• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.2
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• pp.65-92
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• 2019

We survey a recently developed immersed finite element method (IFEM) for the interface problems. The IFEM uses structured grids such as uniform grids, even if the interface is a smooth curve. Instead of fitting the curved interface, the bases are modified so that they satisfy the jump conditions along the interface. The early versions of IFEM [1, 2] were suboptimal in convergence order [3]. Later, the consistency terms were added to the bilinear forms [4, 5], thus the scheme became optimal and the error estimates were proven. For elasticity problems with interfaces, we modify the Crouzeix-Raviart based element to satisfy the traction conditions along the interface [6], but the consistency terms are not needed. To satisfy the Korn's inequality, we add the stabilizing terms to the bilinear form. The optimal error estimate was shown for a triangular grid. Lastly, we describe the multigrid algorithms for the discretized system arising from IFEM. The prolongation operators are designed so that the prolongated function satisfy the flux continuity condition along the interface. The W-cycle convergence was proved, and the number of V-cycle is independent of the mesh size.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.2
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• pp.143-159
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• 2020

We propose a consistent numerical method for elliptic interface problems with nonhomogeneous jumps. We modify the discontinuous bubble immersed finite element method (DB-IFEM) introduced in (Chang et al. 2011), by adding a consistency term to the bilinear form. We prove optimal error estimates in L² and energy like norm for this new scheme. One of the important technique in this proof is the Bramble-Hilbert type of interpolation error estimate for discontinuous functions. We believe this is a first time to deal with interpolation error estimate for discontinuous functions. Numerical examples with various interfaces are provided. We observe optimal convergence rates for all the examples, while the performance of early DB-IFEM deteriorates for some examples. Thus, the modification of the bilinear form is meaningful to enhance the performance.

• The Journal of the Acoustical Society of Korea
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• v.20 no.6
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• pp.94-103
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• 2001

The goal of using numerical methods in this study is two-fold: to replicate a set of measured, individualized HRTFs by a computer simulation, and also to visualise the resultant sound field around the head. Two methods can be wed: the Boundary Element Method (BEM) and the Infinite-Finite Element Method (IFEM). This paper presents the results of a preliminary study carried out on a KEMAR dummy-head, the geometry of which was captured with a high accuracy 3-D laser scanner and digitiser. The scanned computer model was converted to a few valid BEM and IFEM meshes with different polygon resolutions, enabling us to optimise the simulation for different frequency ranges. The results show a good agreement between simulations and measurements of the sound pressure at the blocked ear-canal of the dummy-head. The principle of reciprocity provides an effect method to simulate HRTF database. The BEM was also used to investigate the total sound field around the head, providing a tool to visualise the sound field for different arrangements of virtual acoustic imaging systems.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.04a
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• pp.608-608
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• 2008

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.12 no.7
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• pp.1175-1181
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• 2001

An efficient hybrid method is proposed to analyze discontinuities in a rectangular waveguide. Only with a small number of meshes around a discontinuity, the typical finite element method is shown to give an exact solution through several iterative updates of the boundary conditions. To show the validity of the proposed method, a simple circular aperture in a rectangular waveguide is analyzed and its result is compared with FEBIM.