| Co-Investigator(Kenkyū-buntansha) |
NARA Takaaki National Institute of Informatics, Foundations of Informatics Research Division, Research Associate, 情報学基礎研究系, 助手 (80353423)
NISHIDA Tetsushi The University of Tokyo, Graduate School of Information Science and Technology, Research Associate, 大学院・情報理工学系研究科, 助手 (80302751)
|
|---|
| Research Abstract |
1) Direct simulation of large amplitude standing waves using the boundary element method
We developed a method using the two-dimensional boundary element method for the time dependent direct simulation of the free surface of liquids, and succeeded in the direct simulation of large amplitude standing waves, which was considered to be difficult.
2) Inverse Problem
We developed efficient direct methods for the inverse problem of source term identification of the three-dimensional Poisson equation, which is applied to MEG etc. Depending on whether the source is 1) relatively uniformly distributed in the domain, 2) concentrated near the boundary of the domain, infinite series of the 1) low-order moments, 2) high-order moments of the multipole expansion of the field are used in order to obtain reconstruction formulae concerning the position of the projection of the source on to the 1) xy-plane, 2) Riemann sphere.
3) Iterative methods on singular systems
We analyzed the behavior of Krylov subspace
… More
iterative methods on least-squares problems whose coefficient matrices are singular. Namely, we derived necessary and sufficient conditions for the CR (Conjugate Residual), GCR(k) (Generalized Conjugate Residual) and GMRES (Generalized Minimal Residual) methods to give a least-square solution without break-down. The methodology is to decompose the algorithms in to the range of the coefficient matrix and its orthogonal complement.
We also developed a method of applying the GMRES method after preconditioning by incomplete QR decomposition, for (over-determined) least-squares problems.
4) Iterative methods for eigenvalue problems
We derived necessary and sufficient conditions for a solution to exist to the correction equation of the Jacobi-Davidson method, clarified the relation between the subspace expanded by such a solution and the invariant space of the coefficient matrix, and proposed a method for generating efficient starting vectors for the method. We also proposed methods for the validated numerics of the method. Less
|
