2003 Fiscal Year Final Research Report Summary
Reconstruction methods in inverse boundary value problems
| Project/Area Number |
13640115
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Gunma University |
|---|
Principal Investigator |
TANUMA Kazumi Gunma University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (60217156)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
SAITOH Saburoh Gunma University, Faculty of Engineering, Professor, 工学部, 教授 (10110397)
ASHINO Ryuichi Osaka Kyoiku University, Faculty of education, Associate Professor, 教育学部, 助教授 (80249490)
NAKAMURA Gen Hokkaido University, Faculty of Science, Professor, 大学院・理学研究科, 教授 (50118535)
AMANO Kazuo Gunma University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (90137795)
IKEHATA Masaru Gunma University, Faculty of Engineering, Professor, 工学部, 教授 (90202910)
|
|---|
| Project Period (FY) |
2001 – 2003
|
| Keywords | inverse boundary value problems / impedance tomography / reconstruction formula / crystallographic texture / surface impedance tensor / Rayleigh wave / initial stress / acoustoelastic coefficient |
|---|
| Research Abstract |
1.We considered the problem of determining conductivity of the medium from the measurements of the electric potential on the boundary and the corresponding current flux across the boundary, that is, from the Dirichlet to Neumann map. Three kinds of formulas for reconstructing conductivity and its normal derivative from the localized Dirichlet to Neumann map were obtained. They are the formulas for pointweise reconstruction, reconstruction in a weak form, and reconstruction in the form of Fourier transform. In these formulas, the normal derivative of the conductivity at the boundary is reconstructed from the localized Dirichlet to Neumann map without any information about the conductivity itself, which will give an efficient method in their numerical realization. Since our reconstruction formulas involve limiting process, we also gave the estimates for their convergences.
2.The surface impedance tensor is a Hermitian second-order tensor which, for a homogeneous elastic half-space, maps the displacements given at the surface to the tractions needed to sustain them. We accounted for the effects of crystallographic texture in orthorhombic aggregates of cubic crystallites only up to terms linear in the texture coefficients and gave an explicit formula for the terms in the surface impedance tensor up to those linear in the texture coefficients. By the same method, we gave a dispersion formula for the velocity of Rayleigh waves propagating textured polycrystals with initial stress, which shows how the initial stress and the crystallographic texture have an influence, within terms linear in them, on the angular dependency of the Rayleigh waves velocity. This formula includes terms that describe the effects of texture on the acoustoelastic coefficients.
|
Research Products
(18 results)
