• Communications for Statistical Applications and Methods
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• 제4권1호
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• pp.177-183
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• 1997

A data-adaptive order selection procedure is proposed for local polynomial nonparametric regression. For each given polynomial order, bias and variance are estimated and the adaptive polynomial order that has the smallest estimated mean squared error is selected locally at each location point. To estimate mean squared error, empirical bias estimate of Ruppert (1995) and local polynomial variance estimate of Ruppert, Wand, Wand, Holst and Hossjer (1995) are used. Since the proposed method does not require fitting polynomial model of order higher than the model order, it is simpler than the order selection method proposed by Fan and Gijbels (1995b).

• 한국자동차공학회논문집
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• 제4권4호
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• pp.190-200
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• 1996

Step-by-step time integration methods are widely used for solving structural dynamics problem. One difficult yet critical choice an analyst must make is to decide an appropriate time step size. The choice of time step size has a significant effect on solution accuracy and computational expense. The objective of this research is to derive error estimate for newly developed time integration method and develop automatic time step size control algorithm for structural dynamics. A formula for computing error tolerance is derived based on desired period resolution. An automatic time step size control strategy is proposed based on a normalized local error estimate for the generalized-α method. Numerical examples demonstrate the developed strategy satisfies general design criteria for time step size control algorithm for dynamic problem.

• Structural Engineering and Mechanics
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• 제39권6호
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• pp.767-793
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• 2011

An efficient edge-based smoothed finite element method (ES-FEM) has been recently developed for solving solid mechanics problems. The ES-FEM uses triangular elements that can be generated easily for complicated domains. In this paper, the complexity study of the ES-FEM based on triangular elements is conducted in detail, which confirms the ES-FEM produces higher computational efficiency compared to the FEM. Therefore, the ES-FEM offers an excellent platform for adaptive analysis, and this paper presents an efficient adaptive procedure based on the ES-FEM. A smoothing domain based energy (SDE) error estimate is first devised making use of the features of the ES-FEM. The present error estimate differs from the conventional approaches and evaluates error based on smoothing domains used in the ES-FEM. A local refinement technique based on the Delaunay algorithm is then implemented to achieve high efficiency in the mesh refinement. In this refinement technique, each node is assigned a scaling factor to control the local nodal density, and refinement of the neighborhood of a node is accomplished simply by adjusting its scaling factor. Intensive numerical studies, including an actual engineering problem of an automobile part, show that the proposed adaptive procedure is effective and efficient in producing solutions of desired accuracy.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2001년도 가을 학술발표회 논문집
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• pp.34-42
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• 2001

In this paper, we study on a modified mesh generation method based on the pollution error estimate. This method is designed for the control of the pollution error in any patch of elements of interest. It is a well-known fact that the pollution error estimates are much more than the local one. Reliable a posteriori error estimation is possible by controlling the pollution error in the patch through proper design of the mesh outside the patch. This design is possible by equally distributing the pollution error indicators over the mesh outside the patch. The conventional feedback pollution-adaptive mesh generation algorithm needs many iterations. Therefore, the solution time is significant. But we use the remeshing scheme in the proposed method. We will also show that the pollution error reduces less than the local error.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제24권1호
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• pp.39-78
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• 2020

In this paper, we propose a decoupled local discontinuous Galerkin method for solving the Klein-Gordon-Schrödinger (KGS) equations. The KGS equations is a model of the Yukawa interaction of complex scalar nucleons and real scalar mesons. The advantage of our scheme is that the computation of the nucleon and meson field is fully decoupled, so that it is especially suitable for parallel computing. We present the conservation property of our fully discrete scheme, including the energy and Hamiltonian conservation, and establish the optimal error estimate.

• 대한전기학회논문지
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• 제38권1호
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• pp.22-28
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• 1989

This paper describes error estimate mothod for adaptive finite element analysis of two dimensional electrostatic and magnetostatic field problems. To estimate the local errors, divergence theorem is used for electrostatic field and Ampere's circuital law for magnetostatic field. To confirm the effectiveness of the proposed error estimators, adaptive finite element computations are performed using the proposed error estimators. The rates of convergence of global errors are comparable with those of existing adaptive finite element schemes which make use of field continuity conditions between element boundaries. This algorithm of error estimate can be easily implemented because of its simplicity. Especially, when the value of charge in electrostatic field and the value of current in magnetostatic field are to be figured out, this method is considerded to be preferable to other approaches.

• 대한수학회논문집
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• 제38권1호
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• pp.281-298
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• 2023

A class of systems of Caputo fractional differential equations with integral boundary conditions is considered. A numerical method based on a finite difference scheme on a uniform mesh is proposed. Supremum norm is used to derive an error estimate which is of order κ − 1, 1 < κ < 2. Numerical examples are given which validate our theoretical results.

• Geomechanics and Engineering
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• 제30권5호
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• pp.437-448
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• 2022

Alluvial soil is challenging to work with due to its high compressibility. Thus, consolidation settlement of this type of soil should be accurately estimated. Accurate estimation of the consolidation settlement of alluvial soil requires accurate prediction of compressibility parameters. Geotechnical engineers usually use empirical correlations to estimate these compressibility parameters. However, no attempts have been made to develop correlations to estimate compressibility parameters of alluvial soil. Thus, this paper aims to develop new models to predict the compression and recompression indices (Cc and Cr) of alluvial soils. As part of the study, geotechnical laboratory tests have been conducted on large number of undisturbed samples of local alluvial soil. The obtained results from these tests in addition to available results from the literature from different parts in the world have been compiled to form the database of this study. This database is then employed to examine the accuracy of the available empirical correlations of the compressibility parameters and to develop the new models to estimate the compressibility parameters using the nonlinear regression analysis. The accuracy of the new models has been accessed using mean absolute error, root mean square error, mean, percentage of predictions with error range of ±20%, percentage of predictions with error range of ±30%, and coefficient of determination. It was found that the new models outperform the available correlations. Thus, these models can be used by geotechnical engineers with more confidence to predict Cc and Cr.

• 자연과학논문집
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• 제8권1호
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• pp.5-15
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• 1995

IRR 적응 휠터의 공식오차 방식은 지역 최소값에 관계없이 전역 최소값에 수렴하며 안정성이 높다. 그러나 공식오차 방식은 입력 신호에 잡음이 섞여 경우 예측계수가 바이어스 되는 문제가 있다. 본 논문에서는 사전에 잡음에 대한 지식이 없이 바이어스가 없는 예측계수를 얻을 수 있는 새로운 공식 오차 방식을 위한 알고리즘을 제안한다. 이 알고리즘은 공식오차를 스므딩하는 방식을 이용하여 입력에 추가되는 잡음이 백색잡음인 경우 바이어스 없이 계수를 예측할 수 있다. 시뮬레이션을 통해 새로운 알고리즘이 공식오차의 중요한 장점인 빠른 수렴속도와 안정성을 유지하며 바이어스를 효율적으로 제거함을 볼 수 있다.

• 대한전기학회논문지
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• 제37권3호
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• pp.141-145
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• 1988

This paper reports a new and simple posteriori error estimate method for adaptive finite element mesh genration especially for the magnetic field problems. To estimate local errors, we consider the interelement boundary conditions. Elements which violate much the conditions are considered to have great errors. Magnetic flux density errors are considered as a basis for refinement. This estimator is tested on two dimensional proplems with singular points. The estimated errors are always under estimated but in same order as exact errors, and this algorithm is much simpler and more convenient than other methods. The adaptive mesh gives much better rate of convergence in global errors than the uniform mesh.