Exponentially Fitted Error Correction Methods for Solving Initial Value Problems

Kim, Sang-Dong,Kim, Phil-Su Department of Mathematics 2012 Kyungpook mathematical journal Vol.52 No.2

In this article, we propose exponentially fitted error correction methods(EECM) which originate from the error correction methods recently developed by the authors (see [10, 11] for examples) for solving nonlinear stiff initial value problems. We reduce the computational cost of the error correction method by making a local approximation of exponential type. This exponential local approximation yields an EECM that is exponentially fitted, A-stable and L-stable, independent of the approximation scheme for the error correction. In particular, the classical explicit Runge-Kutta method for the error correction not only saves the computational cost that the error correction method requires but also gives the same convergence order as the error correction method does. Numerical evidence is provided to support the theoretical results.

Error Correction Techniques: Conversation-Analytic Perspective

우수정 ( Sujung Woo ) 대한영어영문학회 2012 영어영문학연구 Vol.38 No.2

This study is to examine the actions in the correction relevant turns using Conversation Analysis (CA) framework. I focus on describing a variety of aspects of correction-in-interaction captured in transcripts of recordings of naturally occurring interaction during the phone interviews in the pedagogical context. Also, this paper aims to shed light on the factors affecting the effectiveness of the various types of the error correction techniques. By using CA methodology, it is possible to look at “finely grained architectural details” (Hall, 2007) of interaction in the activity of correction. The three actions that are observed in the correction relevant turns are (1) locating errors (2) doing of correcting, and (3) repeating the target sentence. And the first two actions are examined for the purpose of this study. All the actions are performed either interactionally-salient or interactionally-not-salient1 ways. While phonological emphasis and specific instructions are given to make the activity of correction salient to the caller, simple repetition the correct form of the answer is not salient enough for the caller to understand what the teachers are trying to do at turn-at-talk. This study does not try to demonstrate how language is operationalized in human’s brain as in SLA but illustrates what it does how it is performed in talk-in-interaction from the CA perspective. (Konyang University)

An In-situ Correction Method of Position Error for an Autonomous Underwater Vehicle Surveying the Sea Floor

Lee, Pan-Mook,Jun, Bong-Huan,Park, Jin-Yeong,Shim, Hyung-Won,Kim, Jae-Soo,Jung, Hun-Sang,Yoon, Ji-Young Korean Society of Ocean Engineers 2011 International journal of ocean system engineering Vol.1 No.2

This paper presents an in-situ correction method to compensate for the position error of an autonomous underwater vehicle (AUV) near the sea floor. AUVs generally have an inertial navigation system assisted with auxiliary navigational sensors. Since the inertial navigation system shows drift in position without the bottom reflection of a Doppler velocity log, external acoustic positioning systems, such as an ultra short baseline (USBL), are needed to set the position without surfacing the AUV. The main concept of the correction method is as follows: when the AUV arrives near the sea floor, the vehicle moves around horizontally in a circular mode, while the USBL transceiver installed on a surface vessel measures the AUV's position. After acquiring one data set, a least-square curve fitting method is adopted to find the center of the AUV's circular motion, which is transferred to the AUV via an acoustic telemetry modem (ATM). The proposed method is robust for the outlier of USBL, and it is independent of the time delay for the data transfer of the USBL position with the ATM. The proposed method also reduces the intrinsic position error of the USBL, and is applicable to the in-situ calibration as well as the initialization of the AUVs' position. Monte Carlo simulation was conducted to verify the effectiveness of the method.

An iteration free backward semi-Lagrangian scheme for solving incompressible Navier–Stokes equations

Piao, Xiangfan,Bu, Sunyoung,Bak, Soyoon,Kim, Philsu Elsevier 2015 Journal of computational physics Vol.283 No.-

<P><B>Abstract</B></P> <P>A backward semi-Lagrangian method based on the error correction method is designed to solve incompressible Navier–Stokes equations. The time derivative of the Stokes equation is discretized with the second order backward differentiation formula. For the induced steady Stokes equation, a projection method is used to split it into velocity and pressure. Fourth-order finite differences for partial derivatives are used to the boundary value problems for the velocity and the pressure. Also, finite linear systems for Poisson equations and Helmholtz equations are solved with a matrix-diagonalization technique. For characteristic curves satisfying highly nonlinear self-consistent initial value problems, the departure points are solved with an error correction strategy having a temporal convergence of order two. The constructed algorithm turns out to be completely iteration free. In particular, the suggested algorithm possesses a good behavior of the total energy conservation compared to existing methods. To assess the effectiveness of the method, two-dimensional lid-driven cavity problems with large different Reynolds numbers are solved. The doubly periodic shear layer flows are also used to assess the efficiency of the algorithm.</P>

A semi-Lagrangian approach for numerical simulation of coupled Burgers’ equations

Bak, Soyoon,Kim, Philsu,Kim, Dojin Elsevier 2019 Communications in nonlinear science & numerical si Vol.69 No.-

<P><B>Abstract</B></P> <P>In this study, we develop a numerical method for solving the coupled viscous Burgers’ equations based on a backward semi-Lagrangian method. The main difficulty associated with the backward semi-Lagrangian method for this problem is treating the nonlinearity in the diffusion-reaction equation, whose reaction coefficients are given in terms of coupled partial derivatives. To handle this difficulty, we use an extrapolation technique which splits the nonlinearity into two linear diffusion-reaction boundary value problems. In the proposed backward semi-Lagrangian method, we use fourth-order finite differences to discretize the diffusion-reaction boundary value problems and employ the so-called error correction method to solve the highly nonlinear initial value problems. Our overall algorithm is completely iteration-free and computationally efficient. We demonstrate the numerical accuracy and efficiency of the present method by comparing our numerical results with analytical solutions and other numerical solutions based on alternative existing methods.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Applications of the proposed BSLM in nonlinear differential equations are discussed. </LI> <LI> The possibility to apply the method in the KP equations is suggested. </LI> </UL> </P>

Numerical Simulation for Synergetic Deformation of Optical Fiber Sensor and Asphalt Mixture

Xiang-fei Zhang,Zhen-dong Qian,Meng Zhang,Lei-lei Chen 대한토목학회 2019 KSCE JOURNAL OF CIVIL ENGINEERING Vol.23 No.7

Owing to the structural and material differences, data obtained by distributed optical fiber sensors (OFS) for asphalt pavement strain measurement lack of precision. For better understanding OFS measurement mechanism and investigating the measurement error correction, this study analyzed the synergetic deformation of OFS and asphalt mixture (AM) under load. Firstly, a threedimensional AM single-edge notched beam (SEB) model with OFS was established and verified using the discrete element method. Secondly, the micro-crack propagation of SEB model during loading procedure was analyzed to explore the debonding behavior between OFS and AM. Thirdly, strain development of OFS and AM was investigated during fracture stage and post-fracture stage. Finally, a measurement error correction method was developed based upon the materials and test conditions in this study. Results demonstrate that debonding occurs on OFS surface when macro-crack extends across OFS position. The key to making the strain measurement accuracy is to ensure the effective bonding between OFS and AM. In addition, this study provides a framework used to develop the measurement error correction, and the research results give the theoretical foundation for data selection and error correction of asphalt pavement strain measurement and crack detection using distributed optical fiber sensors.

A New Time Stepping Method for Solving One Dimensional Burgers' Equations

Piao, Xiang Fan,Kim, Sang-Dong,Kim, Phil-Su,Kim, Do-Hyung Department of Mathematics 2012 Kyungpook mathematical journal Vol.52 No.3

In this paper, we present a simple explicit type numerical method for discretizations in time for solving one dimensional Burgers' equations. The proposed method does not need an iteration process that may be required in most implicit methods and have good convergence and efficiency in computational sense compared to other known numerical methods. For evidences, several numerical demonstrations are also provided.

Error Control Strategy in Error Correction Methods

KIM, PHILSU,BU, SUNYOUNG Department of Mathematics 2015 Kyungpook mathematical journal Vol.55 No.2

In this paper, we present the error control techniques for the error correction methods (ECM) which is recently developed by P. Kim et al. [8, 9]. We formulate the local truncation error at each time and calculate the approximated solution using the solution and the formulated truncation error at previous time for achieving uniform error bound which enables a long time simulation. Numerical results show that the error controlled ECM provides a clue to have uniform error bound for well conditioned problems [1].

세종말뭉치의 오류 수정 방법

김재훈(Jae-Hoon Kim),서형원(Hyung-Won Seo),전길호(Kil-Ho Jeon),최명길(Myung-Gil Choi) 한국마린엔지니어링학회 2010 한국마린엔지니어링학회 학술대회 논문집 Vol.2010 No.4

Sejong corpus is a Korean corpus annotated with various linguistic information. The corpus contains a raw corpus, a part-of-speech (POS) tagged corpus, a syntactic tree bank and so on, according to the annotated information. This paper is related to the POS-tagged corpus, which is annotated with the POS information and used to develop natural language processing (NLP) systems, such as information retrieval, information extract, etc. The Sejong POS-tagged corpus had been built by the National Institute of the Korean Language for 9 years and consists of 10.6 million words. However, it's hard to use the corpus for developing some NLP systems because of various types of errors in the corpus. We treat errors which original words mismatch the concatenation of tagged morphemes. In this paper, we represent a method for detecting the errors and correcting them, and also our results. First, the error detection is to find mismatches of strings between original words and the concatenation of their analyzed words. The mismatches is candidates of errors and contains some valid forms transformed by irregular or phoneme conjugations. We develop a program to filter the valid forms out. The remaining mismatches are modified according to error types as follows: 1) Unnecessarily inserted or deleted words had been corrected by regular expressions, which are made manually. 2) Some special symbols as errors didn't be recognized by annotators correctly and had been corrected manually. 3) Others as the remaining errors account for very small portion and had also been corrected manually. As the result of our effort, the Sejong POS-tagged corpus is improved as good as it is useful for some applications.

반사 광학 표면의 회전대칭형 형상 오차 수정 연마 방법에 관한 연구

이호철(H. C. Lee),김도현(D. H. Kim),송창규(C. K,Song),박천홍(C. H. Park),이후상(H. S. Lee) 한국정밀공학회 2008 한국정밀공학회 학술발표대회 논문집 Vol.2008 No.11월