• Interaction and multiscale mechanics
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• v.2 no.3
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• pp.295-319
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• 2009

In this work, we discuss a reproducing kernel collocation method (RKCM) for solving $2^{nd}$ order PDE based on strong formulation, where the reproducing kernel shape functions with compact support are used as approximation functions. The method based on strong form collocation avoids the domain integration, and leads to well-conditioned discrete system of equations. We investigate the convergence and the computational complexity for this proposed method. An important result obtained from the analysis is that the degree of basis in the reproducing kernel approximation has to be greater than one for the method to converge. Some numerical experiments are provided to validate the error analysis. The complexity of RKCM is also analyzed, and the complexity comparison with the weak formulation using reproducing kernel approximation is presented.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.983-993
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• 2022

The main purpose of this paper is to solve the second kind Volterra integral equations by Clenshaw-Curtis spectral collocation method. First of all, we can transform the integral interval from [-1, x] to [-1, 1] through a simple linear transformation, and discretize the integral term in the equation by Clenshaw-Curtis quadrature formula to obtain the collocation equations. Then we provide a rigorous error analysis for the proposed method. At last, several numerical example are used to verify the results of theoretical analysis.

• Journal of the Korean Geotechnical Society
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• v.21 no.6
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• pp.93-100
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• 2005

The occurrence of multi-segmented hydraulic fractures that show different behavior from the single fracture is common phenomenon. However, it is not easy to evaluate the behavior of multiple fractures computed by most numerical techniques because of complicated process computation. This study presents how to efficiently calculate the displacement of the multi-segmented hydraulic fractures using the boundary collocation method (BCM). First of all, asymptotic solutions are obtained for the closely spaced overlapping fractures and are compared with those by the BCM where the number of collocation points is varied. As a result, the BCM provides an excellent agreement with the asymptotic solutions even when the number of collocation points is reduced ten times as many as that of conventional implementations. Accordingly, the numerical simulation of more realistic and, hence, more complex fracture geometries by the BCM would be valid with such a significant reduction of the number of collocation points.

• Journal of Aerospace System Engineering
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• v.14 no.3
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• pp.17-23
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• 2020

In this paper, the efficient periodic unsteady flow analysis is developed by using a Chebyshev collocation operator applied to the time differential term of the governing equations. The partial implicit time integration method was also applied in the governing equation for a fluid, which means flux terms were implicitly processed for a time integration and the time derivative terms were applied explicitly in the form of the source term by applying the Chebyshev collocation operator. To verify this method, we applied the 1D unsteady Burgers equation and the 2D oscillating airfoil. The results were compared with the existing unsteady flow frequency analysis technique, the Harmonic Balance Method, and the experimental data. The Chebyshev collocation operator can manage time derivatives for periodic and non-periodic problems, so it can be applied to non-periodic problems later.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.439-451
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• 2000

To compute derivatives using matrix vector multiplication method, new algorithms were introduced in [1.2]n By these algorithms, we reduced roundoff error in computing derivative using Chebyshev collocation methods (CCM). In this paper, some applications of these algorithms ar presented.

• Journal of KIISE:Software and Applications
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• v.27 no.3
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• pp.302-313
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• 2000

In English-Korean machine translation, transitive verb-objective collocation is utilized for accurate translation of an English verbal phrase into Korean. This paper presents an algorithm for correct verb translation based on the k-nearest neighbor learning. The semantic distance is defined on the WordNet for the k-nearest neighbor learning. And we also present algorithms for automatic collocation dictionary optimization. The algorithms extract transitive verb-objective pairs as training examples from large corpora and minimize the examples, considering the tradeoff between translation accuracy and example size. Experiments show that these algorithms optimized collocation dictionary keeping about 90% accuracy for a verb 'build'.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.8 s.179
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• pp.2100-2107
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• 2000

The wavelet theory is relatively a new development and now acquires popularity and much interest in many areas including mathematics and engineering. This work presents an adaptive wavelet method for a numerical solution of partial differential equations in a collocation sense. Due to the multi-resolution nature of wavelets, an adaptive strategy can be easily realized it is easy to add or delete the wavelet coefficients as resolution levels progress. Typical wavelet-collocation methods use interpolating wavelets having no vanishing moment, but we propose a new wavelet-collocation method on modified interpolating wavelets having 2 vanishing moments. The use of the modified interpolating wavelets obtained by the lifting scheme requires a smaller number of wavelet coefficients as well as a smaller condition number of system matrices. The latter property makes a preconditioned conjugate gradient solver more useful for efficient analysis.

• Proceedings of the Korea Water Resources Association Conference
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• 2019.05a
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• pp.315-315
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• 2019

증산과 증발의 합으로 나타내지는 증발산은 지구내에서의 수문 순환에 영향을 미치는 중요한 인자로써, 지표와 대기의 에너지 교환을 담당하고 있다. 정확한 관측을 위해서 오래전부터 증발산에 대해서 관측하기 위하여 직접관측 방법들인 증발산계를 이용한 관측방법, 에디 공분산 방법을 이용한 플럭스타워 관측 방법 등을 사용하였으며, 물리 및 경험적인 방법인 Penman (1948), Monteith (1965) 방법, PT (Priestley and Taylor, 1972) 방법 등을 이용함으로써 증발산과 관계를 가진 수문기상인자를 이용함으로써 증발산에 대해서 추정하여 왔다. 대부분 지상 관측에 의존하기 때문에 시공간적인 값의 표현이 어렵다는 문제를 가지고 있으며, 관측 장비의 관리 및 유지비용이 증대로 인하여 조밀한 관측망을 구축하기 어렵다. 이러한 단점을 개선하고자 인공위성 및 재분석 자료를 활용하여 여러 경험식을 통해서 증발산 자료가 제공되고 있다. 그러나 이러한 자료들의 문제점은 각기 다른 경험식 및 다른 입력자료를 제공하고 있을 뿐만 아니라, 자료별 지역별 정확성이 차이가 발생한다. 따라서, 최근 연구에서는 지점자료와 인공위성 자료 및 재분석 자료를 모두 사용함으로써 수문기상인자를 개선하고자 하는 연구가 진행되어왔으며, 정확성 또한 개선된 것을 확인 할 수 있다. 그러나, 이러한 방법들의 가장 큰 문제점은 관측 자료가 필수적으로 필요하다는 것에 있다. 대부분의 나라나 지역에서는 조밀한 구축망을 구축하기 어렵기 때문에 실질적으로 적용하기가 어렵다는데 있다. 따라서 본 연구에서는 이러한 문제를 해결하기 위하여 지점자료가 필요없는 융합방법을 triple collocation 방법을 이용함으로써 제안하고자 한다.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.23 no.4
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• pp.385-392
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• 2005

This paper describes an accuracy analysis of newly developed gravimetric geoid and an improvement of developed geoid using GPS/Levelling data. We developed the KGEOID05 model corrected with the correction term. The correction term is modelled using the difference between GPS/Levelling derived geoidal heights and gravimetric geoidal heights. The stochastic model used in the calculation of correction term is the least squares collocation technique based on second-order Markov covariance function. 373 GPS stations were used to model the correction term. The standard deviation of KGEOID05 is about 11 cm and it indicates that we can be determined accurate heights ($2{\sim}3\;cm$) when we made precise modelling using KGEOID05 and a few GPS measurements for the local area.

• Journal of KIISE
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• v.44 no.11
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• pp.1165-1177
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• 2017

Many developers utilize specific APIs to develop software, and to identify the use of a particular API, a developer can refer to a website that provides the API or can retrieve the API from the web. However, the site that provides the API does not necessarily provide guidance on how to use it while it can be partially provided in many other cases. In this paper, we propose a novel system JACE (Java AST collocation-pattern extractor) as a method to reuse commonly-used code as a supplement. The JACE extracts the API call nodes, collocation patterns and analyzes the relations between the collocations to extract significant API patterns from the source code. The following experiment was performed to verify the accuracy of a defined pattern: 794 open source projects were analyzed to extract about 15M API call nodes. Then, the Eclipse plug-in test program was utilized to retrieve the pattern using the top 10 classes of API call nodes. Finally, the code search results from reference pages of the API classes and the Searchcode [1] were compared with the test program results.