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

• 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.

• East Asian mathematical journal
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• v.40 no.1
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• pp.109-118
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• 2024

This paper proposes a numerical method based on domain decomposition to find approximate solutions for one-dimensional convection-diffusion equations with Neumann boundary conditions. First, the equations are transformed into convection-diffusion equations with Dirichlet conditions. Second, the author introduces the Prediction/Correction Domain Decomposition (PCDD) method and estimates errors for the interface prediction scheme, interior scheme, and correction scheme using known error estimations. Finally, the author compares the PCDD algorithm with the fully explicit scheme (FES) and the fully implicit scheme (FIS) using three examples. In comparison to FES and FIS, the proposed PCDD algorithm demonstrates good results.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.735-750
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• 1995

We present a domain decomposition algorithm for solving large sparse linear systems of equations arising from queuing networks. Such techniques are attractive since the problems in subdomains can be solved independently by parallel processors. Many of the methods proposed so far use some form of the preconditioned conjugate gradient method to deal with one large interface problem between subdomains. However, in this paper, we propose a "nested" domain decomposition method where the subsystems governing the interfaces are small enough so that they are easily solvable by direct methods on machines with many parallel processors. Convergence of the algorithms is also shown.lso shown.

• International Journal of Precision Engineering and Manufacturing
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• v.8 no.1
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• pp.3-10
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• 2007

A new approach based on implicit surface interpolation combined with domain decomposition is proposed for filling complex-shaped holes in a large polygon model, A surface was constructed by creating a smooth implicit surface from an incomplete polygon model through which the actual surface would pass. The implicit surface was defined by a radial basis function, which is a continuous scalar-value function over the domain $R^{3}$. The generated surface consisted of the set of all points at which this scalar function is zero. It was created by placing zero-valued constraints at the vertices of the polygon model. The well-known domain decomposition method was used to treat the large polygon model. The global domain of interest was divided into smaller domains in which the problem could be solved locally. The LU decomposition method was used to solve the set of small local problems; the local solutions were then combined using weighting coefficients to obtain a global solution. The validity of this new approach was demonstrated by using it to fill various holes in large and complex polygon models with arbitrary topologies.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.12 no.8
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• pp.3384-3390
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• 2011

This paper describes a domain decomposition method of parallel finite element analysis for elasto-plastic structural problems. As a parallel numeral algorithm for the finite element analysis, the authors have utilized the domain decomposition method combined with an iterative solver such as the conjugate gradient method. Here the domain decomposition method algorithm was applied directly to elasto-plastic problem. The present system was successfully applied to three-dimensional elasto-plastic structural problems.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.1 s.178
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• pp.174-184
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• 2006

In order to fill the holes with complex shapes in the large polygon model, a new approach which is based on the implicit surface interpolation method combined with domain decomposition method is presented. In the present study, a surface is constructed by creating smooth implicit surface from the incomplete polygon model through which the surface should pass. In the method an implicit surface is defined by a radial basis function, a continuous scalar-valued function over the domain $R^3$ The generated surface is the set of all points at which this scalar function takes on the value zero and is created by placing zero-valued constraints at the vertices of the polygon model. In this paper the well-known domain decomposition method is used in order to treat the large polygon model. The global domain of interest is divided into smaller domains where the problem can be solved locally. LU decomposition method is used to solve a set of small local problems and their local solutions are combined together using the weighting coefficients to obtain a global solution. In order to show the validity of the present study, various hole fillings are carried out fur the large and complex polygon model of arbitrary topology.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.523-538
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• 1999

A new preconditioning method is investigated to reduce the roundoff error in computing derivatives using Chebyshev col-location methods(CCM). Using this preconditioning causes ration of roundoff error of preconditioning method and CCm becomes small when N gets large. Also for accuracy enhancement of differentiation we use a domain decomposition approach. Error analysis shows that for this domain decomposition method error reduces proportional to the length of subintervals. Numerical results show that using domain decomposition and preconditioning simultaneously gives super accu-rate approximate values for first derivative of the function and good approximate values for moderately high derivatives.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.1
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• pp.35-44
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• 2009

This paper describes an application of domain decomposition method for parallel finite element analysis which is required to large scale 3D structural analysis. A parallel finite element method system which adopts a domain decomposition method is developed. Node is generated if its distance from existing node points is similar to the node spacing function at the point. The node spacing function is well controlled by the fuzzy knowledge processing. The Delaunay triangulation method is introduced as a basic tool for element generation. Domain decomposition method using automatic mesh generation system holds great benefits for 3D analyses. Aa parallel numerical algorithm for the finite element analyses, domain decomposition method was combined with an iterative solver, i.e. the conjugate gradient(CG) method where a whole analysis domain is fictitiously divided into a number of subdomains without overlapping. Practical performance of the present system are demonstrated through several examples.