在不均勻介質中重建可穿透聲波的障礙物

Reconstruction of penetrable obstacles in acoustic in an inhomogeneous medium

林奕亘(Yi-Hsuan Lin)

指導教授 ： 王振男

國立臺灣大學/理學院/數學研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.10435

摘要

我們將用可穿透聲波來重建非凸集合的障礙物，在二維或者三維的非均勻介質下考慮這個問題。我們需要利用complex geometrical optics solution 來幫助我們重建未知的障礙物。

關鍵字

可穿透 ； 障礙物

並列摘要

We develop reconstruction schemes to determine nonconvex penetrable in a region in 2-dimensional or 3-dimensional in an inhomogeneous medium. This algorithm use complex geometrical optics solutions to the equation with general phase in 2-dimension and logarithm phase in 3-dimension. The 2-dimensional case will be demonstrated in section 2 and 3-dimensional case will be demonstrated in 3-dimension.

並列關鍵字

reconstruction ； penetrable

參考文獻

[1] A. L. Bukhgeim and G. Uhlmann, Recovering a potential from partial Cauchy data, Commun. in PDEs, 27 (2002), 635-668.

[2] C. E. Kenig, J. Sjstrand, and G. Uhlmann, The Caldern problems with partial data, Ann. of Math. (2), 165 (2007), 567-591.

[3] D. Dos Santos Ferreira, C. E. Kenig, J. Sjstrand, and G. Uhlmann, Determining a magnetic Schrdinger operators from partial Cauchy data. Comm. Math. Physics. 271 (2007), no. 2, 467-488.

[4] D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order. Second edition, Springer, Berlin, 1983.

[5] G. Nakamura and K. Yoshida, Identification of a non-convex obstacle for acoustical scattering. J. Inverse Ill-Posed Probl. 15 (2007), 611-624.