• Nuclear Engineering and Technology
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• v.48 no.3
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• pp.635-641
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• 2016

Because of prohibitive data storage requirements in large-scale simulations, the memory problem is an obstacle for Monte Carlo (MC) codes in accomplishing pin-wise three-dimensional (3D) full-core calculations, particularly for whole-core depletion analyses. Various kinds of data are evaluated and quantificational total memory requirements are analyzed based on the Reactor Monte Carlo (RMC) code, showing that tally data, material data, and isotope densities in depletion are three major parts of memory storage. The domain decomposition method is investigated as a means of saving memory, by dividing spatial geometry into domains that are simulated separately by parallel processors. For the validity of particle tracking during transport simulations, particles need to be communicated between domains. In consideration of efficiency, an asynchronous particle communication algorithm is designed and implemented. Furthermore, we couple the domain decomposition method with MC burnup process, under a strategy of utilizing consistent domain partition in both transport and depletion modules. A numerical test of 3D full-core burnup calculations is carried out, indicating that the RMC code, with the domain decomposition method, is capable of pin-wise full-core burnup calculations with millions of depletion regions.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2009.04a
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• pp.534-535
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• 2009

This paper deals with BEM analysis of transient elastodynamic problems using domain decomposition method and particular integrals. The particular method is used to approximate the acceleration term in the governing equation. The domain decomposition method is examined to consider multi-region problems. The domain of the original problem is subdivided into sub-regions, which are modeled by the particular integral BEM. The iterative coupling employing Schwarz algorithm is used for the successive update of the interface boundary conditions until convergence is achieved. The numerical results, compared with those by ABAQUS, demonstrate the validity of the present formulation.

• Transactions of Materials Processing
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• v.8 no.3
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• pp.284-293
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• 1999

The rigid-plastic finite element analysis requires a large amount of computation time due to its non-linearity. For economic computation, mismatching refinement, and efficient domain decomposition method with different mesh density for each sub domain, is developed. A modified velocity alternating scheme for the interface treatment is proposed in order to obtain good convergence and accuracy. As a numerical example, the axisymmetric extrusion process is analyzed. The results are discussed for the various velocity update schemes form the viewpoint of convergence and accuracy. The three-dimen-sional extrusion process with rectangular section is analyzed in order to verify the effectiveness of the proposed method. Comparing the results with those of the conventional method of full region analysis, the accuracy and the computational efficiency of the proposed method are then discussed.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.471-474
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• 2007

A domain/boundary decomposition technique is applied to carry out efficient finite element analyses of 3-D contact problems. Appropriate penalty functions are selected for connecting an interface and contact interfaces with neighboring subdomains that satisfy continuity constraints. As a consequence, all the effective stiffness matrices have positive definiteness, and computational efficiency can be improved to a considerable degree. If necessary, any complex-shaped 3-D domain can be divided into several simple-shaped subdomains without considering the conformity of meshes along the interface. With a set of numerical examples, the basic characteristics of computational efficiency are investigated carefully.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.475-484
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• 2023

Let R be a commutative ring with identity. In this paper, we characterize the prime submodules of a free R-module F of finite rank with at most n generators, when R is a GCD domain. Also, we show that if R is a Bézout domain, then every prime submodule with n generators is the row space of a prime matrix. Finally, we study the existence of primary decomposition of a submodule of F over a Bézout domain and characterize the minimal primary decomposition of this submodule.

• Journal of the Korean GEO-environmental Society
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• v.25 no.4
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• pp.21-28
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• 2024

In this study, a polyhedral domain decomposition method for Smoothed Particle Hydrodynamics (SPH) analysis is introduced. SPH which is one of meshless methods is a numerical analysis method for fluid flow simulation. It can be useful for analyzing fluidic soil or fluid-structure interaction problems. SPH is a particle-based method, where increased particle count generally improves accuracy but diminishes numerical efficiency. To enhance numerical efficiency, parallel processing algorithms are commonly employed with the Cartesian coordinate-based domain decomposition method. However, for parallel analysis of complex geometric shapes or fluidic problems under dynamic boundary conditions, the Cartesian coordinate-based domain decomposition method may not be suitable. The introduced polyhedral domain decomposition technique offers advantages in enhancing parallel efficiency in such problems. It allows partitioning into various forms of 3D polyhedral elements to better fit the problem. Physical properties of SPH particles are calculated using information from neighboring particles within the smoothing length. Methods for sharing particle information physically separable at partitioning and sharing information at cross-points where parallel efficiency might diminish are presented. Through numerical analysis examples, the proposed method's parallel efficiency approached 95% for up to 12 cores. However, as the number of cores is increased, parallel efficiency is decreased due to increased information sharing among cores.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.2
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• pp.153-161
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• 2009

A domain/boundary decomposition method is applied for efficient analyses of thermo-elasto-viscoplastic damage and contact problems under the assumption of infinitesimal deformation. For the decomposition of a whole domain and contact boundaries, all the equality constraints on the interface and contact interfaces are restated with simple penalty functional. Therefore, the non-linearity of the problem is localized within finite element matrices in a few subdomains and on contact interfaces. By setting up suitable solution algorithms, the computational efficiency can be improved considerably. The general tendency of the computational efficiency is illustrated with some numerical experiments.

• Journal of Mechanical Science and Technology
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• v.19 no.11
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• pp.2007-2015
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• 2005

A large-scale analysis to evaluate complex material and structural behaviors is one of interesting topic in diverse engineering and scientific fields. Also, the utilization of massively parallel processors has been a recent trend of high performance computing. The objective of this paper is to introduce a parallel process system which consists of general purpose finite element analysis solver as well as parallelized PC cluster. The later was constructed using eight processing elements and the former was developed adopting both hierarchical domain decomposition method and balancing domain decomposition method. Then, to verify the efficiency of the established system, it was applied for structural analysis of steam generator in nuclear power plant. Since the prototypal evaluation results agreed well to the corresponding reference solutions it is believed that, after reinforcement of PC cluster by increasing number of processing elements, the promising parallel process system can be utilized as a useful tool for advanced structural integrity evaluation.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.27-44
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• 2001

A fast Poisson solver on irregular domains, based on bound-ary methods, is presented. The harmonic polynomial approximation of the solution of the associated homogeneous problem provides a good practical boundary method which allows a trivial parallel processing for solution evaluation or straightfoward computations of the interface values for domain decomposition/embedding. AMS Mathematics Subject Classification : 65N35, 65N55, 65Y05.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.5 no.7
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• pp.1346-1353
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• 2001

This paper presents an algorithm for the design of 2 dimension separable denominator digital filter(SDDF). The proposed algorithm is based on the reduced dimensional decomposition not only 2 dimension SDDF's but also of given 2 dimension specification. The frequency domain design of 2 dimension separable denominator digital filters based on the reduced dimensional decomposition can be realized when the given 2 dimension frequency specification are optimally decomposed into a pair of 1 dimension digital filter specification via singular value decomposition. the algorithm is computationally efficient and numerically stable. In case of the low pass filter, the approximation error of the proposed design algorithm is $e_{m}$=5.17, $e_{r1}$ =8.78, $e_{r2}$=7.34, while in case of band pass filter, the approximation error is $e_{m}$=13.00, $e_{r1}$=62.76, $e_{r2}$=62.7676.7676