• 호남수학학술지
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• 제36권4호
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• pp.755-766
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• 2014

In the discrete formulation of the bubble stabilized Legendre Galerkin methods, the system of equations includes the artificial viscosity term as the parameter. We investigate the estimation of this parameter to get the optimal solution which minimizes the maximum error. Some numerical results are reported.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2001년도 봄 학술발표회 논문집
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• pp.76-83
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• 2001

In this study, a new method coupling of Element-Free Galerkin(EFG) method and Infinite Elements(IE) method is presented for extending application of the EFG method to engineering problems in unbounded domain. EFG method and IE method are briefly reviewed, and then the coupling procedure of the two methods is proposed. Numerical Algorithm by way of EFG-lE coupling technique is also developed. Numerical results illustrate the performance of the proposed technique. The accuracy of numerical solutions by the developed algorithm is guaranteed in comparing those of the other methods.

• East Asian mathematical journal
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• 제14권2호
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• pp.399-410
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• 1998

In [3], 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 present computational experiments of W-cycle multigrid method. Computational experiments show that the convergence is uniform as the parameter, $\nu$, goes to 1/2.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제1권1호
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• pp.1-34
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• 1997

In this study, various available meshless methods are briefly reviewed and the connection among them is investigated. The objective of meshless methods is to eliminate some difficulties which are originated from reliance on a mesh by constructing the approximation entirely in terms of nodes. Especially, focusing on Element Free Galerkin Method(EFGM) based on moving least square interpolants(MLSI), a new implementation is developed based on a variational principle with penalty function method were used to enforce the essential boundary condition. In addition, the weighted orthogonal basis functions are constructed to overcome disadvantage of MLSI.

• Wind and Structures
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• 제31권1호
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• pp.75-84
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• 2020

The aerostatic stability analysis of a long-span suspension bridge by the Element-free Galerkin (EFG) method is presented in this paper. Nonlinear effects due to wind structure interactions should be taken into account in determining the aerostatic behavior of long-span suspension bridges. The EFG method is applied to investigate torsional divergence of suspension bridges, based on both the three components of wind loads and nonlinearities of structural geometric. Since EFG methods, which are based on moving least-square (MLS) interpolation, require only nodal data, the description of the geometry of bridge structure and boundaries consist of defining a set of nodes. A numerical example involving the three-dimensional EFG model of a suspension bridge with a span length of 888m is presented to illustrate the performance and potential of this method. The results indicate that presented method can effectively be applied for modeling suspension bridge structure and the computed results obtained using present modeling strategy for nonlinear suspension bridge structure under wind flow are encouragingly acceptable.

• 대한기계학회논문집A
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• 제28권3호
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• pp.251-258
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• 2004

Since the multiscale wavelet-based numerical methods allow effective adaptive analysis, they have become new analysis tools. However, the main applications of these methods have been mainly on elliptic problems, they are rarely used for eigenvalue analysis. The objective of this paper is to develop a new multiscale wavelet-based adaptive Galerkin method for eigenvalue analysis. To this end, we employ the hat interpolation wavelets as the basis functions of the finite-dimensional trial function space and formulate a multiresolution analysis approach using the multiscale wavelet-Galerkin method. It is then shown that this multiresolution formulation makes iterative eigensolvers very efficient. The intrinsic difference-checking nature of wavelets is shown to play a critical role in the adaptive analysis. The effectiveness of the present approach will be examined in terms of the total numbers of required nodes and CPU times.

• 한국전산유체공학회지
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• 제12권3호
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• pp.29-40
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• 2007

An implicit discontinuous Galerkin method for the two-dimensional Euler equations was developed on unstructured triangular meshes. The method can achieve high-order spatial accuracy by using hierachical basis functions based on Legendre polynomials. Numerical tests were conducted to estimate the convergence order of numerical solutions to the Ringleb flow and the supersonic vortex flow for which analytic solutions are available. Also, the flows around a 2-D circular cylinder and an NACA0012 airfoil were numerically simulated. The numerical results showed that the implicit discontinuous Galerkin methods couples with a high-order representation of curved solid boundaries can be an efficient method to obtain very accurate numerical solutions on unstructured meshes.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2008년도 학술대회
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• pp.57-70
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• 2008

A high-order accurate Euler flow solver based on a discontinuous Galerkin finite-element method has been developed for the numerical simulations of blade-vortex interaction phenomena on unstructured meshes. A free vortex in freestream was investigated to assess the vortex-preserving property and the accuracy of the present flow solver. Blade-vortex interaction problems in subsonic and transonic freestreams were simulated by adopting a multi-level solution-adaptive dynamic mesh refinement/coarsening technique. The results were compared with those of other numerical and experimental methods. It was shown that the present discontinuous Galerkin flow solver can preserve the vortex structure for significantly longer vortex convection time and can accurately capture the complex unsteady blade-vortex interaction flows, including generation and propagation of acoustic waves.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2008년 추계학술대회논문집
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• pp.57-70
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• 2008

A high-order accurate Euler flow solver based on a discontinuous Galerkin finite-element method has been developed for the numerical simulations of blade-vortex interaction phenomena on unstructured meshes. A free vortex in freestream was investigated to assess the vortex-preserving property and the accuracy of the present flow solver. Blade-vortex interaction problems in subsonic and transonic freestreams were simulated by adopting a multi-level solution-adaptive dynamic mesh refinement/coarsening technique. The results were compared with those of other numerical and experimental methods. It was shown that the present discontinuous Galerkin flow solver can preserve the vortex structure for significantly longer vortex convection time and can accurately capture the complex unsteady blade-vortex interaction flows, including generation and propagation of acoustic waves.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2007년도 춘계 학술대회논문집
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• pp.30-40
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• 2007

The implicit discontinuous Galerkin method for the two-dimensional Euler equations was developed on unstructured triangular meshes, which can achieve higher-order accuracy by wing hierachical basis functions based on Legendre polynomials. Numerical tests were conducted to estimate the convergence order of numerical solutions to the Ringleb flow and the supersonic vortex flow for which analytic solutions are available. And, the flows around a circle and a NACA0012 airfoil was also numerically simulated. Numerical results show that the implicit discontinuous Galerkin methods with higher-order representation of curved solid boundaries can be an efficient higher-order method to obtain very accurate numerical solutions on unstructured meshes.