• Journal of computational fluids engineering
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• v.9 no.3
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• pp.57-65
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• 2004

The incompressible Navier-Stokes equations in two dimensions are stabilized by a modified residual method, and then discretized by hierarchical elements. The stabilization is necessary to escape from the Ladyzhenskaya-Babuska-Brezzi(LBB) constraint and hence to achieve an equal order formulation. To expedite a standard iterative method such as the conjugate gradient squared(CGS) method, a preconditioning technique called the Hierarchical Iterative Procedure(HIP) has been applied. In this paper, we increased the order of interpolation within an element up to cubic. The hierarchical elements have been used to achieve a higher order accuracy in fluid flow analyses, but a proper efficient iterative procedure for higher order finite element formulation has not been available so far The numerical results by the present HIP for the lid driven cavity flow and others showed the present procedure to be stable, very efficient and useful in flow analyses in conjunction with hierarchical elements.

• Journal of Electrochemical Science and Technology
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• v.12 no.2
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• pp.257-265
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• 2021

In this study, we report niobium (Nb) with hierarchical porous structure produced by a one-pot, HF-free electrochemical etching process. It is proved experimentally that a well-defined hierarchical porous structure is produced from the combination of a limited repetition of pulse etching and high concentration of aggressive anion (i.e., SO₄^2-), which results in hierarchical pores with high order over 3. A formula is derived for the surface area of porous Nb as a function of the hierarchical order of pores while the experimental surface area is estimated on the basis of the electrochemical gas evolution rate on porous Nb. From the comparison of the theoretical and experimental surface areas, an in-depth understanding was gained about porous structure produced in this work in terms of the actual pore shape and hierarchical pore order.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.9
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• pp.1209-1217
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• 2002

The use of a two dimensional hierarchical elements are investigated for the incompressible flow computation. The construction of hierarchical elements are explained by both a geometric configuration and a determination of degrees of freedom. Also a systematic treatment of essential boundary values has been developed for the degrees of freedom corresponding to higher order terms. The numerical study for the poisson problem shows that the computation with hierarchical higher order elements can increase the convergence rate and accuracy of finite element solutions in more efficient manner than the use of standard first order element. for Stokes and Cavity flow cases, a mixed version of penalty function approach has been introduced in connection with the hierarchical elements. Solutions from hierarchical elements showed better resolutions with consistent trends in both mesh shapes and the order of elements.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.422-429
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• 2001

A two dimensional hierarchical elements are investigated for a use on the incompressible flow computation. The construction of hierarchical elements are explained through the tensor product of 1-D hierarchical functions, and a systematic treatment of essential boundary values has been developed for the degrees of freedom corresponding to higher order terms. The numerical study for the poisson problem showed that the present scheme can increase the convergence and accuracy of finite element solutions, and can be more efficient than the standard first order with many elements. Also, for Stokes and cavity flow cases, solutions from hierarchical elements showed better resolutions and future promises for higher order solutions.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2004.05a
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• pp.216-221
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• 2004

In two dimensional incompressible flaws, a preconditioning technique called Hierarchical Iterative Procedure(HIP) has been implemented on a SUPG finite element formulation. By using the SUPG formulation, one can escape from the LBB constraint and hence achieve an equal order formulation. In this paper, we increased the order of interpolation up to cubic. The conjugate gradient squared(CGS) method is used for the outer iteration, and the HIP for the preconditioning for the incompressible Navier-Stokes equation. The hierarchical elements has been used to achieve a higher order accuracy in fluid flaw analyses, but a proper efficient iterative procedure for higher order finite element formulation has not been available so far. The numerical results by the present HIP for the lid driven cavity flaw showed the present procedure to be stable, very efficient and useful in flaw analyses in conjunction with hierarchical elements.

• Journal of Ocean Engineering and Technology
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• v.17 no.5 s.54
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• pp.11-18
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• 2003

In two-dimensional incompressible flows, a preconditioning technique called Hierarchical Iterative Procedure (HIP) has been implemented on a SUPG finite element formulation. By using the SUPG formulation, one can escape from the LBB constraint hence, achieving an equal order formulation. In this paper, we increased the order of interpolation up to cubic. The conjugate gradient squared (CGS) method is used for the outer iteration, and the HIP for the preconditioning for the incompressible Navier-Stokes equation. The hierarchical elements have been used to achieve a higher order accuracy in fluid flow analyses, but a proper and efficient iterative procedure for higher order finite element formulation has not been available, thus far. The numerical results by the present HIP for the lid driven cavity flow showed the present procedure to be stable, very efficient, and useful in flow analyses, in conjunction with hierarchical elements.

• 한국전산유체공학회:학술대회논문집
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• 2004.03a
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• pp.91-98
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• 2004

In two dimensional incompressible flows, a preconditioning technique called Hierarchical Iterative Procedure(HIP) has been implemented on a stabilized finite element formulation. The stabilization has been peformed by a modified residual method proposed by Illinca et. al.[3]. The stabilization which is necessary to escape from the LBB constraint renders an equal order formulation. In this paper, we increased the order of interpolation whithin an element up to cubic. The conjugate gradient squared(CGS) method is used for the outer iteration, and the HIP for the preconditioning for the incompressible Navier-Stokes equation. The hierarchical elements has been used to achieve a higher order accuracy in fluid flow analyses, but a proper efficient iterative procedure for higher order finite element formulation has not been available so far. The numerical results by the present HIP for the lid driven cavity flow showed the present procedure to be stable, very efficient and useful in flow analyses in conjunction with hierarchical elements.

• Journal of the Korean Operations Research and Management Science Society
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• v.16 no.2
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• pp.125-125
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• 1991

This paper presents a framework for the hierarchical PPC(Production Planning and Control) in make-to-order environment with job shop. The characteristics of the environment are described as : 1) project with non-repetitive and individual production, 2) short delivery date, 3) process layout with large scales manufacturing. 4) job shops. The PPC in a make-to-order typically are organized along hierarchical fashions. A model is proposed for the hierarchical job shop scheduling based on new concepts of production system, work and worker organization. Then, a new integrated hierarchical framework is also developed for the PPC based on concepts of the proposed job shops scheduling model. Finally, the proposed framework has been implemented in the Electric Motor Manufacturing and the results showed good performance.

• Korean Management Science Review
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• v.16 no.2
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• pp.125-135
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• 1999

This paper presents a framework for the hierarchical PPC(Production Planning and Control) in make-to-order environment with job shop. The characteristics of the environment are described as : 1) project with non-repetitive and individual production, 2) short delivery date, 3) process layout with large scales manufacturing. 4) job shops. The PPC in a make-to-order typically are organized along hierarchical fashions. A model is proposed for the hierarchical job shop scheduling based on new concepts of production system, work and worker organization. Then, a new integrated hierarchical framework is also developed for the PPC based on concepts of the proposed job shops scheduling model. Finally, the proposed framework has been implemented in the Electric Motor Manufacturing and the results showed good performance.

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.429-441
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• 2014

In this work we study two a posteriori error estimators of hierarchical type for lowest-order mixed finite element methods. One estimator is computed by solving a global defect problem based on the splitting of the lowest-order Brezzi-Douglas-Marini space, and the other estimator is locally computable by applying the standard localization to the first estimator. We establish the reliability and efficiency of both estimators by comparing them with the standard residual estimator. In addition, it is shown that the error estimator based on the global defect problem is asymptotically exact under suitable conditions.