• 제목/요약/키워드: mixed formulation

검색결과 352건 처리시간 0.026초

SMOOTHING ANALYSIS IN MULTIGRID METHOD FOR THE LINEAR ELASTICITY FOR MIXED FORMULATION

  • KANG, KAB SEOK
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • 제5권1호
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    • pp.11-24
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    • 2001
  • We introduce an assumption about smoothing operator for mixed formulations and show that convergence of Multigrid method for the mixed finite element formulation for the Linear Elasticity. And we show that Richardson and Kaczmarz smoothing satisfy this assumption.

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FINITE ELEMENT ANALYSIS FOR A MIXED LAGRANGIAN FORMULATION OF INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

  • Kim, Hong-Chul
    • 대한수학회지
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    • 제34권1호
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    • pp.87-118
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    • 1997
  • This paper is concerned with a mixed Lagrangian formulation of the wiscous, stationary, incompressible Navier-Stokes equations $$ (1.1) -\nu\Delta u + (u \cdot \nabla)u + \nabla_p = f in \Omega $$ and $$ (1.2) \nubla \cdot u = 0 in \Omega $$ along with inhomogeneous Dirichlet boundary conditions on a portion of the boundary $$ (1.3) u = ^{0 on \Gamma_0 _{g on \Gamma_g, $$ where $\Omega$ is a bounded open domain in $R^d, d = 2 or 3$, or with a boundary $\Gamma = \partial\Omega$, which is composed of two disjoint parts $\Gamma_0$ and $\Gamma_g$.

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유체-구조물 상호작용을 위한 유한요소 결합공식화의 예조건화에 대한 연구 (Preconditioning Method of a Finite Element Combined Formulation for Fluid-Structure Interaction)

  • 최형권
    • 대한기계학회논문집B
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    • 제33권4호
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    • pp.242-247
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    • 2009
  • AILU type preconditioners for a two-dimensional combined P2P1 finite element formulation of the interaction of rigid cylinder with incompressible fluid flow have been devised and tested by solving fluid-structure interaction (FSI) problems. The FSI code simulating the interaction of a rigid cylinder with an unsteady flow is based on P2P1 mixed finite element formulation coupled with combined formulation. Four different preconditioners were devised for the two-dimensional combined P2P1 finite element formulation extending the idea of Nam et al., which was proposed for the preconditioning of a P2P1 mixed finite element formulation of the incompressible Navier-Stokes equations. It was found that PC-III or PC-IV among them perform well with respect to computational memory and convergence rate for some bench-mark problems.

AN UPSTREAM PSEUDOSTRESS-VELOCITY MIXED FORMULATION FOR THE OSEEN EQUATIONS

  • Park, Eun-Jae;Seo, Boyoon
    • 대한수학회보
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    • 제51권1호
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    • pp.267-285
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    • 2014
  • An upstream scheme based on the pseudostress-velocity mixed formulation is studied to solve convection-dominated Oseen equations. Lagrange multipliers are introduced to treat the trace-free constraint and the lowest order Raviart-Thomas finite element space on rectangular mesh is used. Error analysis for several quantities of interest is given. Particularly, first-order convergence in $L^2$ norm for the velocity is proved. Finally, numerical experiments for various cases are presented to show the efficiency of this method.

The use of discontinuous first and second-order mixed boundary elements for 2D elastostatics

  • Severcan, M.H.;Tanrikulu, A.K.;Tanrikulu, A.H.;Deneme, I.O.
    • Structural Engineering and Mechanics
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    • 제34권6호
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    • pp.703-718
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    • 2010
  • In classical higher-order discontinuous boundary element formulation for two-dimensional elastostatics, interpolation functions for different boundary variables (i.e., boundary displacements and tractions) are assumed to be the same. However, there is a derivational relationship between these variables. This paper presents a boundary element formulation, called Mixed Boundary Element Formulation, for two dimensional elastostatic problems in which above mentioned relationship is taking into account. The formulations are performed by using discontinuous first and second-order mixed boundary elements. Based on the formulations presented in this study, two computer softwares are developed and verified through some example problems. The results show that the present formulation is credible.

A coupled Ritz-finite element method for free vibration of rectangular thin and thick plates with general boundary conditions

  • Eftekhari, Seyyed A.
    • Steel and Composite Structures
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    • 제28권6호
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    • pp.655-670
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    • 2018
  • A coupled method, that combines the Ritz method and the finite element (FE) method, is proposed to solve the vibration problem of rectangular thin and thick plates with general boundary conditions. The eigenvalue partial differential equation(s) of the plate is (are) first reduced to a set of eigenvalue ordinary differential equations by the application of the Ritz method. The resulting eigenvalue differential equations are then reduced to an eigenvalue algebraic equation system using the finite element method. The natural boundary conditions of the plate problem including the free edge and free corner boundary conditions are also implemented in a simple and accurate manner. Various boundary conditions including simply supported, clamped and free boundary conditions are considered. Comparisons with existing numerical and analytical solutions show that the proposed mixed method can produce highly accurate results for the problems considered using a small number of Ritz terms and finite elements. The proposed mixed Ritz-FE formulation is also compared with the mixed FE-Ritz formulation which has been recently proposed by the present author and his co-author. It is found that the proposed mixed Ritz-FE formulation is more efficient than the mixed FE-Ritz formulation for free vibration analysis of rectangular plates with Levy-type boundary conditions.

Imidacloprid 피복 요소 혼합제제의 특성 및 시용효과 (Properties and Application Effects of Imidacloprid Coated Urea)

  • 박기도;강위금;이재성;박창영;박경배;하호성;강규영
    • 한국환경농학회지
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    • 제16권4호
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    • pp.285-290
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    • 1997
  • 벼 배재시 시비 및 농약살포의 성력화를 위하여 완효성요소에 살충제 imidacloprid를 피복하여 제조한 농약비료혼합제의 특성 및 시용효과를 검토한 결과를 요약하면 다음과 같다. 1. 농약비료혼합제중 전질소와 농약주성분의 수중용충률은 접착제의 함량이 많을수록 용출이 지연되었으나, 농약주성분은 24시간내에 모든 시제품에서 95% 이상 용출되었으며, 시제품별 전질소 용출은 처리후 40일까지는 차이가 있었으나 40일 이후부터는 뚜렷한 차이가 없었다. 2. 토양중 $NH_4-N$함량은 처리후 10일까지는 농약+요소구에서, 10일후에는 농약비료혼합제와 피복요소구에서 각각 높았는데, 이중 피복요소구의 $NH_4-N$ 함량이 약간 높은 경향이었다. 3. 벼 유수형성기와 출수기의 식물체중 질소량 및 질소흡수량은 피복요소구에서 가장 높았다. 4. 시험된 토양중의 탈질균 및 질산환원균 밀도는 농약+요소구보다 농약비료혼합제구와 피복요소구에서 낮았다. 5. 토양중 imidacloprid의 잔류량은 농약처리구에서 농약비료혼합제구와 농약+요소구보다 약간 높았으며, 처리별 벼멸구의 밀도 및 방제효과는 처리구간에 뚜렷한 차이가 없었다.

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A mixed 8-node hexahedral element based on the Hu-Washizu principle and the field extrapolation technique

  • Chen, Yung-I;Wu, Guan-Yuan
    • Structural Engineering and Mechanics
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    • 제17권1호
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    • pp.113-140
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    • 2004
  • A mixed eight-node hexahedral element formulated via the Hu-Washizu principle as well as the field extrapolation technique is presented. The mixed element with only three translational degrees of freedom at each node can provide extremely accurate and reliable performance for popular benchmark problems such as spacial beams, plates, shells as well as general three-dimensional elasticity problems. Numerical calculations also show that when extremely skewed and coarse meshes and nearly incompressible materials are used, the proposed mixed element can still possess excellent behaviour. The mixed formulation starts with introduction of a parallelepiped domain associated with the given general eight-node hexahedral element. Then, the assumed strain field at the nodal level is constructed via the Hu-Washizu variational principle for that associated parallelepiped domain. Finally, the assumed strain field at the nodal level of the given hexahedral element is established by using the field extrapolation technique, and then by using the trilinear shape functions the assumed strain field of the whole element domain is obtained. All matrices involved in establishing the element stiffness matrix can be evaluated analytically and expressed explicitly; however, a 24 by 24 matrix has to be inverted to construct the displacement extrapolation matrix. The proposed hexahedral element satisfies the patch test as long as the element with a shape of parallelepiped.

A NONCONFORMING PRIMAL MIXED FINITE ELEMENT METHOD FOR THE STOKES EQUATIONS

  • Cho, Sungmin;Park, Eun-Jae
    • 대한수학회보
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    • 제51권6호
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    • pp.1655-1668
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    • 2014
  • In this article, we propose and analyze a new nonconforming primal mixed finite element method for the stationary Stokes equations. The approximation is based on the pseudostress-velocity formulation. The incompressibility condition is used to eliminate the pressure variable in terms of trace-free pseudostress. The pressure is then computed from a simple post-processing technique. Unique solvability and optimal convergence are proved. Numerical examples are given to illustrate the performance of the method.

혼합작업장을 고려한 혼합모델 조립라인의 투입순서결정에 관한 탐색적기법 (Heuristics Method for Sequencing Mixed Model Assembly Lines with Hybridworkstation)

  • 김정자;김상천;공명달
    • 산업경영시스템학회지
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    • 제21권48호
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    • pp.299-310
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    • 1998
  • Actually mixed assembly line is mixed with open and close type workstation. This workstation is called hybridworkstation. The propose of this paper is to determine the sequencing of model that minimize line length for actual(hybridworkstation) mixed model assembly line. we developed three mathematical formulation of the problem to minimize the overall length of a line with hybrid station. Mathematical formulation classified model by operato schedule. Mixed model assembly line is combination program and NP-hard program. Thus computation time is often a critical factor in choosing a method of determining the sequence. This study suggests a tabu search technique which can provide a near optimal solution in real time and use the hill climbing heuristic method for selecting initial solution. Modified tabu search method is compared with MIP(Mixed Integer Program). Numerical results are reported to demonstrate the efficiency of the method.

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