• 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.

• Proceedings of the Korea Electromagnetic Engineering Society Conference
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• 2003.11a
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• pp.126-130
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• 2003

The optical power transfer of TM modes in grating-assisted directional couplers (GADCs) with three-guiding channels is rigorously evaluated by defining a novel coupling efficiency amenable to the rigorous analytical solutions of modal transmission-line theory (MTLT). The results reveal that the incident power is sensitively partitioned through three output channels in terms of such grating parameters as the period, the duty cycle, and wavelength.

• Journal of Mechanical Science and Technology
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• v.17 no.11
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• pp.1784-1792
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• 2003

A hybrid method with supercompact multiwavelets is suggested as an efficient and practical method to compress CFD dataset. Supercompact multiwavelets provide various advantages such as compact support and orthogonality in CFD data compression. The compactness is a crucial condition for approximated representation of CFD data to avoid unnecessary interaction between remotely spaced data across various singularities such as shock and vortices. But the supercompact multiwavelet method has to fit the CFD grid size to a product of integer and power of two, m${\times}$2$^n$. To resolve this problem, the hybrid method with combination of 3, 2 and 1 dimensional version of wavelets is studied. With the hybrid method, any arbitrary size can be handled without any shrinkage or expansion of the original problem. The presented method allows high data compression ratio for fluid simulation data. Several numerical tests substantiate large data compression ratios for flow field simulation successfully.