• East Asian mathematical journal
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• v.39 no.1
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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.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1998.03a
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• pp.246-249
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• 1998

In the present study, domain decomposition using the substructuring method is developed for the computational efficiency of the finite element analysis of metal forming processes. In order to avoid calculation of an inverse matrix during the substructuring procedure, the modified Cholesky decomposition method is implemented. As obtaining the data independence by the substructuring method, the program is easily parallelized using the Parallel Virtual Machine(PVM) library on a workstation cluster connected on networks. A numerical example for a simple upsetting is calculated and the speed-up ratio with respect to various domain decompositions and number of processors. Comparing the results, it is concluded that the improvement of performance is obtained through the proposed method.

• Korea-Australia Rheology Journal
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• v.21 no.1
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• pp.1-12
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• 2009

This paper reports the suitability of a domain decomposition technique for the hybrid simulation of dilute polymer solution flows using Eulerian Brownian dynamics and Radial Basis Function Networks (RBFN) based methods. The Brownian Configuration Fields (BCF) and RBFN method incorporates the features of the BCF scheme (which render both closed form constitutive equations and a particle tracking process unnecessary) and a mesh-less method (which eliminates element-based discretisation of domains). However, when dealing with large scale problems, there appear several difficulties: the high computational time associated with the Stochastic Simulation Technique (SST), and the ill-condition of the system matrix associated with the RBFN. One way to overcome these disadvantages is to use parallel domain decomposition (DD) techniques. This approach makes the BCF-RBFN method more suitable for large scale problems.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.1
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• pp.55-64
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• 2023

In this paper, we propose a two-level overlapping domain decomposition preconditioner for three dimensional vector field problems posed in H(div). We introduce a new coarse component, which reduces the computational complexity, associated with the coarse vertices. Numerical experiments are also presented.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.1
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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.

• Korean Journal of Mathematics
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• v.31 no.4
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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.

• Nuclear Engineering and Technology
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• v.52 no.11
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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.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.11 s.188
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• pp.93-102
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• 2006

In this study an advanced domain decomposition method is suggested in order to construct surface models from very large amount of points. In this method the spatial domain of interest that is occupied by the input set of points is divided in repetitive manner. First, the space is divided into smaller domains where the problem can be solved independently. Then each subdomain is again divided into much smaller domains where the problem can be solved locally. These local solutions of subdivided domains are blended together to obtain a solution of each subdomain using partition of unity function. Then the solutions of subdomains are merged together in order to construct whole surface model. The suggested methods are conceptually very simple and easy to implement. Since RDDM(Repetitive Domain Decomposition Method) is effective in the computation time and memory consumption, the present study is capable of providing a fast and accurate reconstructions of complex shapes from large amount of point data containing millions of points. The effectiveness and validity of the suggested methods are demonstrated by performing numerical experiments for the various types of point data.

• Transactions of Materials Processing
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• v.7 no.5
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• pp.474-480
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• 1998

In the present study a domain decomposition scheme using the substructuring method is developed for the computational efficiency of the finite element analysis of metal forming processes. in order to avoid calculation of an inverse matrix during the substructuring procedure, the modified Cholesky decomposition method is implemented. As obtaining the data independence by the substructuring method the program is easily paralleized using the Parallel Virtual machine(PVM) library on a work-station cluster connected on networks. A numerical example for a simple upsetting is calculated and the speed-up ratio with respect to various number of subdomains and number of processors. The efficiency of the parallel computation is discussed by comparing the results.

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