• 대한수학회보
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• 제50권3호
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• pp.747-752
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• 2013

It's known that one could use a fixed loxodromic or parabolic element in $M(\bar{\mathbb{R}}^n)$ as a test map to test the discreteness of a non-elementary M$\ddot{o}$bius group G. In this paper, we discuss the discreteness of G by using a fixed elliptic element.

• 대한수학회지
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• 제50권1호
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• pp.81-93
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• 2013

We consider a distributed optimal flux control problem: finding the potential of which gradient approximates the target vector field under an elliptic constraint. Introducing the Lagrange multiplier and a change of variables the Euler-Lagrange equation turns into a coupled equation of an elliptic equation and a reaction diffusion equation. The change of variables reduces iteration steps dramatically when the Gauss-Seidel iteration is considered as a solution method. For the elliptic equation solver we consider the Cell Boundary Element (CBE) method, which is the finite element type flux preserving methods.

• Steel and Composite Structures
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• 제45권3호
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• pp.437-454
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• 2022

Elliptic-braced simple resisting frame as a new lateral bracing system installed in the middle bay of frame in building facades has been recently introduced. This system not only creates a problem for opening space from the architectural viewpoint but also improves the structural behavior. Despite the researches on the seismic performance of lateral bracing systems, there are few studies performed on the effect of the stiffness parameters on the elastic story drift and calculation of period in simple braced steel frames. To overcome this shortcoming, in this paper, for the first time, an analytical solution is presented for calculating elastic lateral stiffness in a simple steel frame equipped with elliptic brace subjected to lateral load. In addition, for the first time, in this study, a precise formulation has been developed to evaluate the elastic stiffness variation in a steel frame equipped with a two-dimensional single-story single-span elliptic brace using strain energy and Castigliano's theorem. Thus, all the effective factors, including axial and shear loads as well as bending moments of elliptic brace could be considered. At the end of the analysis, the lateral stiffness can be calculated by an improved and innovative relation through the energy method based on the geometrical properties of the employed sections and specification of the used material. Also, an equivalent element of an elliptic brace was presented for the ease of modeling and use in linear designs. Application of the proposed relation have been verified through a variety of examples in OpenSees software. Based on the results, the error percentage between the elastic stiffness derived from the developed equations and the numerical analyses of finite element models was very low and negligible.

• Steel and Composite Structures
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• 제46권3호
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• pp.293-318
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• 2023

This study aims to examine the elastic stiffness properties of Elliptic-Braced Moment Resisting Frame (EBMRF) subjected to lateral loads. Installing the elliptic brace in the middle span of the frames in the facade of a building, as a new lateral bracing system not only it can improve the structural behavior, but it provides sufficient space to consider opening it needed. In this regard, for the first time, an accurate theoretical formulation has been developed in order that the elastic stiffness is investigated in a two-dimensional single-story single-span EBMRF. The concept of strain energy and Castigliano's theorem were employed to perform the analysis. All influential factors were considered, including axial and shearing loads in addition to the bending moment in the elliptic brace. At the end of the analysis, the elastic lateral stiffness could be calculated using an improved relation through strain energy method based on geometric properties of the employed sections as well as specifications of the utilized materials. For the ease of finite element (FE) modeling and its use in linear design, an equivalent element was developed for the elliptic brace. The proposed relation was verified by different examples using OpenSees software. It was found that there is a negligible difference between elastic stiffness values derived by the developed equations and those of numerical analysis using FE method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제24권2호
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• pp.215-227
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• 2020

A new multiscale finite element method for elliptic problems with highly oscillating coefficients are introduced. A hybridization yields a locally flux-conserving numerical scheme for multiscale problems. Our approach naturally induces a homogenized equation which facilitates error analysis. Complete convergence analysis is given and numerical examples are presented to validate our analysis.

• 한국전자파학회지:전자파기술
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• 제2권3호
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• pp.26-31
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• 1991

The scattering property of TMz illuminated a elliptic dielectric cylinders with arbitrary cross section are analyzed by the boundary element techniques. The boundary element equations are for- mulated via Maxwell's equations, weighted residual of Green's theorem, and the boundary conditions. The unknown surface fields on the boundaries are then calculated by the boundary element integral equations. Once the surface fields are found, the scattered fields in far-zone and scattering widths (SW) are readily determined. To show the validity and usefulness of this formulation, computations are compared with those obtained using analytical method and one layer circular cylinder. As exten- sion to arbitrary cross-sectioned cylinders, plane wave scattering from a elliptic dielectric cylinders are numerically analyzed. A general computer program has been developed using the quadratic ele- ments(Higher order borndary elements) and the Gaussian quadrature.

• 대한수학회보
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• 제51권2호
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• pp.595-612
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• 2014

The spectral collocation method for a second order elliptic boundary value problem on a domain ${\Omega}$ with curved boundaries is studied using the Gordon and Hall transformation which enables us to have a transformed elliptic problem and a square domain S = [0, h] ${\times}$ [0, h], h > 0. The preconditioned system of the spectral collocation approximation based on Legendre-Gauss-Lobatto points by the matrix based on piecewise bilinear finite element discretizations is shown to have the high order accuracy of convergence and the efficiency of the finite element preconditioner.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권4호
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• pp.387-407
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• 2015

This paper analyzes the $h{\times}p$ version of the finite element method for optimal control problems constrained by elliptic partial differential equations with random inputs. The main result is that the $h{\times}p$ error bound for the control problems subject to stochastic partial differential equations leads to an exponential rate of convergence with respect to p as for the corresponding direct problems. Numerical examples are used to confirm the theoretical results.

• Journal of applied mathematics & informatics
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• 제8권2호
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• pp.371-386
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• 2001

In this work we investigate the finite element preconditioning method for the $C^1$-cubic spline collocation discretizations for an elliptic operator A defined by $Au := -{\Delta}u + a_1u_x+a_2u_y+a_0u$ in the unit square with some boundary conditions. We compute the condition number and the numerical solution of the preconditioning system for the several example problems. Finally, we compare the this preconditioning system with the another preconditioning system.

• 대한수학회지
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• 제53권6호
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• pp.1411-1429
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• 2016

We consider the nite volume element method for elliptic problems using isoparametric bilinear elements on quadrilateral meshes. A gradient recovery method is presented by using the patch interpolation technique. Based on some superclose estimates, we prove that the recovered gradient $R({\nabla}u_h)$ possesses the superconvergence: ${\parallel}{\nabla}u-R({\nabla}u_h){\parallel}=O(h^2){\parallel}u{\parallel}_3$. Finally, some numerical examples are provided to illustrate our theoretical analysis.