抄録
Offer Organization: Japan Society for the Promotion of Science, System Name: Grants-in-Aid for Scientific Research, Category: Grant-in-Aid for Scientific Research (C), Fund Type: -, Overall Grant Amount: - (direct: 4000000, indirect: -)
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 numerical 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.