• Structural Engineering and Mechanics
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• v.14 no.1
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• pp.57-70
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• 2002

This work presents an iterative mesh partitioning approach to improve the efficiency of parallel substructure finite element computations. The proposed approach employs an iterative strategy with a set of empirical rules derived from the results of numerical experiments on a number of different finite element meshes. The proposed approach also utilizes state-of-the-art partitioning techniques in its iterative partitioning kernel, a cost function to estimate the computational cost of each submesh, and a mechanism that adjusts element weights to redistribute elements among submeshes during iterative partitioning to partition a mesh into submeshes (or substructures) with balanced computational workloads. In addition, actual parallel finite element structural analyses on several test examples are presented to demonstrate the effectiveness of the approach proposed herein. The results show that the proposed approach can effectively improve the efficiency of parallel substructure finite element computations.

• 한국전산유체공학회:학술대회논문집
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• 2006.05a
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• pp.21-26
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• 2006

A large-scale finite element simulation and modeling method is presented for environmental flows in urban area. Parallel stabilized finite element method based on domain decomposition method is employed for the numerical simulation. Several GIS and CAD data are used for the preparation of the shape model for landform and urban structures. The present method Is applied to the simulation of flood flow and wind flow In urban area. The present method is shown to be a useful planning and design tool for the natural disasters and the change of environments in urban area.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.1
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• pp.40-45
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• 2008

This paper presents an optimal design of a permanent magnet actuator(PMA) using a parallel genetic algorithm. Dynamic characteristics of permanent magnet actuator model are analyzed by coupled electromagnetic-mechanical finite element method. Dynamic characteristics of PMA such as holding force, operating time, and peak current are obtained by no load test and compared with the analyzed results by coupled finite element method. The permanent magnet actuator model is optimized using a parallel genetic algorithm. Some design parameters of vertical length of permanent magnet, horizontal length of plunger, and depth of permanent magnet actuator are predefined for an optimal design of permanent magnet actuator model. Furthermore dynamic characteristics of the optimized permanent magnet actuator model are analyzed by coupled finite element method. A displacement of plunger, flowing current of the coil, force of plunger, and velocity of plunger of the optimized permanent magnet actuator model are compared with the results of a primary permanent magnet actuator model.

• Proceedings of the KSME Conference
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• 2008.11b
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• pp.2558-2561
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• 2008

In the present study, a parallel Taylor-Galerkin/level set based two-phase flow code was developed using finite element discretization and domain decomposition method based on MPI (Message Passing Interface). The proposed method can be utilized for the analysis of a large scale free surface problem in a complex geometry due to the feature of FEM and domain decomposition method. Four-step fractional step method was used for the solution of the incompressible Navier-Stokes equations and Taylor-Galerkin method was adopted for the discretization of hyperbolic type redistancing and advection equations. A Parallel ILU(0) type preconditioner was chosen to accelerate the convergence of a conjugate gradient type iterative solvers. From the present parallel numerical experiments, it has been shown that the proposed method is applicable to the simulation of large scale free surface flows.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.2
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• pp.69-79
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• 2008

Multigrid methods finite element/finite volume methods and their convergence properties are reviewed in a general setting. Some early theoretical results in simple finite element methods in variational setting method are given and extension to nonnested-noninherited forms are presented. Finally, the parallel theory for nonconforming element[13] and for cell centered finite difference methods [15, 23] are discussed.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1411-1429
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• 2016

We consider the nite volume element method for elliptic problems using isoparametric bilinear elements on quadrilateral meshes. A gradient recovery method is presented by using the patch interpolation technique. Based on some superclose estimates, we prove that the recovered gradient $R({\nabla}u_h)$ possesses the superconvergence: ${\parallel}{\nabla}u-R({\nabla}u_h){\parallel}=O(h^2){\parallel}u{\parallel}_3$. Finally, some numerical examples are provided to illustrate our theoretical analysis.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.1
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• pp.35-44
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• 2009

This paper describes an application of domain decomposition method for parallel finite element analysis which is required to large scale 3D structural analysis. A parallel finite element method system which adopts a domain decomposition method is developed. Node is generated if its distance from existing node points is similar to the node spacing function at the point. The node spacing function is well controlled by the fuzzy knowledge processing. The Delaunay triangulation method is introduced as a basic tool for element generation. Domain decomposition method using automatic mesh generation system holds great benefits for 3D analyses. Aa parallel numerical algorithm for the finite element analyses, domain decomposition method was combined with an iterative solver, i.e. the conjugate gradient(CG) method where a whole analysis domain is fictitiously divided into a number of subdomains without overlapping. Practical performance of the present system are demonstrated through several examples.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.6
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• pp.753-765
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• 2003

A finite element code for the numerical solution of the Navier-Stokes equation is parallelized by vertex-oriented domain decomposition. To accelerate the convergence of iterative solvers like conjugate gradient method, parallel block ILU, iterative block ILU, and distributed ILU methods are tested as parallel preconditioners. The effectiveness of the algorithms has been investigated when P1P1 finite element discretization is used for the parallel solution of the Navier-Stokes equation. Two-dimensional and three-dimensional Laplace equations are calculated to estimate the speedup of the preconditioners. Calculation domain is partitioned by one- and multi-dimensional partitioning methods in structured grid and by METIS library in unstructured grid. For the domain-decomposed parallel computation of the Navier-Stokes equation, we have solved three-dimensional lid-driven cavity and natural convection problems in a cube as benchmark problems using a parallelized fractional 4-step finite element method. The speedup for each parallel preconditioning method is to be compared using upto 64 processors.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.2
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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.

• International Journal of Aeronautical and Space Sciences
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• v.9 no.2
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• pp.79-86
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• 2008

High performance direct-iterative hybrid linear solver for large scale finite element problem is developed. Direct solution method is robust but difficult to parallelize, whereas iterative solution method is opposite for direct method. Therefore, combining two solution methods is desired to get both high performance parallel efficiency and numerical robustness for large scale structural analysis problems. Hybrid method mentioned in this paper is based on FETI-DP (Finite Element Tearing and Interconnecting-Dual Primal method) which has good parallel scalability and efficiency. It is suitable for fourth and second order finite element elliptic problems including structural analysis problems. We are using the hybrid concept of theses two solution method categories, combining the multifrontal solver into FETI-DP based iterative solver. Hybrid solver is implemented for our general structural analysis code, IPSAP.