| Project/Area Number |
14540106
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | The University of Electro-Communications |
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Principal Investigator |
KAKO Takashi The University of Electro-Communications, Faculty of Electro-Communications, Professor, 電気通信学部, 教授 (30012488)
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| Co-Investigator(Kenkyū-buntansha) |
USHIJIMA Teruo The University of Electro-Communications, Faculty of Electro-Communications, Professor, 電気通信学部, 教授 (10012410)
YOSHIDA Toshinobu The University of Electro-Communications, Faculty of Electro-Communications, Professor, 電気通信学部, 教授 (30114341)
KOYAMA Daisuke The University of Electro-Communications, Faculty of Electro-Communications, Research Associate, 電気通信学部, 助手 (60251708)
ZHANG Shao-liang The University of Tokyo, Graduate School of Engineering, Associate Professor, 大学院・工学系研究科, 助教授 (20252273)
SUITO Hiroshi Okayama University, Department of Environmental and Mathematical Sciences, Associate Professor, 環境理工学部, 助教授 (10302530)
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| Project Period (FY) |
2002 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥4,000,000 (Direct Cost: ¥4,000,000)
Fiscal Year 2004: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2003: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2002: ¥1,600,000 (Direct Cost: ¥1,600,000)
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| Keywords | Exterior Helmholtz problem / Finite element method / Variational formula of eigenvalue / Dirichlet to Neumann mapping / Fundamental solution method / Voice generation / Fictitious domain method / Articulation model / 超音波 / 反復解法 |
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| Research Abstract |
The purpose of this research project is to develop the approximation methods for wave propagation problems in unbounded region and as its applications we study the numerical simulation of voice generation. We formulate the problem as the exterior Helmholtz equation, and reduce the problem to the one in a bounded region by introducing the artificial boundary condition on an artificial boundary. We developed the numerical methods for this problem based on the finite element discretization method and study the application problems including the voice generation.
The results of the head investigator Kako are the followings. He found out the variational formula of the complex eigenvalues with respect to the deformation of vocal tract. The eigenvalues are related to the formants of frequency response function that is important for voice generation. He then developed the algorithm for designing the shape of vocal tract by use of the variational formula, and validated the algorithm through nume
… More
rical simulations. He also studied the application of the Finite Difference Time Domain method to the acoustic problem and obtained several basic results.
For the voice problem, Yoshida developed the method to obtain the mapping from the articulation parameters to the phonetic transmission characteristics by use of the neural networks. Suito studied the shape optimization problem for minimizing the reflection of the wave propagating in a tubular region with spatially changing impedance parameters and obtained unusual numerical results.
Related to the numerical methods for the wave problem, Koyama studied the three dimensional Helmholtz problem by use of the fictitious domain method and derived the a priori error estimates for the approximation, and investigated the validity by some numerical experiences. Ushijima studied the Helmholtz problem by the collocation method based on the fundamental solutions and obtained a sufficient condition for the exponential convergence of the approximate solution and tried to validate of the theoretical results by multi-precision arithmetic computation.
As for the numerical methods for solving large linear equations appearing in the application problems including the Helmholtz equation, Zhang studied the fast and efficient iteration methods. Imamura developed the automatic tuning techniques with high actuary and stability in the implementation for the parallel computation methods for the large linear systems. Less
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