• 대한전기학회논문지
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• 제40권12호
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• pp.1296-1301
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• 1991

This paper presents a hybrid image mode Galerkin method for the analysis of the transmission line structures suspended between infinite parallel ground planes. A Green's function that consists of numerically accelerated image mode terms is developed, which is used in boundary integral equation. Transmission lines of arbitrary cross section are analyzed using Galerkin's method. Two kinds of configurations of transmission lines are studied in sample problems.

• 한국안전학회지
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• 제19권1호
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• pp.38-43
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• 2004

Many analysis methods, including finite element method, have been suggested and used for assessing the integrity of cracked structures. In the paper, in order to analyze arbitrary three dimensional cracks, the finite element alternating method is extended. The crack is modeled by the symmetric Galerkin boundary element method as a distribution of displacement discontinuities, which is formulated as singularity-reduced integral equations. And the finite element method is used to calculate the stress values for the uncracked body only. Applied the proposed method to several example problems for planner cracks in finite bodies, the accuracy and efficiency of the method were demonstrated.

• International Journal of Safety
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• 제2권1호
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• pp.17-22
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• 2003

In order to analyze general three dimensional cracks in an infinite body, the symmetric Galerkin boundary element method formulated by Li and Mear is used. A crack is modelled as distribution of displacement discontinuities, and the governing equation is formulated as singularity-reduced integral equations. With the proposed method several example problems for three dimensional cracks in an infinite solid, as well as their growth under fatigue, are solved and the accuracy and efficiency of the method are demonstrated.

• East Asian mathematical journal
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• 제26권5호
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• pp.615-626
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• 2010

In this paper, we analyze discontinuous Galerkin methods with penalty terms, namly symmetric interior penalty Galerkin methods, to solve nonlinear parabolic equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ${\ell}^{\infty}$ ($L^2$) error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.

• 대한수학회논문집
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• 제15권1호
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• pp.143-153
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• 2000

In [8], Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated linear systems. In this work, we propose the block diagonal preconditioners. The preconditioned conjugate residual method is robust in that the convergence is uniform as the parameter, v, goes to $\sfrac{1}{2}$. Computational experiments are included.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2010년 춘계학술대회논문집
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• pp.534-541
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• 2010

A high-order accurate Euler flow solver based on a discontinuous Galerkin method has been developed for the numerical simulation of unsteady flows on unstructured meshes. A multi-level solution-adaptive mesh refinement/coarsening technique was adopted to enhance the resolution of numerical solutions efficiently by increasing mesh density in the high-gradient region. An acoustic wave scattering problem was investigated to assess the accuracy of the present discontinuous Galerkin solver, and a supersonic flow in a wind tunnel with a forward facing step was simulated by using the adaptive mesh refinement technique. It was shown that the present discontinuous Galerkin flow solver can capture unsteady flows including the propagation and scattering of the acoustic waves as well as the strong shock waves.

• Journal of Mechanical Science and Technology
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• 제20권1호
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• pp.110-124
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• 2006

The multi scale wavelet-Galerkin method implemented in an adaptive manner has an advantage of obtaining accurate solutions with a substantially reduced number of interpolation points. The method is becoming popular, but its numerical efficiency still needs improvement. The objectives of this investigation are to present a new numerical scheme to improve the performance of the multi scale adaptive wavelet-Galerkin method and to give detailed implementation procedure. Specifically, the subdomain technique suitable for multiscale methods is developed and implemented. When the standard wavelet-Galerkin method is implemented without domain subdivision, the interaction between very long scale wavelets and very short scale wavelets leads to a poorly-sparse system matrix, which considerably worsens numerical efficiency for large-sized problems. The performance of the developed strategy is checked in terms of numerical costs such as the CPU time and memory size. Since the detailed implementation procedure including preprocessing and stiffness matrix construction is given, researchers having experiences in standard finite element implementation may be able to extend the multi scale method further or utilize some features of the multiscale method in their own applications.

• 한국전산구조공학회논문집
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• 제18권2호
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• pp.103-111
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• 2005

본 논문에서는 수치적분 정도를 향상시킬 수 있는 새로운 무요소 기법을 제안한파 저자들에 의해 페트로프-갤러킨 자연요소법(PG-NEM)이라 명명된 이 새로운 기법은 보로노이 다이어그램과 델라우니 삼각화에 기반을 두고 있으며, 이는 BG-NEM이라 불리는 기존의 자연요소법과 개념적으로 동일하다. 하지만, 동일한 시험 형상함수와 시도 형상함수를 선택하는 BG-NEM과는 달리, PG-NEM에서는 지지영역이 적분을 위한 배경격자에 정확하게 일치하도록 시험 형상함수를 독립적으로 선택하는 페트로프-갤러킨 개념에 기반을 두고 있다. 따라서, 제안된 기법은 BG-NEM과 비교하여 수치적분 정도를 현저히 향상시킬 것으로 기대된다.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.317-329
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• 2006

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.

• 한국전산유체공학회지
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• 제16권4호
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• pp.72-83
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• 2011

A high-order discontinuous Galerkin method for the two-dimensional compressible Navier-Stokes equations was developed on unstructured triangular meshes. For this purpose, the BR2 methd(the second Bassi and Rebay discretization) was adopted for space discretization and an implicit Euler backward method was used for time integration. Numerical tests were conducted to estimate the convergence order of the numerical solutions of the Poiseuille flow for which analytic solutions are available for comparison. Also, the flows around a flat plate, a 2-D circular cylinder, and an NACA0012 airfoil were numerically simulated. The numerical results showed that the present implicit discontinuous Galerkin method is an efficient method to obtain very accurate numerical solutions of the compressible Navier-Stokes equations on unstructured meshes.