• Title/Summary/Keyword: Approximation theory

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Fast GPU Implementation for the Solution of Tridiagonal Matrix Systems (삼중대각행렬 시스템 풀이의 빠른 GPU 구현)

  • Kim, Yong-Hee;Lee, Sung-Kee
    • Journal of KIISE:Computer Systems and Theory
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    • v.32 no.11_12
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    • pp.692-704
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    • 2005
  • With the improvement of computer hardware, GPUs(Graphics Processor Units) have tremendous memory bandwidth and computation power. This leads GPUs to use in general purpose computation. Especially, GPU implementation of compute-intensive physics based simulations is actively studied. In the solution of differential equations which are base of physics simulations, tridiagonal matrix systems occur repeatedly by finite-difference approximation. From the point of view of physics based simulations, fast solution of tridiagonal matrix system is important research field. We propose a fast GPU implementation for the solution of tridiagonal matrix systems. In this paper, we implement the cyclic reduction(also known as odd-even reduction) algorithm which is a popular choice for vector processors. We obtained a considerable performance improvement for solving tridiagonal matrix systems over Thomas method and conjugate gradient method. Thomas method is well known as a method for solving tridiagonal matrix systems on CPU and conjugate gradient method has shown good results on GPU. We experimented our proposed method by applying it to heat conduction, advection-diffusion, and shallow water simulations. The results of these simulations have shown a remarkable performance of over 35 frame-per-second on the 1024x1024 grid.

Animation Generation for Chinese Character Learning on Mobile Devices (모바일 한자 학습 애니메이션 생성)

  • Koo, Sang-Ok;Jang, Hyun-Gyu;Jung, Soon-Ki
    • Journal of KIISE:Computer Systems and Theory
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    • v.33 no.12
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    • pp.894-906
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    • 2006
  • There are many difficulties to develop a mobile contents due to many constraints on mobile environments. It is difficult to make a good mobile contents with only visual reduction of existing contents on wire Internet. Therefore, it is essential to devise the data representation and to develop the authoring tool to meet the needs of the mobile contents market. We suggest the compact mobile contents to learn Chinese characters and developed its authoring tool. The animation which our system produces is realistic as if someone writes letters with pen or brush. Moreover, our authoring tool makes a user generate a Chinese character animation easily and rapidly although she or he has not many knowledge in computer graphics, mobile programming or Chinese characters. The method to generate the stroke animation is following: We take basic character shape information represented with several contours from TTF(TrueType Font) and get the information for the stroke segmentation and stroke ordering from simple user input. And then, we decompose whole character shape into some strokes by using polygonal approximation technique. Next, the stroke animation for each stroke is automatically generated by the scan line algorithm ordered by the stroke direction. Finally, the ordered scan lines are compressed into some integers by reducing coordinate redundancy As a result, the stroke animation of our system is even smaller than GIF animation. Our method can be extended to rendering and animation of Hangul or general 2D shape based on vector graphics. We have the plan to find the method to automate the stroke segmentation and ordering without user input.

Stereo Image-based 3D Modelling Algorithm through Efficient Extraction of Depth Feature (효율적인 깊이 특징 추출을 이용한 스테레오 영상 기반의 3차원 모델링 기법)

  • Ha, Young-Su;Lee, Heng-Suk;Han, Kyu-Phil
    • Journal of KIISE:Computer Systems and Theory
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    • v.32 no.10
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    • pp.520-529
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    • 2005
  • A feature-based 3D modeling algorithm is presented in this paper. Since conventional methods use depth-based techniques, they need much time for the image matching to extract depth information. Even feature-based methods have less computation load than that of depth-based ones, the calculation of modeling error about whole pixels within a triangle is needed in feature-based algorithms. It also increase the computation time. Therefore, the proposed algorithm consists of three phases, which are an initial 3D model generation, model evaluation, and model refinement phases, in order to acquire an efficient 3D model. Intensity gradients and incremental Delaunay triangulation are used in the Initial model generation. In this phase, a morphological edge operator is adopted for a fast edge filtering, and the incremental Delaunay triangulation is modified to decrease the computation time by avoiding the calculation errors of whole pixels and selecting a vertex at the near of the centroid within the previous triangle. After the model generation, sparse vertices are matched, then the faces are evaluated with the size, approximation error, and disparity fluctuation of the face in evaluation stage. Thereafter, the faces which have a large error are selectively refined into smaller faces. Experimental results showed that the proposed algorithm could acquire an adaptive model with less modeling errors for both smooth and abrupt areas and could remarkably reduce the model acquisition time.

Evaluations of the Equations of State and Thermodynamic Quantities of Fluid Metal at High Temperatures and Densities

  • Shin, Hyun-Joon;Hong, Jong-Ha;Oh, Byung-Wan
    • Nuclear Engineering and Technology
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    • v.10 no.3
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    • pp.127-136
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    • 1978
  • We have applied the temperature dependent Thomas-Fermi theory to evaluate the equations of state, chemical potentials, entropies, % ionizations, total energies and kinetic energies of an atom, and seveal thermodynamic quantifies of one of metallic substance, Na, for a density range of 0.1$\rho$$_{0}$ ~ 10$\rho$$_{0}$, where $\rho$$_{0}$ is the normal density of Na at its melting point, and for a temperature range of 60.88Ryd. ~0.0216 Ryd., where the system is expected to be in a gaseous or liquid state. The main interest of present work lies in physical quantities at high temperatures and high densities, however, we have included those quantities of Na at sufficiently low temperatures and low densities to show that the approximation is not so crude as one might expect. Particularly, at high temperatures, the calculated equations of state, kinetic energies of an atom, chemical potentials and entropies are compared with those, of an ideal Fermi gas. The results show that, at high temperatures, the agreement seems good for chemical Potentials. However, the differences in, entropy, kinetic energy of an atom, and equation of state are not negligible even at such high temperature as $textsc{k}$T=60.88Ryd.

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Study of the Molecular Reorientation in Ammonium Sulfate by Neutron Scattering

  • Kim, Huhn-Jun
    • Nuclear Engineering and Technology
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    • v.4 no.4
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    • pp.306-321
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    • 1972
  • Molecular reorientation in (NH$_4$)$_2$SO$_4$, has been studied by cold neutron scattering. For T=300$^{\circ}$K data, the isolated quasielastic spectra and form-factors at various scattering angles are compared with four reorientational models based on SKOLD theory. Front these, it is concluded that the NH$_4$ions are performing either 3-fold four axes or 2-fold three axes reorientation with $\tau$$_{c}$=2.0$\times$10$^{-11}$ sec. The temperature dependence of f. is studied over 100$^{\circ}$K-413$^{\circ}$K and for the high-temperature phase, the widths of composite spectra are compared with the results from NMR relaxation measurements. All the results have shown that the neutron scattering method is capable of giving detalis of the reorientational modes in solids and therefore some discussions are given on the application of this method. A study of the form-factor is applied for NH$_4$I (Phase I) by comparing the measurement with the calculation based on free rotation approximation and proposed a reorientation model of NH$_4$ ions in the octahedral potential cage with $\tau$$_{c}$$\leq$10$^{-12}$ sec. Also a brief theoretical prediction for the effect of reorientational motions on the inelastic spectrum is discussed.sed.

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A Finite Element Simulation of Cancellous Bone Remodeling Based on Volumetric Strain (스폰지 뼈의 Remodeling 예측을 위한 체적 변형률을 이용한 유한요소 알고리즘)

  • Kim, Young;Vanderby, Ray
    • Journal of Biomedical Engineering Research
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    • v.21 no.4
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    • pp.373-384
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    • 2000
  • The goal of this paper is to develop a computational method to predict cancellous bone density distributions based upon continuum levels of volumetric strain. Volumetric strain is defined as the summation of normal strains, excluding shear strains, within an elastic range of loadings. Volumetric strain at a particular location in a cancellous structure changes with changes of the boundary conditions (prescribed displacements, tractions, and pressure). This change in the volumetric strain is postulated to predict the adaptive change in the bone apparent density. This bone remodeling theory based on volumetric strain is then used with the finite element method to compute the apparent density distribution for cancellous bone in both lumbar spine and proximal femur using an iterative algorithm, considering the dead zone of strain stimuli. The apparent density distribution of cancellous bone predicted by this method has the same pattern as experimental data reported in the literature (Wolff 1892, Keller et al. 1989, Cody et al. 1992). The resulting bone apparent density distributions predict Young's modulus and strength distributions throughout cancellous bone in agreement with the literature (Keller et al. 1989, Carter and Hayes 1977). The method was convergent and sensitive to changes in boundary conditions. Therefore, the computational algorithm of the present study appears to be a useful approach to predict the apparent density distribution of cancellous bone (i.e. a numerical approximation for Wolff's Law)

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Characteristic of Wave Diffraction and Reflection for Irregular Waves in SWASH Model Around Small Port Structures (소규모 항만 구조물 주변에서 불규칙파에 대한 SWASH 모형의 반사 및 회절)

  • Kwon, Kyong Hwan;Park, Chang Wook;Park, Il Heum;Kim, Jong Hoon
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.31 no.6
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    • pp.468-477
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    • 2019
  • The numerical model of Boussinesq approximation, which is mainly used for evaluating the port calmness due to the irregular waves, has a limit of applicability of lattice size in ports such as marinas with narrow port openings of around 30m. The SWASH model controls the partial reflection according to the depth, porosity coefficient and structure size when applying the reflected wave incident on the structure and terrain. In this study, the partial reflection evaluation at the front of the structure according to the bottom shape and the shape of the structure are examined. In order to evaluate the reproducibility of the model due to the diffraction waves entering the term, the area of incidence at right angles and inclination of the structure is constructed and compared with the diffraction theory suggested by Goda et al. (1978). The experimental results of the sectional structure reflectances calculated as the depth mean show reflectances similar to the approximate values of the reflectances presented by Stelling and Ahrens (1981). It is considered that the reflected wave is well reproduced according to the control of the reflected wave at the boundary and the shape and topography of the structure. Compared with previous studies to examine the diffraction of the wave incident from the breakwater opening, the wave incidence angle and the shape of the diffraction wave are very similar to the theoretical values, but both oblique and rectangular incidence In the case where the direction concentration is small, the diffraction degree is underestimated in some sections with the crest ratio of 0.5 to 0.6.

The Relationships between Dry Matter Yield and Days of Summer Depression in different Regions with Mixed Pasture (혼파초지에서 지역별 건물수량과 하고일수 간 관계)

  • Oh, Seung Min;Kim, Moonju;Peng, Jinglun;Lee, Bae Hun;Kim, Ji Yung;Chemere, Befekadu;Kim, Si Chul;Kim, Kyeong Dae;Kim, Byong Wan;Jo, Mu Hwan;Sung, Kyung Il
    • Journal of The Korean Society of Grassland and Forage Science
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    • v.38 no.1
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    • pp.53-60
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    • 2018
  • Yield prediction model for mixed pasture was developed with a shortage that the relationship between dry matter yield (DMY) and days of summer depression (DSD) was not properly reflected in the model in the previous research. Therefore, this study was designed to eliminate the data of the regions with distinctly different climatic conditions and then investigate their relationships DMY and DSD using the data in each region separately of regions with distinct climatic characteristics and classify the data based on regions for further analysis based on the previous mixed pasture prediction model. The data set used in the research kept 582 data points from 11 regions and 41 mixed pasture types. The relationship between DMY and DSD in each region were analyzed through scatter plot, correlation analysis and multiple regression analysis in each region separately. In the statistical analysis, DMY was taken as the response variable and 5 climatic variables including DSD were taken as explanatory variables. The results of scatter plot showed that negative correlations between DMY and DSD were observed in 7 out of 9 regions. Therefore, it was confirmed that analyzing the relationship between DMY and DSD based on each region is necessary and 5 regions were selected (Hwaseong, Suwon, Daejeon, Siheung and Gwangju) since the data size in these regions is large enough to perform the further statistical analysis based on large sample approximation theory. Correlation analysis showed that negative correlations were found between DMY and DSD in 3 (Hwaseong, Suwon and Siheung) out of the 5 regions, meanwhile the negative relationship in Hwaseong was confirmed through multiple regression analysis. Therefore, it was concluded that the interpretability of the yield prediction model for mixed pasture could be improved based on constructing the models using the data from each region separately instead of using the pooled data from different regions.