• Title, Summary, Keyword: A Posteriori 오차

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Finite Element Analysis and Local a Posteriori Error Estimates for Problems of Flow through Porous Media (다공매체를 통과하는 유동문제의 유한요소해석과 부분해석후 오차계산)

  • Lee, Choon-Yeol
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.21 no.5
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    • pp.850-858
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    • 1997
  • A new a posteriori error estimator is introduced and applied to variational inequalities occurring in problems of flow through porous media. In order to construct element-wise a posteriori error estimates the global error is localized by a special mixed formulation in which continuity conditions at interfaces are treated as constraints. This approach leads to error indicators which provide rigorous upper bounds of the element errors. A discussion of a compatibility condition for the well-posedness of the local error analysis problem is given. Two numerical examples are solved to check the compatibility of the local problems and convergence of the effectivity index both in a local and a global sense with respect to local refinements.

Local A Posteriori Error Estimates for Obstacle Contact Problems (장애물 접촉문제에서의 지역 A Posteriori 오차계산)

  • 이춘열
    • Journal of the Korean Society for Precision Engineering
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    • v.15 no.5
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    • pp.120-127
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    • 1998
  • Differential inequalities occurring in problems of obstacle contact problems are recast into variational inequalities and analyzed by finite element methods. A new a posteriori error estimator, which is essential in adaptive finite element method, is introduced to capture the errors in finite element approximations of these variational inequalities. In order to construct a posteriori error estimates, saddle point problems are introduced using Lagrange parameters and upper bounds are provided. The global upper bound is localized by a special mixed formulation, which leads to upper bounds of the element errors. A numerical experiment is performed on an obstacle contact problem to check the effectivity index both in a local and a global sense.

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Adaptive Delaunay Mesh Generation Technique Based on a Posteriori Error Estimation and a Node Density Map (오차 예측과 격자밀도 지도를 이용한 적응 Delaunay 격자생성방법)

  • 홍진태;이석렬;박철현;양동열
    • Transactions of Materials Processing
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    • v.13 no.4
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    • pp.334-341
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    • 2004
  • In this study, a remeshing algorithm adapted to the mesh density map using the Delaunay mesh generation method is developed. In the finite element simulation of forging process, the numerical error increases as the process goes on because of discrete property of the finite elements and distortion of elements. Especially, in the region where stresses and strains are concentrated, the numerical error will be highly increased. However, it is not desirable to use a uniformly fine mesh in the whole domain. Therefore, it is necessary to reduce the analysis error by constructing locally refined mesh at the region where the error is concentrated such as at the die corner. In this paper, the point insertion algorithm is used and the mesh size is controlled by using a mesh density map constructed with a posteriori error estimation. An optimized smoothing technique is adopted to have smooth distribution of the mesh and improve the mesh element quality.

A Minimum-Error-Rate Training Algorithm for Pattern Classifiers and Its Application to the Predictive Neural Network Models (패턴분류기를 위한 최소오차율 학습알고리즘과 예측신경회로망모델에의 적용)

  • 나경민;임재열;안수길
    • Journal of the Korean Institute of Telematics and Electronics B
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    • v.31B no.12
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    • pp.108-115
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    • 1994
  • Most pattern classifiers have been designed based on the ML (Maximum Likelihood) training algorithm which is simple and relatively powerful. The ML training is an efficient algorithm to individually estimate the model parameters of each class under the assumption that all class models in a classifier are statistically independent. That assumption, however, is not valid in many real situations, which degrades the performance of the classifier. In this paper, we propose a minimum-error-rate training algorithm based on the MAP (Maximum a Posteriori) approach. The algorithm regards the normalized outputs of the classifier as estimates of the a posteriori probability, and tries to maximize those estimates. According to Bayes decision theory, the proposed algorithm satisfies the condition of minimum-error-rate classificatin. We apply this algorithm to NPM (Neural Prediction Model) for speech recognition, and derive new disrminative training algorithms. Experimental results on ten Korean digits recognition have shown the reduction of 37.5% of the number of recognition errors.

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A Simple Posteriori Error Estimate Method For Adaptive Finite Element Mesh Generation Using Quadratic Shape Funtion (적응 유한 요소법을 위한 2차 형상 함수 오차 추정)

  • Kim, Hyeong-Seok;Choi, Hong-Soon;Choi, Kyung;Hahn, Song-Yop
    • Proceedings of the KIEE Conference
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    • pp.87-90
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    • 1988
  • This paper reports a simple posteriori error estimate method for adaptive finite element mesh generation using quadratic shape function especially for the magnetic field problems. The elements of quadratic shape function have more precise solution than those of linear shape function. Therefore, the difference of two solutions gives error quantity. The method uses the magnetic flux density error as a basis for refinement. This estimator is tested on two dimensional problem which has singular points. The estimated error is always under estimated but in same order as exact error, and this method is much simpler and more convenient than other methods. The result shows that the adaptive mesh gives even better rate of convergence in global error than the uniform mesh.

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A Posteriori Error Estimation Based On The Variation Of Mapping Function For Finite Element Method (사상 함수의 변분을 이용한 유한요소 해석의 오차 분석)

  • 박시형;김지환
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.86-93
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    • 2002
  • A new error estimation method is proposed. This utilizes the variation of energy functional about the mapping function between the global and the master elements. The resultant system of equations is the weak form of the generalized conservation checks. However, This formulation has an important information about the relations between the connected elements. In other words, some relations between the connected elements are obtained and these can be used very usefully to measure it posteriori error. In this paper, the explicit formulations are presented for the 1-dimensional model and the 2-dimensional model problems. Numerical results are provided for first order shear deformation theody of beam model and the plane stress problem.

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A Weighted Block Adaptive Estimation for STBC Single-Carrier System in Frequency-Selective Time-Varying Channels (다중 경로 시변 채널 환경에서 시공간 블록 부호 단일 반송파 시스템을 위한 가중치 블록 적응형 채널 추정 알고리즘)

  • Baek, Jong-Seob;Kwon, Hyuk-Jae;Seo, Jong-Soo
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.32 no.3C
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    • pp.338-347
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    • 2007
  • In this paper, a weighted block adaptive channel estimation (WBA-CE) for a space-time block-coded (STBC) single-carrier transmission with a cyclic-prefix is proposed. In operation of the WBA-CE, a STBC matrix-wise block for filter input symbols is first formulated. Applying a weighted a posteriori error vector-based least-square (LS) criterion for this block, the coefficient correction terms of the WBA-CE are then computed. An approximate steady-state excess mean-square error (EMSE) of the WBA-CE for the stationary optimal coefficient is also analyzed. Simulation results show in a time-varying typical urban (TU) channel that the proposed channel estimator provides better bit-error-rate (BER) performances than conventional algorithms such as the NLMS and RLS channel estimators.

A New Remeshing Technique of Tetrahedral Elements by Redistribution of Nodes in Subdomains and its Application to the Finite Element Analysis (영역별 절점 재분포를 통한 사면체 격자 재구성 방법 및 유한요소해석에의 적용)

  • Hong J.T.;Lee S.R.;Yang D.Y.
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • pp.607-610
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    • 2005
  • A remeshing algorithm using tetrahedral elements has been developed, which is adapted to the mesh density map constructed by a posteriori error estimation. In the finite element analyses of metal forging processes, numerical error increases as deformation proceeds due to severe distortion of elements. In order to reduce the numerical error, the desired mesh sizes in each region of the workpiece are calculated by a posteriori error estimation and the density map is constructed. Piecewise density functions are then constructed with the radial basis function in order to interpolate the discrete data of the density map. The sample mesh is constructed based on the point insertion technique which is adapted to the density function and the mesh size is controlled by moving and deleting nodes to obtain optimal distribution according to the mesh density function and the quality optimization function as well. After finishing the redistribution process of nodes, a tetrahedral mesh is constructed with the redistributed nodes, which is adapted to the density map and resulting in good mesh quality. A goodness and adaptability of the constructed mesh is verified with a testing measure. The proposed remeshing technique is applied to the finite element analyses of forging processes.

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Stress Recovery Technique by Ordinary Kriging Interpolation in p-Adaptive Finite Element Method (적응적 p-Version 유한요소법에서 정규 크리깅에 의한 응력복구기법)

  • Woo, Kwang Sung;Jo, Jun Hyung;Lee, Dong Jin
    • Journal of The Korean Society of Civil Engineers
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    • v.26 no.4A
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    • pp.677-687
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    • 2006
  • Kriging interpolation is one of the generally used interpolation techniques in Geostatistics field. This technique includes the experimental and theoretical variograms and the formulation of kriging interpolation. In contrast to the conventional least square method for stress recovery, kriging interpolation is based on the weighted least square method to obtain the estimated exact solution from the stress data at the Gauss points. The weight factor is determined by variogram modeling for interpolation of stress data apart from the conventional interpolation methods that use an equal weight factor. In addition to this, the p-level is increased non-uniformly or selectively through a posteriori error estimation based on SPR (superconvergent patch recovery) technique, proposed by Zienkiewicz and Zhu, by auto mesh p-refinement. The cut-out plate problem under tension has been tested to validate this approach. It also provides validity of kriging interpolation through comparing to existing least square method.

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