Study of Numerical Methods for Wave Propagation Phenomena in Unbounded Region and its Applications

无界区域波传播现象的数值方法研究及其应用

基本信息

批准号：
14540106
负责人：
KAKO Takashi
金额：
$ 2.56万
依托单位：
The University of Electro-Communications
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540106/
关键词：
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

项目摘要

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

本研究项目的目的是开发无界区域中波传播问题的近似方法，作为其应用，我们研究了语音生成的数值模拟，我们将问题表述为外亥姆霍兹方程，并将问题简化为方程。通过在人工边界上引入人工边界条件，我们开发了基于有限元离散化方法的有界区域的数值方法，并研究了包括语音生成在内的应用问题。首席研究员Kako的结果是他找到了关于声道变形的复特征值的变分公式，该特征值与对语音生成很重要的频率响应函数的共振峰有关。他还研究了时域有限差分方法在声学问题中的应用，并获得了一些基本结果。为了解决这个问题，Yoshida 开发了一种方法，利用神经网络获得从发音参数到语音传输特性的映射，Suite 研究了形状优化问题，以最小化在具有空间变化的阻抗参数的管状区域中传播的波的反射。获得了不同寻常的数值结果。与波浪问题的数值方法相关，小山利用虚拟域方法研究了三维亥姆霍兹问题，并推导了近似的先验误差估计，并Ushijima等人通过一些数值经验研究了亥姆霍兹问题的基本解的配置方法，得到了近似解指数收敛的充分条件，并尝试通过多精度算术计算来验证理论结果。针对亥姆霍兹方程等应用问题中出现的求解大型线性方程组的数值方法，张教授研究了快速高效的迭代方法，在实施过程中发展了精算度高、稳定性好的自动整定技术。大型线性系统的并行计算方法。