• Korean Journal of Mathematics
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• 제31권4호
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• pp.419-431
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• 2023

In this paper, we propose an iterative method for a symmetric interior penalty Galerkin method for heterogeneous elliptic problems. The iterative method consists mainly of two parts based on a non-overlapping domain decomposition approach. One is an intermediate preconditioner constructed by understanding the properties of the discontinuous finite element functions and the other is a preconditioning related to the dual-primal finite element tearing and interconnecting (FETI-DP) methodology. Numerical results for the proposed method are presented, which demonstrate the performance of the iterative method in terms of various parameters associated with the elliptic model problem, the finite element discretization, and non-overlapping subdomain decomposition.

• East Asian mathematical journal
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• 제39권1호
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• pp.75-85
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• 2023

In this paper, a non-overlapping rectangular domain decomposition method is presented in order to numerically solve two-dimensional telegraph equations. The method is unconditionally stable and efficient. Spectral radius of the iteration matrix and convergence rate of the method are provided theoretically and confirmed numerically by MATLAB. Numerical experiments of examples are compared with several methods.

• 대한수학회지
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• 제57권5호
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• pp.1267-1286
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• 2020

We pay attention to a coupled problem by a penalty term which is induced from non-overlapping domain decomposition methods based on augmented Lagrangian methodology. The coupled problem is composed by two parts mainly; one is a problem associated with local problems in non-overlapping subdomains and the other is a coupled part over all subdomains due to the penalty term. For the speedup of iterative solvers for the coupled problem, we propose two different types of preconditioners: a block-diagonal preconditioner and an additive Schwarz preconditioner as overlapping domain decomposition methods. We analyze the coupled problem and the preconditioned problems in terms of their condition numbers. Finally we present numerical results which show the performance of the proposed methods.

• 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.

• 한국전산구조공학회논문집
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• 제26권4호
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• pp.301-308
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• 2013

본 논문에서는 새로운 비중첩 영역 분할 기법을 바탕으로 한 병렬해석의 정확도 분석이 수행된다. Tak 등(2013)에 의해 제안된 이 방법에서 분할된 하위도메인들은 서로 중첩되지 않으며 계면요소(interfacial element)라 불리는 가상연결유한요소를 통해 서로 간의 관계가 결정된다. 이 접근법의 주요 장점은 영역 분할시 floating 도메인에서 발생할 수 있는 특이강성행렬(singular stiffness matrix)을 계면요소의 결합을 이용하여 가역행렬(invertible matrix)로 변환할 수 있다는 것과 기존의 FETI법에 비하여 해석시간과 스토리지(storage) 사용을 줄일 수 있다는 것이다. 반면에 3개 이상의 하위도메인들이 한 점에서 연결되는 경우를 의미하는 cross point에서는 해석의 정확도가 저하되는 경향이 나타났다. 따라서 본 논문에서는 새로운 비중첩 영역 분할기법에 대해 다양한 영역분할의 경우에 따라 발생하는 하나의 cross point에 접촉하는 하위도메인의 개수에 따른 정확도 분석이 수행되고 정확도가 저하되는 원인분석 및 대책이 논의된다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제5권2호
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• pp.71-99
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• 2001

The model and analytical method for solving the problem of coupled fluid flow in the reservoir/well system is presented. The 3-D drainage area is composed of three connected media: the tubing, the annuli as a super conducting collector, and the reservoir itself. To couple these three types of fluid flows a non-overlapping Dirichlet-Neumann domain decomposition method is developed. The method allows us to apply an analytical hybrid simulator for accurate evaluation of the impact of main geometrical and hydrodynamic parameters of the 3-D system on the pressure drop along the horizontal well and its production index.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제24권2호
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• pp.199-214
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• 2020

This paper describes the development of a parallel computational algorithm based on the finite element tearing and interconnecting (FETI) method that uses a local Lagrange multiplier. In this approach, structural computational domain is decomposed into non-overlapping sub-domains using local Lagrange multiplier. The local Lagrange multipliers are imposed at interconnecting nodes. 8-node solid element using extra shape function is adopted by using the representative volume element (RVE). The parallel computational algorithm is further established based on message passing interface (MPI). Finally, the present FETI-local approach is implemented on parallel hardware and shows improved performance.

• Journal of Information Processing Systems
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• 제12권4호
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• pp.765-778
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• 2016

In watermarking schemes, the discrete wavelet transform (DWT) is broadly used because its frequency component separation is very useful. Moreover, LU decomposition has little influence on the visual quality of the watermark. Hence, in this paper, a novel blind watermark algorithm is presented based on LU transform and DWT for the copyright protection of digital images. In this algorithm, the color host image is first performed with DWT. Then, the horizontal and vertical diagonal high frequency components are extracted from the wavelet domain, and the sub-images are divided into $4{\times}4$ non-overlapping image blocks. Next, each sub-block is performed with LU decomposition. Finally, the color image watermark is transformed by Arnold permutation, and then it is inserted into the upper triangular matrix. The experimental results imply that this algorithm has good features of invisibility and it is robust against different attacks to a certain degree, such as contrast adjustment, JPEG compression, salt and pepper noise, cropping, and Gaussian noise.

• Smart Structures and Systems
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• 제17권2호
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• pp.209-230
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• 2016

The Canton Tower is a high-rise slender structure with a height of 610 m. A structural health monitoring system has been instrumented on the structure, by which data is continuously monitored. This paper presents an investigation on the identified modal properties of the Canton Tower using ambient vibration data collected during a whole day (24 hours). A recently developed Fast Bayesian FFT method is utilized for operational modal analysis on the basis of the measured acceleration data. The approach views modal identification as an inference problem where probability is used as a measure for the relative plausibility of outcomes given a model of the structure and measured data. Focusing on the first several modes, the modal properties of this supertall slender structure are identified on non-overlapping time windows during the whole day under normal wind speed. With the identified modal parameters and the associated posterior uncertainty, the distribution of the modal parameters in the future is predicted and assessed. By defining the modal root-mean-square value in terms of the power spectral density of modal force identified, the identified natural frequencies and damping ratios versus the vibration amplitude are investigated with the associated posterior uncertainty considered. Meanwhile, the correlations between modal parameters and temperature, modal parameters and wind speed are studied. For comparison purpose, the frequency domain decomposition (FDD) method is also utilized to identify the modal parameters. The identified results obtained by the Bayesian method, the FDD method and a finite element model are compared and discussed.