• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.761-781
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• 2014

An exponentially accurate nonconforming spectral element method for elasticity systems with discontinuities in the coefficients and the flux across the interface is proposed in this paper. The method is least-squares spectral element method. The jump in the flux across the interface is incorporated (in appropriate Sobolev norm) in the functional to be minimized. The interface is resolved exactly using blending elements. The solution is obtained by the preconditioned conjugate gradient method. The numerical solution for different examples with discontinuous coefficients and non-homogeneous jump in the flux across the interface are presented to show the efficiency of the proposed method.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.442-447
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• 2008

This paper presents a new approach to simulate fluid-solid interaction problems involving non-matching interfaces. The coupling between fluid and solid domains with dissimilar finite element meshes consisting of 4-node quadrilateral elements is achieved by using the interface element method (IEM). Conditions of compatibility between fluid and solid meshes are satisfied exactly by introducing the interface elements defined on interfacing regions. Importantly, a consistent transfer of loads through matching interface element meshes guarantees the present method to be an efficient approach of the solution strategy to fluid-solid interaction problems. An arbitrary Lagrangian-Eulerian (ALE) description is adopted for the fluid domain, while for the solid domain an updated Lagrangian formulation is considered to accommodate finite deformations of an elastic structure. The stabilized equal order velocity-pressure elements for incompressible flows are used in the motion of fluids. Fully coupled equations are solved simultaneously in a single computational domain. Numerical results are presented for fluid-solid interaction problems involving nonmatching interfaces to demonstrate the effectiveness of the methodology.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.2
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• pp.65-92
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• 2019

We survey a recently developed immersed finite element method (IFEM) for the interface problems. The IFEM uses structured grids such as uniform grids, even if the interface is a smooth curve. Instead of fitting the curved interface, the bases are modified so that they satisfy the jump conditions along the interface. The early versions of IFEM [1, 2] were suboptimal in convergence order [3]. Later, the consistency terms were added to the bilinear forms [4, 5], thus the scheme became optimal and the error estimates were proven. For elasticity problems with interfaces, we modify the Crouzeix-Raviart based element to satisfy the traction conditions along the interface [6], but the consistency terms are not needed. To satisfy the Korn's inequality, we add the stabilizing terms to the bilinear form. The optimal error estimate was shown for a triangular grid. Lastly, we describe the multigrid algorithms for the discretized system arising from IFEM. The prolongation operators are designed so that the prolongated function satisfy the flux continuity condition along the interface. The W-cycle convergence was proved, and the number of V-cycle is independent of the mesh size.

• Journal of computational fluids engineering
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• v.16 no.2
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• pp.1-10
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• 2011

A new computational program, which is based on the CIP/CCUP(Constraint Interpolation Profile/CIP Combined Unified Procedure) method, has been developed to numerically analyse sloshing phenomena dealt as multiphase-flow problems. For the convection terms of Navier-Stokes equations, the RCIP(Rational function CIP) method was adopted and the THINC-WLIC(Tangent of Hyperbola for Interface Capturing-Weighted Line Interface Calculation) method was used to capture the air/water interface. To validate the present numerical method, two-dimensional dam-breaking and sloshing problems in a rectangular tank were solved by the developed method in a stationary Cartesian grid system. In the case of sloshing problems, simulations by using a improved MPS(Moving Particle Simulation) method, which is named as PNU-MPS(Pusan National University-MPS), were also carried out. The computational results are compared with those of experiments and most of the comparisons are reasonably good.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.5
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• pp.1158-1168
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• 1994

For BEM analyses of the impact problems of dissimilar materials, the connected multi-region method using perfect bonded conditions on the interface boundaries was added to two-dimensional Laplace transformed-domain BEM program for a single region analysis. It was confirmed that the BEM results of impact problems of a single-region and multi-regions for a homogeneous isotropic material are agreed well. The two-dimensional Laplace transformed-domain BEM program combined with connected multi-region method was applied to analyse several impact problems of dissimilar materials. Also the feasibility of BEM impact analyses was investigated for dissimilar materials by the analysis of the BEM results for impact problems of dissimilar materials in terms of physical aspects. As for an application, the two-dimensional Laplace transformed BEM concerning impact problems of cracks at the interface of dissimilar materials and the determinating process of the dynamic stress intensity factors by extrapolation method are presented in this paper.

• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.311-334
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• 2020

The solution of the elliptic partial differential equation has interface singularity at the points which are either the intersections of interfaces or the intersections of interfaces with the boundary of the domain. The singularities that arises in the elliptic interface problems are very complex. In this article we propose an exponentially accurate nonconforming spectral element method for these problems based on [7, 18]. A geometric mesh is used in the neighbourhood of the singularities and the auxiliary map of the form z = ln ξ is introduced to remove the singularities. The method is essentially a least-squares method and the solution can be obtained by solving the normal equations using the preconditioned conjugate gradient method (PCGM) without computing the mass and stiffness matrices. Numerical examples are presented to show the exponential accuracy of the method.

• Journal of Mechanical Science and Technology
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• v.14 no.2
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• pp.197-206
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• 2000

A boundary integral equation method in the shape design sensitivity analysis is developed for the elasticity problems with axisymmetric non-homogeneous bodies. Functionals involving displacements and tractions at the zonal interface are considered. Sensitivity formula in terms of the interface shape variation is then derived by taking derivative of the boundary integral identity. Adjoint problem is defined such that displacement and traction discontinuity is imposed at the interface. Analytic example for a compound cylinder is taken to show the validity of the derived sensitivity formula. In the numerical implementation, solutions at the interface for the primal and adjoint system are used for the sensitivity. While the BEM is a natural tool for the solution, more generalization should be made since it should handle the jump conditions at the interface. Accuracy of the sensitivity is evaluated numerically by the same compound cylinder problem. The endosseous implant-bone interface problem is considered next as a practical application, in which the stress value is of great importance for successful osseointegration at the interface. As a preliminary step, a simple model with tapered cylinder is considered in this paper. Numerical accuracy is shown to be excellent which promises that the method can be used as an efficient and reliable tool in the optimization procedure for the implant design. Though only the axisymmetric problem is considered here, the method can be applied to general elasticity problems having interface.

• Journal of KSNVE
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• v.9 no.4
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• pp.643-651
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• 1999

A brief description of the current technology (contact-start-stop) employed in most of today's hard disk drive is presented. The dynamics and head/disk interactions during a start/stop process are very complicated and no one has been able to accurately model the interactions. Thus, the head/disk interface that meets the start/stop durability and stiction requirements are always developed statistically. In arriving at a solution. many sets of statistical tests are run by varying several parameters. such as, the carbon overcoat thickness. lubricant thickness. disk surface roughness, etc. Consequently, the cost associated III developing an interface could be significant since the outcome is difficult to predict. An alternative method known as Load/Unload technology alters the problem set. such that. the start/stop performance can be designed in a predictable manner. Although this techno¬logy offers superior performance and significantly reduces statistical testing time, it also has some potential problems. However. contrary to the CSS technology. most of the problems can be solved by design and not by trial and error. One critical problem is that of head/disk contacts during the loading and unloading processes. These contact can cause disk and slider damage because the contacts are likely to occur at high disk speeds resulting in large friction forces. Use of glass substrate disks also may present problems if not managed correctly. Due to the low thermal conductivity of glass substrates. any head/disk contacts may result in erasure due to frictional heating of the head/disk interface. In spite of these and other potential problems. the advantage with L/UL system is that these events can be understood. analyzed. and solved in a deterministic manner.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.20 no.41
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• pp.177-188
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• 1997

This study describes the important information for establishing Human Computer Interface System for solving the large scale Traveling Saleman Problem in Printed Circuit Board production. Appropriate types and sizes of partitioning of large scale problems are discussed. Optimal tours for the special patterns appeared in PCB's are given. The comparision of optimal solutions of non-Euclidean problems and Euclidean problems shows the possibilities of using human interface in solving the Chebyshev TSP. Algorithm for the large scale problem using described information and coputational result of the practical problem are given.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.446-451
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• 2004

Over testing problems of satellites and theirs components have been issued due to their effects on satellite development cost and schedule. Force limited vibration tests were introduced as solution of the problems in 1980s. Over testing phenomena occurs due to the lack of similarity on interface impedance. Force limited vibration tests control interface force to simulate actual interface impedance. In this research, force limited vibration tests are applied on two satellites environmental tests. Force limits are calculated by using TDFS method and Semi-Empirical method. Four force sensors are employed to control interface force. The tests prove that force limited control reduced maximum interface acceleration in order of 3.