• East Asian mathematical journal
• /
• v.37 no.3
• /
• pp.295-305
• /
• 2021

In this paper, we analyze the efficiency of a domain decomposition method for the two-dimensional telegraph equations. We formulate the theoretical spectral radius of the iteration matrix generated by the domain decomposition method, because the rate of convergence of an iterative algorithm depends on the spectral radius of the iteration matrix. The theoretical spectral radius is confirmed by the experimental one using MATLAB. Speedup and operation ratio of the domain decomposition method are also compared as the two measurements of the efficiency of the method. Numerical results support the high efficiency of the domain decomposition method.

• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.4
• /
• pp.409-420
• /
• 2019

In this article, we discussed semi-analytical approximated methods for solving mixed Volterra-Fredholm integro-differential equations, namely: Adomian decomposition method and modified Adomian decomposition method. Moreover, we prove the uniqueness results and convergence of the techniques. Finally, an example is included to demonstrate the validity and applicability of the proposed techniques.

• Journal of the Korean Society for Railway
• /
• v.5 no.3
• /
• pp.174-180
• /
• 2002

In multibody dynamics, DAE(Differential Algebraic Equations) that combine differential equations of motion and kinematic constraint equations should be solved. To solve these equations, either coordinate partitioning method or constraint stabilization method is commonly used. The most typical coordinate partitioning methods are LU decomposition, QR decomposition, and SVD(singular value decomposition). The objective of this research is to suggest a hybrid coordinate partitioning method in the dynamic analysis of multibody systems containing singular configurations. Two coordinate partitioning methods, i.e. LU decomposition and QR decomposition for constrained multibody systems, are combined for a new hybrid coordinate partitioning method. The proposed hybrid method reduces the simulation time while keeping accuracy of the solution.

• Journal of the Korean Society of Industry Convergence
• /
• v.4 no.1
• /
• pp.87-94
• /
• 2001

In multibody dynamics, differential and algebraic equations which can satisfy both equation of motion and kinematic constraint equation should be solved. To solve this equation, coordinate partitioning method and constraint stabilization method are commonly used. The coordinate partitioning method divides the coordinate into independent and dependent coordinates. The most typical coordinate partitioning method arc LU decomposition, QR decomposition, projection method and SVD(sigular value decomposition).The objective of this research is to find a efficient coordinate partitioning method in flexible multibody systems and a hybrid decomposition algorithm which employs both LU and projection methods is proposed. The accuracy of the solution algorithm is checked with a slider-crank mechanism.

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

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

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.21 no.8
• /
• pp.1311-1321
• /
• 1997

In multibody dynamics, differential and algebraic equations which can satisfy both equation of motion and kinematic constraint equation should be solved. To solve these equations, coordinate partitioning method and constraint stabilization method are commonly used. In the coordinate partitioning method, the coordinates are divided into independent and dependent and coordinates. The most typical coordinate partitioning method are LU decomposition, QR decomposition, and SVD (singular value decomposition). The objective of this research is to find an efficient coordinate partitioning method in the dynamic analysis of flexible multibody systems. Comparing two coordinate partitioning methods, i.e. LU and QR decomposition in the flexible multibody systems, a new hybrid coordinate partitioning method is suggested for the flexible multibody analysis.

• Journal of the Korean Institute of Telematics and Electronics B
• /
• v.31B no.5
• /
• pp.50-57
• /
• 1994

In the non-destructive evaluation techniques using ultrasonic signal, backscattering noise from grain interface decreases the SNR of received signal. In this paper, SSP(split-spectrum processing) based on the constant FBR decomposition method has been applied to enhance the SNR. This algorithm helps to find optimal parameters of filter bank through a simple theory and has an advantage that reduce the signal processing time compared with the conventional constant bandwidth decomposition method. In this experiment, the 304 stainless steel sample is heat-treated and received ultrasonic signal is processed by SSP using the constand bandwidth decomposition method and the constand FBR decomposition method enhanced the SNR by 1.4 dB and reduced the required number of filters by 4 compared with the constant bandwidth decomposition method.

• Transactions on Electrical and Electronic Materials
• /
• v.1 no.2
• /
• pp.18-22
• /
• 2000

An ozone condensation system is evaluated from the viewpoint of an ozone supplier fro oxide thin film growth. Ozone is condensed by the adsorption method and its concentration is analyzed using the thermal decomposition method, The concentration of ozone exceeds 90mol% and ozone is supplied for a sufficiently long time to grow oxide thin films. Investigation of the ozone decomposition rate demonstrates that ozone can be transferred into the film growth chamber without marked decomposition. The ozone concentration is also evaluated using a quardrupole mass analyzer and the accuracy of this method is compared with the results of the thermal decomposition method.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.18 no.4
• /
• pp.305-316
• /
• 2014

The Hodge-Helmholtz decomposition splits a vector field into the unique sum of a divergence-free vector field (solenoidal part) and a gradient field (irrotational part). In a bounded domain, a boundary condition needs to be supplied to the decomposition. The decomposition with the non-penetration boundary condition is equivalent to solving the Poisson equation with the Neumann boundary condition. The Gibou-Min method is an application of the Poisson solver by Purvis and Burkhalter to the decomposition. Using the $L^2$-orthogonality between the error vector and the consistency, the convergence for approximating the divergence-free vector field was recently proved to be $O(h^{1.5})$ with step size h. In this work, we analyze the convergence of the irrotattional in the decomposition. To the end, we introduce a discrete version of the Poincare inequality, which leads to a proof of the O(h) convergence for the scalar variable of the gradient field in a domain with general intersection property.