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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 王振男 | |
| dc.contributor.author | Rui-Heng Lan | en |
| dc.contributor.author | 藍瑞衡 | zh_TW |
| dc.date.accessioned | 2021-06-08T05:07:14Z | - |
| dc.date.copyright | 2011-07-06 | |
| dc.date.issued | 2011 | |
| dc.date.submitted | 2011-06-21 | |
| dc.identifier.citation | [1] Lawrene C. Evans, Partial differential equations, American Mathematical Society Providence, Rhode Island.
[2] David Colton and Rainer Kress, Integral equation methods in scattering theory,Wiley-Interscience Publication. [3] David Colton and Rainer Kress, Inverse acoustic and electromagnetic scattering theory, Springer-Verlag. [4] Mezhlum A. Sumbatyan and Antonio Scalia, Equations of mathematical diffraction theory, Chapman and Hall/CRC. [5] H.D. Alber and A.G. Ramm, Scattering amplitude and algorithm for solving the inverse scattering problem for a class of non-convex obstacles, Journal of Mathematical Analysis And Applications 117, 570-597(1986). [6] Andrew Majda, High frequency asymptotics for the scattering matrix and the inverse problem of acoustical scattering, Communications of Pure and Applied Mathematics, vol. XXIX, 261-291(1976). [7] Michael E. Taylor, Pseudodifferential operators, Princeton University Press. [8] Howard David Yingst, The Kirchoff approximation for the Neumann problem, Thesis, Rice University, Houston, 1979. [9] Courant and Hilbert, Methods of mathematical physics, volume 2, Wiley-Interscience Publication. [10] R.Wong, Asymptotic approximations of integrals, SIAM. [11] David Colton, Qualitative methods in inverse scattering theory, an introduction, Springer-Verlag. [12] David Colton, Partial differential equations : an introduction, Dover Publications. [13] A.G. Ramm, On the inverse diffraction problem, Journal Of Mathematical Analysis And Applications 103, 139-14(1984). [14] L. Nirenberg, The Weyl And Minkowiski problems in differential geometry in the large, Communications of Pure and Applied Mathematics, vol 6, 337-394(1953). [15] Frank Natterer, Mathematical methods in image reconstruction, SIAM Monographs on Mathematical Modeling and Computation. [16] F Natterer, An error bound for the Born approximation, Inverse Problems 20(2004)447-452. [17] Shulin Zhou and Tie Zhou, An LP bound for the Born approximation In 3D. [18] Noboru Suzuki, On the convergence of Neumann series in Banach space, Math.Ann.220,143-146(1976). [19] A.J Devaney, A filtered backpropagation algorithm for diffraction tomography, Ultrasonic Imaging 4,336-350(1982). [20] Albert D. Wheelon, Electromagnetic scintillation volume 2, weak scattering, National Oceanic and Atmospheric Administration, District of Columbia. [21] George A. Tsihrintzis and Anthony J.Devaney, Higher order(nonlinear) diffraction tomography:inversion of the Rytov series, IEEE Transactions on Information Theory, Vol, 46, No.5, august 2000. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/23689 | - |
| dc.description.abstract | 我們將探討二維空間與三維空間中散射問題的某些近似方法。考慮的問題包括不均勻介質與障礙物的單一散射問題。我們討論應用於齊次Helmholtz方程式的克西荷夫近似。應用於非其次Helmholtz方程式的波恩與雷多夫近似也將給予討論。 | zh_TW |
| dc.description.abstract | We shall study some approximation schemes in inverse scattering problems in $R^{2}$ and $R^{3}$. Single scattering by an obstacle and by an inhomogeneous medium are of our considerations. We study the Kirchhoff approximation in the homogeneous Helmholtz equation. Some properties of Born and Rytov approximation in the inhomogeneous Helmholtz equation are discussed. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T05:07:14Z (GMT). No. of bitstreams: 1 ntu-100-R98221023-1.pdf: 485689 bytes, checksum: a65d898e356a3becd3e4f647f3e16333 (MD5) Previous issue date: 2011 | en |
| dc.description.tableofcontents | 口試審定書i
誌謝iii Abstract (in Chinese) iv Abstract (in English) v 1 Introduction 1 2 Scattering by an obstacle 3 2.1 Kirchhoff approximation 5 2.1.1 Kirchhoff’s theory 5 2.1.2 Justifications of Kirchhoff approximation 8 2.1.3 The scattering amplitudes using Kirchhoff approximation 19 2.1.4 Some applications of the scattering amplitudes 28 3 Scattering by an inhomogeneous medium 30 3.1 Born approximation 31 3.1.1 Born’s theory 31 3.1.2 Validity of Born approximation 33 3.1.3 Application : Near-field inversion 37 3.1.4 Application : Far-field inversion 41 3.1.5 Some estimates of error bounds 42 3.2 Rytov approximation 46 3.2.1 Rytov’s theory 46 3.2.2 Rytov’s solution 47 3.2.3 Validity of Rytov approximation 49 3.2.4 Application : Near-field inversion 49 3.2.5 Application : Far-field inversion 51 Bibliography 52 | |
| dc.language.iso | en | |
| dc.title | 散射問題中的某些近似方法與其應用 | zh_TW |
| dc.title | On Some Approximation Schemes And Their Applications To Scattering Problems | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 99-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 夏俊雄,林太家,陳俊全 | |
| dc.subject.keyword | 散射,克西荷夫,波恩,雷多夫, | zh_TW |
| dc.subject.keyword | Scattering,Kirchhoff,Born,Rytov, | en |
| dc.relation.page | 54 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2011-06-21 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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