• The Pure and Applied Mathematics
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• v.13 no.4 s.34
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• pp.281-294
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• 2006

Many partial differential equations defined on a rectangular domain can be solved numerically by using a domain decomposition method. The most commonly used decompositions are the domain being decomposed in stripwise and rectangular way. Theories for non-overlapping domain decomposition(in which two adjacent subdomains share an interface) were often focused on the stripwise decomposition and claimed that extensions could be made to the rectangular decomposition without further discussions. In this paper we focus on the comparisons of the two ways of decompositions. We consider the unconditionally stable scheme, the MIP algorithm, for solving parabolic partial differential equations. The SOR iterative method is used in the MIP algorithm. Even though the theories are the same but the performances are different. We found out that the stripwise decomposition has better performance.

• The KIPS Transactions:PartB
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• v.10B no.3
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• pp.265-272
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• 2003

In this paper, we propose a novel improved algorithm for the rectangular decomposition technique for the purpose of performing data mining from large scaled database in a dynamic environment. The proposed algorithm performs the rectangular decompositions by transforming a binary matrix to bipartite graph and finding bicliques from the transformed bipartite graph. To demonstrate its effectiveness, we compare the proposed one which is based on the newly derived mathematical properties with those of other methods with respect to the classification rate, the number of rules, and complexity analysis.

• East Asian mathematical journal
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• v.39 no.1
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• pp.75-85
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• 2023

In this paper, a non-overlapping rectangular domain decomposition method is presented in order to numerically solve two-dimensional telegraph equations. The method is unconditionally stable and efficient. Spectral radius of the iteration matrix and convergence rate of the method are provided theoretically and confirmed numerically by MATLAB. Numerical experiments of examples are compared with several methods.

• Korean Journal of Computational Design and Engineering
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• v.12 no.4
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• pp.274-282
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• 2007

In this paper, a method of constructing a rectangular net from unorganized point cloud data is presented. In the method an implicit surface that fits the given point data is generated by using principal component analysis(PCA) and adaptive domain decomposition method(ADDM). Then a complete and quality rectangular net can be obtained by extracting voxel data from the implicit surface and projecting exterior faces of extracted voxels onto the implicit surface. The main advantage of the proposed method is that a quality rectangular net can be extracted from randomly scattered 3D points only without any further information. Furthermore the results of this works can be used to obtain many useful information including a slicing data, a solid STL model and a NURBS surface model in many areas involved in treatment of large amount of point data by proper processing of implicit surface and rectangular net generated previously.

• Structural Engineering and Mechanics
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• v.14 no.4
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• pp.401-416
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• 2002

This paper presents a domain decomposition method for buckling analysis of rectangular Kirchhoff plates subjected to uniaxial inplane load and with mixed edge support conditions. A plate is decomposed into two rectangular subdomains along the change of the discontinuous support conditions. The automated Ritz method is employed to derive the governing eigenvalue equation for the plate system. Compatibility conditions are imposed for transverse displacement and slope along the interface of the two subdomains by modifying the Ritz trial functions. The resulting Ritz function ensures that the transverse displacement and slope are continuous along the entire interface of the two subdomains. The validity and accuracy of the proposed method are verified with convergence and comparison studies. Buckling results are presented for several selected rectangular plates with various combination of mixed edge support conditions.

• Communications for Statistical Applications and Methods
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• v.17 no.6
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• pp.803-810
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• 2010

The singular value decomposition of a rectangular matrix is a basic tool to understand the structure of the data and particularly the relationship between row and column factors. However, conventional singular value decomposition used the least squares method and is not robust to outliers. We propose a simple robust singular value decomposition algorithm based on the weighted least absolute deviation which is not sensitive to leverage points. Its implementation is easy and the computation time is reasonably low. Numerical results give the data structure and the outlying information.

• Wind and Structures
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• v.25 no.3
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• pp.301-328
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• 2017

Multivariate fluctuating pressures acting on a 2:1 rectangular section (2-D) with dimensions of 9 cm by 4.5 cm has been studied using wind tunnel experiments under uniform and smooth flow condition for various angles of wind incidence. Based on the variation of mean pressure coefficient distributions along the circumference of the rectangular section with angle of wind incidence, and with the aid of skin friction coefficients, three distinct flow regimes with two transition regimes have been identified. Further, variations of mean drag and lift coefficients, Strouhal number with angles of wind incidence have been studied. The applicability of Universal Strouhal number based on vortex street similarity of wakes in bluff bodies to the 2:1 rectangular section has been studied for different angles of wind incidence. The spatio-temporal correlation features of the measured pressure data have been studied using Proper Orthogonal Decomposition (POD) technique. The contribution of individual POD modes to the aerodynamic force components, viz, drag and lift, have been studied. It has been demonstrated that individual POD modes can be associated to different physical phenomena, which contribute to the overall aerodynamic forces.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2009.11a
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• pp.236-241
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• 2009

To identify turbulent flow characteristics of non-reacting case resulted from cooling flow injection in a rectangular swirl combustor, 3D Large Eddy Simulation(LES) was implemented and Proper Orthogonal Decomposition(POD) analysis was used for post-processing. The combustor of concern is the LM6000, lean premixed dry low-NOx annular combustor, developed by GEAE. It was observed that increase in speed of shear layer resulted from the inflow of cooling flow caused intensified vorticity magnitude in central toroidal recirculation zone. In the case of vorticity magnitude in corner recirculation zone, however, was weakened. In addition, pressure fluctuation in combustor was damped down and longitudinal acoustic mode was significantly dissipated

• Journal of Korean Society of Steel Construction
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• v.20 no.6
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• pp.751-759
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• 2008

In this study, the effect of an unsteady flow field around a body of aerostatic/aerodynamic forces were investigated using rectangular cylinders (B/D = 2, 3, 4, 5). Proper orthogonal decomposition (POD) was introduced to the analysis of the fluctuating pressure field that was measured on the stationary/oscillatory B/D=4 rectangular cylinder, and the characteristics of the proper functions with flow patterns were identified. In addition, the physical decoupling and interactions in the different co-existing flow patterns were investigated through POD. The comparison with the identified proper function associated with a particular flow pattern revealed that the Karman vortex is almost not affected by the separation bubble, but that the Karman vortex considerably interferes in the development of the separation bubble around the trailing edge. It can be considered that the Karman vortex induces the increment of the curvature of the substantial separated flow.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.17 no.5
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• pp.1049-1054
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• 2013

In this paper, two-dimensional(2-D) Finite Difference Time Domain(FDTD) method using the domain decomposition method is proposed. We calculated the electromagnetic scattering field of a two dimensional rectangular Perfect Electric Conductor(PEC) structure using the 2-D FDTD method with Schur complement method as a domain decomposition method. Four domain decomposition and eight domain decomposition are applied for the analysis of the proposed structure. To validate the simulation results, the general 2-D FDTD algorithm for the total domain are applied to the same structure and the results show good agreement with the 2-D FDTD using the domain decomposition method.