method is easy to be performed in design procedure, which can be coupled with an analysis solver such as commercial finite element package. In this paper, implementation procedure fur the semi-analytical design sensitivity analysis outside of the commercial finite element package is studied and the computational technique is proposed for evaluating the partial differentiation of internal nodal force, so called pseudo-load. Numerical examples coupled with commercial finite element package are shown to verify usefulness of proposed semi-analytical sensitivity analysis procedure and computational technique for pseudo-load.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
• /
• 2002.04a
• /
• pp.102-105
• /
• 2002

A new finite difference model is developed for solute transport in a fractured medium that can consider advection, adsorption, first-order decay, and scale-dependent dispersivity of individual fractures. In the model, the dispersivity of individual fractures is employed as a variable increasing with travel distance from a source. The model is verified using an analytical solution for a single fracture. A solution from the new model is independent of the outlet boundary condition of fractures, and has little numerical dispersion error.

• Journal of Environmental Health Sciences
• /
• v.26 no.3
• /
• pp.50-54
• /
• 2000

Ventilation rates can be measured directly by a tracer decay method, although little is known of the effects of different sampling intervals on decay rte calculations. This study determined variations in decay rates calculated by three techniques using residential ozone decay data. The calculation techniques were a regression technique, decay techniques using half-life and average-life, and finite difference techniques using two different time intervals. Variation associated with regression technique calculations for residential ozone decay rates based on data from both sample intervals were within 10% (2.81$\pm$1.88 hr-1). However, both half-life and finite difference technique calculations using a shorter-time interval were significantly different from those obtained with the regression technique(p<0.05). Therefore, the use of short sampling intervals in tracer decay may cause significant error in decay rate calculations.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.1893-1912
• /
• 2017

In this paper, we aim to construct a nonstandard finite difference (NSFD) scheme to solve numerically a mathematical model for cholera epidemic dynamics. We first show that if the basic reproduction number is less than unity, the disease-free equilibrium (DFE) is locally asymptotically stable. Moreover, we mainly establish the global stability analysis of the DFE and endemic equilibrium by using suitable Lyapunov functionals regardless of the time step size. Finally, numerical simulations with different time step sizes and initial conditions are carried out and comparisons are made with other well-known methods to illustrate the main theoretical results.

• Journal of the Optical Society of Korea
• /
• v.13 no.2
• /
• pp.272-278
• /
• 2009

Recently, there has been a growing interest in optical imaging of neural activity because the optical neuroimaging has considerable advantages over conventional imaging. Birefringence of the axon has been reported to change during neural activation, but the neurophysiological origin of the change is still unresolved. This study hypothesizes that the birefringence signal is at least partially attributed to the transient cellular volume change associated with nerve excitation. To examine this hypothesis, we investigated how the intensity of cross-polarized light transmitting through the axon would change as the size of the axon changes. For this purpose, a two-dimensional finite-difference time-domain program was developed with the improvement of the total-field/scattered-field method which reduces numerical noise. The results support our hypothesis in that the computed cross-polarized signals exhibit some agreement with previously-reported birefringence signals.

• Journal of the Society of Naval Architects of Korea
• /
• v.47 no.3
• /
• pp.430-437
• /
• 2010

In this paper, we develop a shape design optimization method for thermo-elastoplasticity problems that is applicable to the welding or thermal deformation problems of ship structures. Shell elements and a programming language APDL in a commercial finite element analysis code, ANSYS, are employed in the shape optimization. The point of developed method is to determine the design parameters such that the deformed shape after welding fits very well to a desired design. The geometric parameters of surfaces are selected as the design parameters. The modified method of feasible direction (MMFD) and finite difference sensitivity are used for the optimization algorithm. Two numerical examples demonstrate that the developed shape design method is applicable to existing hull structures and effective for the structural design of ships.

• Journal of the Korean Ceramic Society
• /
• v.30 no.3
• /
• pp.229-235
• /
• 1993

Thermal history and thermal stress of alumina specimen, which occured from thermal shock process, were calculated by finite difference method. Stress intensity factor and crack growth in cyclic thermal fatigue were calculated from single thermal shock temperature history and thermal stress. Cyclic thermal life were estimated by bending strength after cyclic thermal shock under critical thermal shock temperature. Calculated stress intensity factor was compared with real experimental thermal fatigue life of specimen. Fatigue life until critical stress intensity factor and real experimental result were comparable.

• Tribology and Lubricants
• /
• v.16 no.4
• /
• pp.295-301
• /
• 2000

The dynamic simulation of slider in hard disk drive is performed using Factored Implicit Finite Difference method. The modified Reynolds equation with Fukui and Kaneko model is employed as a governing equation. Equations of motion for the slider of three degrees of freedom are solved simultaneously with the modified Reynolds equation. The transient responses of the slider for disk step bumps and slider impulse forces are shown for various cases and are compared for the iteration algorithm and new algorithm.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.4 no.2
• /
• pp.135-142
• /
• 2000

We consider a multigrid algorithm for higher order finite difference scheme for the Poisson problem on rectangular domain. Several smoothers including Jacobi, Red-black Gauss-Seidel are tested and compared. Since higher order scheme gives much more accurate result then 5-point scheme, one may use small number of levels with higher order scheme and thus the overall cost is reduced quite a lot. The numerical experiment compares the two cases.