• 충청수학회지
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• 제10권1호
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• pp.147-159
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• 1997

It is important to solve the large sparse linear system appeared in many application field such as $AA^Ty={\beta}$ efficiently. In solving this linear system, the sparse solver using the splitting method for the relatively dense column is experimentally better than the direct solver using the Cholesky method.

• Structural Engineering and Mechanics
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• 제45권5호
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• pp.613-629
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• 2013

In this article we will present a method to directly evaluate the critical point of a non-linear system by using the solution of a polynomial eigenvalue approximation as a starting point for an iterative non-linear system solver. This method will be used to evaluate out-of-plane buckling properties of truss structures for which the lateral displacement of the upper chord has been prevented. The aim is to assess for a number of example structures whether or not the linearized eigenvalue solution gives a relevant starting point for an iterative non-linear system solver in order to find the minimum positive critical load.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2010년 춘계학술대회논문집
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• pp.397-403
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• 2010

The Immersed boundary method(IBM) is one of CFD techniques which can simulate flow field around complex objectives using simple Cartesian grid system. In the previous studies the IBM has mostly been implemented to fractional step method based Navier-Stokes solvers. In these cases, pressure buildup near IB was found to occur when linear interpolation and stadard mass conservation is used and the interpolation scheme became complicated when higher order of interpolation is adopted. In this study, we implement the IBM to an incompressible Navier-Stokes solver which uses SIMPLE algorithm. Bi-linear and quadratic interpolation equations were formulated by using only geometric information of boundary to reconstruct velocities near IB. Flow around 2D circular cylinder at Re=40 and 100 was solved by using these formulations. It was found that the pressure buildup was not observed even when the bi-linear interpolation was adopted. The use of quadratic interpolation made the predicted aerodynamic forces in good agreement with those of previous studies.

• Nuclear Engineering and Technology
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• 제49권6호
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• pp.1125-1134
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• 2017

In this paper, we present a new multilevel in space and energy diffusion (MSED) method for solving multigroup diffusion eigenvalue problems. The MSED method can be described as a PI scheme with three additional features: (1) a grey (one-group) diffusion equation used to efficiently converge the fission source and eigenvalue, (2) a space-dependent Wielandt shift technique used to reduce the number of PIs required, and (3) a multigrid-in-space linear solver for the linear solves required by each PI step. In MSED, the convergence of the solution of the multigroup diffusion eigenvalue problem is accelerated by performing work on lower-order equations with only one group and/or coarser spatial grids. Results from several Fourier analyses and a one-dimensional test code are provided to verify the efficiency of the MSED method and to justify the incorporation of the grey diffusion equation and the multigrid linear solver. These results highlight the potential efficiency of the MSED method as a solver for multidimensional multigroup diffusion eigenvalue problems, and they serve as a proof of principle for future work. Our ultimate goal is to implement the MSED method as an efficient solver for the two-dimensional/three-dimensional coarse mesh finite difference diffusion system in the Michigan parallel characteristics transport code. The work in this paper represents a necessary step towards that goal.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1988년도 전기.전자공학 학술대회 논문집
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• pp.666-668
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• 1988

A new tridiagonal Toeplitz linear system (TTLS) solver is proposed. The solver decomposes a strictly diagonally dominant TTLS equation into a number of subsystems using a limit convergent of an analytic solution of a continued fraction. Subsystem equations can be solved employing a modified Gaussian elimination method. The solver fully exploits parallelism. Optimized operational environment for the algorithm is discussed.

• 방사성폐기물학회지
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• 제21권1호
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• pp.165-173
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• 2023

Various linear system solvers with multi-physics analysis schemes are compared focusing on the near-field region considering thermal-hydraulic-chemical (THC) coupled multi-physics phenomena. APro, developed at KAERI for total system performance assessment (TSPA), performs a finite element analysis with COMSOL, for which the various combinations of linear system solvers and multi-physics analysis schemes should to be compared. The KBS-3 type disposal system proposed by Sweden is set as the target system and the near-field region, which accounts for most of the computational burden is considered. For comparison of numerical analysis methods, the computing time and memory requirement are the main concerns and thus the simulation time is set up to one year. With a single deposition hole problem, PARDISO and GMRES-SSOR are selected as representative direct and iterative solvers respectively. The performance of representative linear system solvers is then examined through a problem with an increasing number of deposition holes and the GMRES-SSOR solver with a segregated scheme shows the best performance with respect to the computing time and memory requirement. The results of the comparative analysis are expected to provide a good guideline to choose better numerical analysis methods for TSPA.

• 인터넷정보학회논문지
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• 제6권6호
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• pp.23-34
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• 2005

대규모 병렬 연산에 있어서, 계산 노드 혹은 통신 네트워크의 장애는 연산 실패로 끝나 계산자원이 낭비된다. 이를 해결하는 무정지형 MPI 라이브러리들이 제안되어 있으나 이들은 MPI 표준을 따르지 않아 이식성의 문제가 있다. 본 논문에서는 응용 프로그램의 수준에서 비동기 연산과 표준 MPI 함수만 사용하여 이식성의 문제를 해결하고 장애 복구 메커니즘을 단순화하며 수렴속도를 높이는 무정지형 선형 시스템의 해법을 제안한다.

• 정보처리학회논문지A
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• 제12A권5호
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• pp.421-426
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• 2005

대규모 병렬 연산에 있어서, 계산 노드 혹은 이들을 연결한 통신 네트워크의 장애는 연산 실패로 끝나며, 소중한 계산 시간이 낭비된다. 그러나 현재의 MPI 표준은 이에 대한 대안을 제시하지 않고 있다. 본 논문에서는, 비표준의 무정지형 MPI 라이브러리가 아닌 MPI 표준 함수들만을 사용하여, MPMD 방식의 비동기 연산을 도입한 응용 수준의 무정지형 선형 시스템의 해법을 제안한다.

• Journal of applied mathematics & informatics
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• 제6권1호
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• pp.65-78
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• 1999

We present a fast/parallel Poisson solver on disks, based on efficient evaluation of the exact solution given by the Newtonian potential and the Poisson integral. Derived from an integral formula-tion it is more accurate and simpler in parallel implementation and in upgrading to a higher order algorithm than an algorithm which solves the linear system obtained from a differential formulation.

• 대한수학회논문집
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• 제32권1호
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• pp.215-224
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• 2017

In this paper, we propose a method of order two for the computation of positive solutions to a boundary value problem of the linear beam equation. The method is based on the Power method for the eigenvector associated with the dominant eigenvalue and the Crout-like factorization algorithm for the banded system of linear equations. It is extremely fast due to the linear complexity of the linear system solver. Numerical result of a test problem is included.