Browsing by Author "Wu, Chin-Tien"

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A Novel Stretch Energy Minimization Algorithm for Equiareal Parameterizations
(2019-03-01)
Yueh, Mei-Heng
;
Lin, Wen-Wei
;
Wu, Chin-Tien
;
Yau, Shing-Tung
;
應用數學系
Surface parameterizations have been widely applied to computer graphics and digital geometry processing. In this paper, we propose a novel stretch energy minimization (SEM) algorithm for the computation of equiareal parameterizations of simply connected open surfaces with very small area distortions and highly improved computational efficiencies. In addition, the existence of nontrivial limit points of the SEM algorithm is guaranteed under some mild assumptions of the mesh quality. Numerical experiments indicate that the accuracy, effectiveness, and robustness of the proposed SEM algorithm outperform the other state-of-the-art algorithms. Applications of the SEM on surface remeshing, registration and morphing for simply connected open surfaces are demonstrated thereafter. Thanks to the SEM algorithm, the computation for these applications can be carried out efficiently and reliably.
A skew freeform reflector design method for prescribed off-axis irradiance
(2019-06-01)
Su, Jian-Jia
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Tien, Chung-Hao
;
Tsai, Yu-Lin
;
Wu, Chin-Tien
;
應用數學系
In this paper we proposed a new methodology for designing freeform reflectors tailored to redistribute the radiant flux emitted by a point light source onto a target plane with the prescribed irradiance pattern. Based on the laws of reflection and energy conservation, a skew freeform model with a set of second-order ordinary differential equations formulating the ray tracing between the source and target domain was presented. A 3D freeform reflector was constructed by using such skew freeform model with quadric surface fitting accordingly. Proposed scheme is applicable for arbitrary geometric-based mapping without the restrictions subject to the target, source, collective solid angle, or target topography, respectively.
ADAPTIVE MESH REFINEMENT FOR ELLIPTIC INTERFACE PROBLEMS USING THE NON-CONFORMING IMMERSED FINITE ELEMENT METHOD
(2011)
Wu, Chin-Tien
;
Li, Zhilin
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Lai, Ming-Chih
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應用數學系
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數學建模與科學計算所(含中心)
In this paper, an adaptive mesh refinement technique is developed and analyzed for the non-conforming immersed finite element (IFE) method proposed in [27]. The IFE method was developed for solving the second order elliptic boundary value problem with interfaces across which the coefficient may be discontinuous. The IFE method was based on a triangulation that does not need to fit the interface. One of the key ideas of IFE method is to modify the basis functions so that the natural jump conditions are satisfied across the interface. The IFE method has shown to be order of O(h(2)) and O(h) in L(2) norm and H(1) norm, respectively. In order to develop the adaptive mesh refinement technique, additional priori and posterior error estimations are derived in this paper. Our new a-priori error estimation shows that the generic constant is only linearly proportional to ratio of the diffusion coefficient beta(-) and beta(+), which improves the corresponding result in [27]. We also show that a-posteriori error estimate similar to the one obtained by Bernardi and Verfurth [4] holds for the IFE solutions. Numerical examples support our theoretical results and show that the adaptive mesh refinement strategy is effective for the IFE approximation.
An Efficient Energy Minimization for Conformal Parameterizations
(2017-10-01)
Yueh, Mei-Heng
;
Lin, Wen-Wei
;
Wu, Chin-Tien
;
Yau, Shing-Tung
;
應用數學系
Surface parameterizations have been widely applied to digital geometry processing. In this paper, we propose an efficient conformal energy minimization (CEM) algorithm for computing conformal parameterizations of simply-connected open surfaces with a very small angular distortion and a highly improved computational efficiency. In addition, we generalize the proposed CEM algorithm to computing conformal parameterizations of multiply-connected surfaces. Furthermore, we prove the existence of a nontrivial accumulation point of the proposed CEM algorithm under some mild conditions. Several numerical results show the efficiency and robustness of the CEM algorithm comparing to the existing state-of-the-art algorithms. An application of the CEM on the surface morphing between simply-connected open surfaces is demonstrated thereafter. Thanks to the CEM algorithm, the whole computations for the surface morphing can be performed efficiently and robustly.
An efficient semi-coarsening multigrid method for variable diffusion problems in cylindrical coordinates
(2007-05-01)
Lai, Ming-Chih
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Wu, Chin-Tien
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Tseng, Yu-Hou
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應用數學系
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Department of Applied Mathematics
In this paper, we present an efficient multigrid (MG) algorithm for solving the three-dimensional variable coefficient diffusion equation in cylindrical coordinates. The multigrid V-cycle combines a semi-coarsening in azimuthal direction with the red-black Gauss-Seidel plane (radial-axial plane) relaxation. On each plane relaxation, we further semi-coarsen the axial direction with red-black line relaxation in the radial direction. We also prove the convergence of two-level MG with plane Jacobi relaxation. Numerical results show that the present multigrid method indeed is scalable with the mesh size. (c) 2006 IMACS. Published by Elsevier B.V. All rights reserved.
Momentum-time flux conservation method for one-dimensional wave equations
(2010-03-01)
Huang, Zhen-Ting
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Hsu, Huan-Chun
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Chang, Chau-Lyan
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Wu, Chin-Tien
;
Jiang, T. F.
We present a conservation element and solution element method in time and momentum space. Several paradigmatic wave problems including simple wave equation, convection-diffusion equation, driven harmonic oscillating charge and nonlinear Korteweg-cle Vries (KdV) equation are solved with this method and calibrated with known solutions to demonstrate its use. With this method, time marching scheme is explicit, and the nonreflecting boundary condition is automatically fulfilled. Compared to other solution methods in coordinate space, this method preserves the complete information of the wave during time evolution which is an useful feature especially for scattering problems. (C) 2009 Elsevier B.V. All rights reserved.
Neuroimaging Spectrum at Pre-, Early, and Late Symptomatic Stages of SCA17 Mice
(1970-01-01)
Chen, Chiao-Chi
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Yao, Nai-Wei
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Lin, Chia-Wei
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Su, Wei-Shuo
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Wu, Chin-Tien
Spinocerebellar ataxia (SCA) is a hereditary neurodegenerative disease. We have generated SCA17 transgenic mice bearing human TBP with 109 CAG repeats under the Purkinje cell-specific L7/pcp2 promoter. These mice recapitulate the patients' phenotypes and are suitable for the study of the SCA17 pathomechanism. Magnetic resonance imaging (MRI) and immunostainings were performed to identify the neuroimaging spectrum during disease progression. The results indicate that despite an overall normal appearance at birth, postnatal brain damage takes place rapidly in SCA17. Cerebellar atrophy, fourth-ventricle enlargement, and reduced cerebellar N-acetylaspartate levels were detected at the presymptomatic stage, when the mice were juvenile. The aberrations, which included reductions in body weight; cerebral size; striatal size; and the mean, radial, and axial diffusivities of the cerebellum, became more salient as the disease progressed to the old, late-symptomatic stage. Phosphorylated H2A histone family, member X (gamma H2AX) immunostaining revealed that the cerebellum underwent severe cell senescence in the old stage while the striatum appeared relatively unaffected by aging. Morphometric analysis indicated that the cerebellar atrophy occurred in all subregions with aging. The data establish that the SCA17 mouse brain appears normal at birth but becomes aberrant at the presymptomatic/juvenile stage. More widespread deficits add to the pathological spectrum at the old stage. The study provides information for the expression and expansion of L7/pcp2 promoter and implies the disease progression of SCA17 patients.
New approach to construct freeform surface by numerically differential formulation
(2014-03-01)
Tsai, Yu-Lin
;
Chiang, Ming-Chen
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Chang, Ray
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Tien, Chung-Hao
;
Wu, Chin-Tien
We proposed a new design method for single freeform reflective (or refractive) surface tailored to redistribute the radiant flux onto a prescribed illumination pattern. Unlike the conventional optimization approaches based on the grid mapping, in this study we estimated each segmental freeform surface by locally solving a second-order differential equation, which formulates the energy transportation between each domain cell. With finite element method via Hermite element, we validated a series of smooth reflective/refractive surfaces to reallocate the radiant flux from a point source toward a target plane with specific patterns. The proposed technique offers a large flexibility by varying the vectors of each ray with multiple refraction (or reflection), which imposes no restriction on the target distribution, collective solid angle, or even target topography. (C) The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.
Numerical studies on structure-preserving algorithms for surface acoustic wave simulations
(2013-05-15)
Huang, Tsung-Ming
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Li, Tiexiang
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Lin, Wen-Wei
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Wu, Chin-Tien
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應用數學系
We study the generalized eigenvalue problems (GEPs) derived from modeling the surface acoustic wave in piezoelectric materials with periodic inhomogeneity. The eigenvalues appear in the reciprocal pairs due to periodic boundary conditions in the modeling. By transforming the GEP into a T-palindromic quadratic eigenvalue problem (TPQEP), the reciprocal relationship of the eigenvalues can be maintained. In this paper, we outline four recently developed structure-preserving algorithms, SA, SDA, TSHIRA and GTSHIRA, for solving the TPQEP. Numerical comparisons on the accuracy and the computational costs of these algorithm are presented. The eigenvalues close to unit circle on the complex plane are of interest in the area of filter and sensor designs. Our numerical results show that the Arnoldi-type structure-preserving algorithms TSHIRA and GTSHIRA with "re-symplectic" and "re-bi-isotropic" processes, respectively, are as accurate as the SA and SDA algorithms, and more efficient in finding these eigenvalues. (c) 2012 Elsevier B.V. All rights reserved.
PALINDROMIC EIGENVALUE PROBLEMS: A BRIEF SURVEY
(2010-06-01)
Chu, Eric King-wah
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Huang, Tsung-Ming
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Lin, Wen-Wei
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Wu, Chin-Tien
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應用數學系
The T-palindromic quadratic eigenvalue problem (lambda(2)B + lambda C + A)x = 0, with A, B,C is an element of C(nxn), C(T) = C and B(T) = A, governs the vibration behaviour of trains. Other palindromic eigenvalue problems, quadratic or higher order, arise from applications in surface acoustic wave filters, optimal control of discrete-time systems and crack modelling. Numerical solution of palindromic eigenvalue problems is challenging, with unacceptably low accuracy from the basic linearization approach. In this survey paper, we shall talk about the history of palindromic eigenvalue problems, in terms of their history, applications, numerical solution and generalization. We shall also speculate on some future directions of research.
Reconstruction of inclusions in an elastic body
(2009-06-01)
Uhlmann, Gunther
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Wang, Jenn-Nan
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Wu, Chin-Tien
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應用數學系
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Department of Applied Mathematics
We consider the reconstruction of elastic inclusions embedded inside of a planar region, hounded or unbounded, with isotropic inhomogeneous elastic parameters by measuring displacements and tractions at the boundary. We probe the medium with complex geometrical Optics Solutions having polynomial-type phase functions. Using these solutions we develop all algorithm to reconstruct the exact shape of a large class of inclusions including star-shaped domains and we implement numerically this algorithm for some examples. (C) 2009 Elsevier Masson SAS. All rights reserved.
Structure-preserving Arnoldi-type algorithm for solving eigenvalue problems in leaky surface wave propagation
(2013-06-01)
Huang, Tsung-Ming
;
Lin, Wen-Wei
;
Wu, Chin-Tien
;
應用數學系
;
Department of Applied Mathematics
We study the generalized eigenvalue problems (GEPs) that arise from modeling leaky surface wave propagation in an acoustic resonator with an infinite amount of periodically arranged interdigital transducers. The constitutive equations are discretized by finite element methods with mesh refinements along the electrode interfaces and corners. The non-zero eigenvalues of the resulting GEP appear in reciprocal pairs (lambda, 1/lambda). We transform the GEP into a T-palindromic quadratic eigenvalue problem (TPQEP) to reveal the important reciprocal relationships of the eigenvalues. The TPQEP is then solved by a structure-preserving algorithm incorporating a generalized T-skew-Hamiltonian implicitly restarted Arnoldi method so that the reciprocal relationship of the eigenvalues may be automatically preserved. Compared with applying the Arnoldi method to solve the GEPs, our numerical results show that the eigenpairs produced by the proposed structure-preserving method not only preserve the reciprocal property but also possess high efficiency and accuracy. (C) 2013 Elsevier Inc. All rights reserved.