• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권4호
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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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• 제40권1호
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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.

• East Asian mathematical journal
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• 제37권3호
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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.

• Smart Structures and Systems
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• 제8권4호
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• pp.343-365
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• 2011

Structural system identification (SSI) is an inverse problem of difficult solution. Currently, difficulties lie in the development of algorithms which can cater to large size problems. In this paper, a parameter estimation technique based on evolutionary strategy is presented to overcome some of the difficulties encountered in using the traditional system identification methods in terms of convergence. In this paper, a non-traditional form of system identification technique employing evolutionary algorithms is proposed. In order to improve the convergence characteristics, it is proposed to employ immune algorithms which are proved to be built with superior diversification mechanism than the conventional evolutionary algorithms and are being used for several practical complex optimisation problems. In order to reduce the number of design variables, domain decomposition methods are used, where the identification process of the entire structure is carried out in multiple stages rather than in single step. The domain decomposition based methods also help in limiting the number of sensors to be employed during dynamic testing of the structure to be identified, as the process of system identification is carried out in multiple stages. A fifteen storey framed structure, truss bridge and 40 m tall microwave tower are considered as a numerical examples to demonstrate the effectiveness of the domain decomposition based structural system identification technique using immune algorithm.

• Nuclear Engineering and Technology
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• 제52권11호
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• pp.2667-2677
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• 2020

A domain decomposition (DD) scheme for GPU-based Monte Carlo (MC) calculation which is essential for whole-core depletion is introduced within the framework of the modified history-based tracking algorithm. Since GPU-offloaded MC calculations suffer from limited memory capacity, employing DDMC is inevitable for the simulation of depleted cores which require large storage to save hundreds of newly generated isotopes. First, an automated domain decomposition algorithm named wheel clustering is devised such that each subdomain contains nearly the same number of fuel assemblies. Second, an innerouter iteration algorithm allowing overlapped computation and communication is introduced which enables boundary neutron transactions during the tracking of interior neutrons. Third, a bank update scheme which is to include the boundary sources in a way to be adequate to the peculiar data structures of the GPU-based neutron tracking algorithm is presented. The verification and demonstration of the DDMC method are done for 3D full-core problems: APR1400 fresh core and a mock-up depleted core. It is confirmed that the DDMC method performs comparably with the standard MC method, and that the domain decomposition scheme is essential to carry out full 3D MC depletion calculations with limited GPU memory capacities.

• 한국산학기술학회논문지
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• 제12권8호
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• pp.3384-3390
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• 2011

본 논문은 탄소성 구조해석을 위한 병렬유한요소해석에 필요한 영역분할법에 대해 제시하고 있다. 유한요소해석을 위한 알고리즘으로서 CG방법과 결합한 영역분할법을 이용하였다. 적용된 영역분할법은 탄소성문제를 해석하는데 직접적으로 사용되어 지며 효용성 검토를 위해 3차원 탄소성 구조문제에 적용하여 해석해 본 결과 높은 병렬효과를 발휘함을 알 수 있었다.

• 대한수학회논문집
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• 제10권3호
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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.

• 한국정보통신학회논문지
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• 제17권5호
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• pp.1049-1054
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• 2013

본 논문에서는 영역분할법을 이용한 2차원 유한차분시간영역법을 제안하였다. 영역분할법은 전체 해석구조를 분할하여 해석하는 수치해석방법으로 본 논문에서는 영역분할법 중 Schur complement 방법을 적용한 유한차분 시간영역법을 구현하고 시뮬레이션 모델로 2차원 해석구조를 설정하고 사각형의 도체에 입사하는 전자파의 산란특성을 해석하였다. 2차원 해석구조를 4개의 영역과 8개의 영역으로 각각 나누어 전자파특성을 계산하였고, 제안한 해석방법의 유효함을 입증하기 위해 일반적인 전체영역에 대한 2차원 유한차분 시간영역법의 해석결과와 비교하여 잘 일치하는 것을 확인하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제18권1호
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• pp.17-26
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• 2014

This paper presents development of an improved domain decomposition method for large scale structural problem that aims to provide high computational efficiency. In the previous researches, we developed the domain decomposition algorithm based on augmented Lagrangian formulation and proved numerical efficiency under both serial and parallel computing environment. In this paper, new computational analysis by the proposed domain decomposition method is performed. For this purpose, reduction in computational time achieved by the proposed algorithm is compared with that obtained by the dual-primal FETI method under serial computing condition. It is found that the proposed methods significantly accelerate the computational speed for a linear structural problem.

• 한국정보통신학회논문지
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• 제5권7호
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• pp.1346-1353
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• 2001

본 논문에서는 2차원 분모분리형 디지털 필터의 선계에 대한 알고리즘을 제안한다. 제안된 알고리즘은 진폭 특성과 위상특성으로 주어진 2차원 디지털 필터의 주파수 영역 설계명세조건을 특이치 분해를 이용하여 1차원 디지털 필터의 설계명세조건으로 분해한다. 따라서, 2차원 디지털 필터 설계문제는 1차원 디지털 필터의 설계 문제로 귀착되며 이는 계산적으로 유효하며 수치적으로 안정한 설계법으로 고려되며 설계 예로부터 유효성을 확인한다.