• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.26 no.1
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• pp.85-91
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• 2008

When a large sparse matrix is calculated for a horizontal geodetic network adjustment, it needs to go through the process of matrix reordering for the efficiency of time and space. In this study, several reordering methods for sparse matrix were tested, using Sparse Matrix Manipulation System(SMMS) program, total processing time and Fill-in number produced in factorization process were measured and compared. As a result, Minimum Degree(MD) and Mutiple Minimum Degree(MMD), which are based on Minimum Degree are better than Gibbs-Poole-Stockmeyer(GPS) and Reverse Cuthill-Mckee(RCM), which are based on Minimum Bandwidth. However, the method of the best efficiency can be changed dependent on distribution of non-zero elements in a matrix. This finding could be applied to heighten the efficiency of time and storage space for national datum readjustment and other large geodetic network adjustment.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.11
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• pp.1581-1593
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• 2001

An efficient variable-reordering method for finite element meshes is used and the effect of variable-reordering is investigated. For the element renumbering of unstructured meshes, Cuthill-McKee ordering is adopted. The newsy reordered global matrix has a much narrower bandwidth than the original one, making the ILU preconditioner perform bolter. The effect of variable reordering on the convergence behaviour of saddle point type matrix it studied, which results from P2/P1 element discretization of the Navier-Stokes equations. We also propose and test 'level(0) preconditioner'and 'level(2) ILU preconditioner', which are another versions of the existing 'level(1) ILU preconditioner', for the global matrix generated by P2/P1 finite element method of incompressible Navier-Stokes equations. We show that 'level(2) ILU preconditioner'performs much better than the others only with a little extra computations.

• Communications of the Korean Institute of Information Scientists and Engineers
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• v.5 no.2
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• pp.85-89
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• 1987

The large sparse matrix problems arise in many applications areas, such as structural analysis, network analysis. In dealing with such sparse systems proper preprogramming techniques such as permuting rows and columns simultaneously, will be needed in order to reduce the number of arithmetic operations and storage spaces.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.307-316
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• 2006

Incomplete LU factorization preconditioning techniques often have difficulty on indefinite sparse matrices. We present hybrid reordering strategies to deal with such matrices, which include new diagonal reorderings that are in conjunction with a symmetric nondecreasing degree algorithm. We first use the diagonal reorderings to efficiently search for entries of single element rows and columns and/or the maximum absolute value to be placed on the diagonal for computing a nonsymmetric permutation. To augment the effectiveness of the diagonal reorderings, a nondecreasing degree algorithm is applied to reduce the amount of fill-in during the ILU factorization. With the reordered matrices, we achieve a noticeable improvement in enhancing the stability of incomplete LU factorizations. Consequently, we reduce the convergence cost of the preconditioned Krylov subspace methods on solving the reordered indefinite matrices.

• Journal of Korea Multimedia Society
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• v.7 no.6
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• pp.781-790
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• 2004

This paper presents a fourth-order cumulants based iterative algorithm for blind channel equalization. It is robust with respect to the existence of heavy Gaussian noise in a channel and does not require the minimum phase characteristic of the channel. In this approach, the transmitted signals at the receiver are over-sampled to ensure the channel described by a full-column rank matrix. It changes a single-input/single-output (SISO) finite-impulse response (FIR) channel to a single-input/multi-output (SIMO) channel. Based on the properties of the fourth-order cumulants of the over-sampled channel outputs, the iterative algorithm is derived to estimate the deconvolution matrix which makes the overall transfer matrix transparent, i.e., it can be reduced to the identity matrix by simple reordering and scaling. Both a closed-form and a stochastic version of the proposed algorithm are tested with three-ray multi-path channels in simulation studies, and their performances are compared with a method based on conventional second-order cumulants. Relatively good results are achieved, even when the transmitted symbols are significantly corrupted with Gaussian noise.

• 전기의세계
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• v.39 no.3
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• pp.47-54
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• 1990

유한요소법과 경계요소법의 합성으로 전자계 해석을 하는 기법은 각 방법의 장점을 수용하여 경계가 없는 무한영역의 전자장을 분석하는 기법으로서 어떤 복잡하고 어려운 기하학적 구조의 문제도, 비선형이나 비균질성 재질의 문제도 쉽게 formulation이 가능하여 용이하게 해석할 수 있지만 전체 System matrix방정식이 비대칭이며 부분적인 full matrix를 형성하여 계산시간이 길어 진다는 단점도 있다. 적용예에서 보여 준 것과 같이 합성요소법은 그 해가 실제에 근사한 값을 가질수 있다고 생각되며, 계산시간을 단축시키기 위하여 직접법이나 반복법을 사용한 새로운 해법들이 도입되고 있다. 최근에는 system전체 node의 순서를 고려한 NDRA(Nested Dissection Reordering Algorithm)이 도입되고 있고, System matrix자체를 유한 요소법의 형태로 유지시키며 풀수 있는 방법으로 알려진 Absorbin 경계조건을 사용하여 전자파에 대한 해석을 하고 있다. 유한 및 경계요소 합성법은 초고압 옥외용 전력기기의 전자장 해석과 설계, 레이다나 안테나 등의 전자파 해석문제, 초전도 응용, 전력기기의 전자장해석과 설계, 우주공간에서의 전력전송문제 등을 쉽게 model화하여 적용할 수 있을 것이다.

• Structural Engineering and Mechanics
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• v.76 no.3
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• pp.395-412
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• 2020

In this article, the values of internal force and deformation of a curved beam under any action with the firm or elastic supports are determined by using structural matrices. The article presents the general differential formulation of a curved beam in global coordinates, which is solved in an orderly manner using simple integrals, thus obtaining the transfer matrix expression. The matrix expression of rigidity is obtained through reordering operations on the transfer notation. The support conditions, firm or elastic, provide twelve equations. The objective of this article is the construction of the algebraic system of order twenty-four, twelve transfer equations and twelve support equations, which relates the values of internal force and deformation associated with the two ends of the directrix of the curved beam. This final algebraic system, expressed in matrix form, is divided into two subsystems: twelve algebraic equations of internal force and twelve algebraic equations of deformation. The internal force and deformation values for any point in the curved beam directrix are determined from these values in the initial position. The five examples presented show how to apply the matrix procedures developed in this article, whether they are curved beams with the firm or elastic support.

• Journal of the Society of Naval Architects of Korea
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• v.56 no.1
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• pp.1-10
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• 2019

Naval ship design and related other activities can be characterized by the complexity of the interactions among products, activities, and disciplines. Such complexities often result in inferior designs, cost overrun, and late-delivery. Hence there exist tremendous interests in both improving the design process itself and optimizing the interactions among design activities. This paper looks at the complexity of designing naval ships thereby leading to the innovation of current ship design practices using design structure matrix. It can be used to induce the optimal ordering of design activities as well as identify sources of complexities. The method presented here identifies coupled design activities useful for reducing the complexity of naval ship design as well as optimally reordering design activities. This paper recommends the use of design structure matrix method suitable for numerically optimizing the concept design process of naval ship, and reducing cost and time required in designing naval ships by modeling and analyzing the design activities and engineering tasks, defined in systems engineering planning documents.

• Fibers and Polymers
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• v.4 no.3
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• pp.97-101
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• 2003

Polymer/silicate nanocomposites were prepared via two-step manufacturing process: a master batch preparation and then mixing with matrix polymer. A hybrid of PMMA and Na-MMT with exfoliated structure was first prepared by emulsion polymerization of MMA in the presence of Na-MMT. For the case that SAN24, miscible with PMMA, is used as matrix, we could prepare a nanocomposite with exfoliated structure. However, SAN31 nanocomposite shows the aggregation and/or reordering of the silicate layers due to the immiscibility between SAN31 and PMMA.

• Journal of Korean Institute of Industrial Engineers
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• v.29 no.1
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• pp.78-89
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• 2003

Ordering is performed to reduce the amount of fill-ins of the Cholesky factor of a symmetric positive definite matrix. This paper proposes a new ordering algorithm that reduces the fill-ins of the Cholesky factor iteratively by elimination tree rotations and clique separators. Elimination tree rotations have been used mainly to reorder the rows of the permuted matrix for the efficiency of storage space management or parallel processing, etc. In the proposed algorithm, however, they are repeatedly performed to reduce the fill-ins of the Cholesky factor. In addition, we presents a simple method for finding a minimal node separator between arbitrary two nodes of a chordal graph. The proposed reordering procedure using clique separators enables us to obtain another order of rows of which the number of till-ins decreases strictly.