• Journal of Ocean Engineering and Technology
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• v.19 no.5 s.66
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• pp.1-15
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• 2005

The motion behaviors including hydrodynamic interaction and mechanical coupling effects on multiple-body floating platforms are simulated by using a time domain hull/mooring/riser coupled dynamics analysis program. The objective of this study is to evaluate off-diagonal hydrodynamic interaction effects and mechanical coupling effects on tandem moored FPSO and shuttle taker motions. In the multiple-body floating platforms interaction, hydrodynamic coupling effects with waves and mechanical coupling effects through the connectors should be considered. Thus, in this study, the multiple-body platform motions are calculated by Combined Matrix Method (CMM) as well as Separated Matrix Method (SMM). The advantage of the combined matrix method is that it can include all the 6Nx6N full hydrodynamic and mechanical interaction effects among N bodies. Whereas, due to the larger matrix size, the calculation time of Combined Matrix Method (CMM) is longer than the Separated Matrix Method (SMM). On the other hand, Separated Matrix Method (SMM) cannot include the off-diagonal 6x6 hydrodynamic interaction coefficients although it can fully include mechanical interactions among N bodies. To evaluate hydrodynamic interaction and mechanical coupling effects, tandem moored FPSO and shuttle tanker is simulated by Combined Matrix Method (CMM) and Separated Matrix Method (SMM). The calculation results give a good agreement between Combined Matrix Method (CMM) and Separated Matrix Method (SMM). The results show that the Separated Matrix Method (SMM) is more efficient for tandem moored FPSO and shuttle tanker. In the numerical calculation, the hydrodynamic coefficients are calculated from a 3D diffraction/radiation panel program WAMIT, and wind and current forces are generated by using the respective coefficients given in the OCIMF data sheet.

• Journal of Korea Society of Digital Industry and Information Management
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• v.10 no.4
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• pp.53-61
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• 2014

In this paper, we proposed covariance weight matrix using SPT matrix in order to accurate target estimation. We have estimated a target using modified covariance matrix and beam steering error method. We have minimized beam steering error in order to estimation desired a target. This method obtain optimum covariance weight using modified SPT matrix. This paper of proposal method is showed good performance than general method. We updated a weight of covariance matrix using modified SPT matrix. We obtain optimum covariance matrix weight to application beam steering error method in order to beam steering toward desired target. Through simulation, we showed that compare proposal method with general method. It have improved resolution of estimation target to good performance more proposed method than general method.

• Computational Structural Engineering
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• v.10 no.1
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• pp.193-200
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• 1997

Even though there are many analysis methods of circular tanks on elastic foundation, the finite element method is widely used for that purpose. But the finite element method requires a number of memory spaces, computation time to solve large stiffness equations. In this study many the simplified methods(Analogy of Beam on Elastic Foundation, Foundation Stiffness Matrix, Finite Element Method and Transfer Matrix Method) are applied to analyze a circular tank on elastic foundation. By the given analysis methods, BEF analogy and foundation matrix method, the circular tank was transformed into the skeletonized frame structure. The frame structure was divided into several finite elements. The stiffness matrix of a finite element is related with the transfer matrix of the element. Thus, the transfer matrix of each finite element utilized the transfer matrix method to simplify the analysis of the tank. There were no significant difference in the results of two methods, the finite element method and the transfer matrix method. The transfer method applied to a circular tank on elastic foundation resulted in four simultaneous equations to solve completely.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.11
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• pp.5616-5630
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• 2019

Fully homomorphic encryption allows a third-party to perform arbitrary computation over encrypted data and is especially suitable for secure outsourced computation. This paper investigates secure outsourced computation of multiple matrix multiplication based on fully homomorphic encryption. Our work significantly improves the latest Mishra et al.'s work. We improve Mishra et al.'s matrix encoding method by introducing a column-order matrix encoding method which requires smaller parameter. This enables us to develop a binary multiplication method for multiple matrix multiplication, which multiplies pairwise two adjacent matrices in the tree structure instead of Mishra et al.'s sequential matrix multiplication from left to right. The binary multiplication method results in a logarithmic-depth circuit, thus is much more efficient than the sequential matrix multiplication method with linear-depth circuit. Experimental results show that for the product of ten 32×32 (64×64) square matrices our method takes only several thousand seconds while Mishra et al.'s method will take about tens of thousands of years which is astonishingly impractical. In addition, we further generalize our result from square matrix to non-square matrix. Experimental results show that the binary multiplication method and the classical dynamic programming method have a similar performance for ten non-square matrices multiplication.

• Structural Engineering and Mechanics
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• v.7 no.2
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• pp.203-216
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• 1999

A previously proposed finite element formulation method is refined and modified to generate a new type of elements. The method is based on selecting a set of general solution modes for element formulation. The constant strain modes and higher order modes are selected and the formulation method is designed to ensure that the element will pass the basic single element test, which in turn ensures the passage of the basic patch test. If the element is to pass the higher order patch test also, the element stiffness matrix is in general asymmetric. The element stiffness matrix depends only on a nodal displacement matrix and a nodal force matrix. A symmetric stiffness matrix can be obtained by either modifying the nodal displacement matrix or the nodal force matrix. It is shown that both modifications lead to the same new element, which is demonstrated through numerical examples to be more robust than an assumed stress hybrid element in plane stress application. The method of formulation can also be used to arrive at the conforming displacement and hybrid stress formulations. The convergence of the latter two is explained from the point of view of the proposed method.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.818-821
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• 1995

A MDOF vibration analysis of the rotor is performed using combined modeling of transfer matrix method and finite element method(FETM). The method combines the advantages of both matrix. Each rotor is modelled using transfer matrix method and treated one element or several ones. The finite element method is applied in composing a system matrix and finding roots. The method used in this is more efficient than conventional finite element method in saving calculation time and provides good results in complex MDOF rotor model.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1133-1143
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• 2009

In this work, we successfully extended dimensional differential transform method (DTM), by presenting and proving some new theorems, to solve the non-linear matrix differential Riccati equations(first and second kind of Riccati matrix differential equations). This technique provides a sequence of matrix functions which converges to the exact solution of the problem. Examples show that the method is effective.

• Nuclear Engineering and Technology
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• v.52 no.11
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• pp.2422-2430
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• 2020

In order to improve calculational efficiency of the CAPP code in the analysis of the hexagonal reactor core, we have tried to implement a refined AFEN method with transverse gradient basis functions and interface flux moments in the hexagonal geometry. The numerical scheme for the refined AFEN method adopted here is the response matrix method that uses the interface partial currents as nodal unknowns instead of the interface fluxes used in the original AFEN method. Since the response matrix method is single-node based, it has good properties such as good calculational efficiency and parallel computing affinity. Because a refined AFEN method equivalent nonlinear FDM response matrix method tried first could not provide a numerically stable solution, a direct formulation of the refined AFEN response matrix were developed. To show the numerical performance of this response matrix method against the original AFEN method, the numerical error analyses were performed for several benchmark problems including the VVER-440 LWR benchmark problem and the MHTGR-350 HTGR benchmark problem. The results showed a more than three times speedup in computing time for the LWR and HTGR benchmark problems due to good convergence and excellent calculational efficiency of the refined AFEN response matrix method.

• 전기의세계
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• v.23 no.3
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• pp.43-52
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• 1974

The matrix inversion is very inefficient for computing direct solutions of the large spare systems of linear equations that arise in many network problems as a large electrical power system. Optimally ordered triangular factorization of sparse matrices is more efficient and offers the other important computational advantages in some applications with this method. The direct solutions are computed from sparse matrix factors instead of a full inverse matrix, thereby gaining a significant advantage is speed and computer memory requirements. In this paper, it is shown that the sparse matrix method is superior to the inverse matrix method to solve the linear equations of large sparse networks. In addition, it is shown that the sparse matrix method is superior to the inverse matrix method to solve the linear equations of large sparse networks. In addition, it is shown that the solutions may be applied directly to sove the load flow in an electrical power system. The result of this study should lead to many aplications including short circuit, transient stability, network reduction, reactive optimization and others.

• Structural Engineering and Mechanics
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• v.70 no.2
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• pp.199-207
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• 2019

In this paper, a semi-analytical method will be discussed for free vibration analysis of rotating beams with variable cross sectional area. For this purpose, the rotating beam is discretized through applying the transfer matrix method and assumed the axial force is constant for each element. Then, the transfer matrix is derived based on Euler-Bernoulli's beam differential equation and applying boundary conditions. In the following, the frequencies of the rotating beam with constant and variable cross sections are determined using the transfer matrix method in several case studies. In order to eliminate numerical difficulties in the transfer matrix method, the Riccati transfer matrix is employed for high rotation speed and high modes. The results are compared with the results of the finite elements method and Rayleigh-Ritz method which show good agreement in spite of low computational cost.