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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 洪宏基 | |
| dc.contributor.author | Kuan-Fu Lin | en |
| dc.contributor.author | 林冠甫 | zh_TW |
| dc.date.accessioned | 2021-06-14T16:46:12Z | - |
| dc.date.available | 2009-08-04 | |
| dc.date.copyright | 2008-08-04 | |
| dc.date.issued | 2008 | |
| dc.date.submitted | 2008-07-30 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/40382 | - |
| dc.description.abstract | 對於待求場量為調和函數 (即控制方程式為拉普拉斯方程式) 之平面問題, 若以複數形式來呈現, 則在進行解題及分析上極為有效, 因複變分析擁有強大的運算能力及豐富完整的函數論. 有鑑於此, 本論文擬在保有這些特性的情況下, 將之由二維推廣至高維的邊界積分方程式來處理調和函數問題. 考慮到實際問題的需要, 在此推導出的奇異與超奇異邊界積分方程式, 皆適用於任意形狀的邊界問題, 即便是包含角點的邊界. 我們亦證實了實變數、複變數、四元數與克氏值的邊界積分方程式之間存在著關連性, 同時三套克氏值的邊界積分方程式亦可彼此轉換. | zh_TW |
| dc.description.abstract | It is well known that plane problems of harmonic functions are analyzed and solved effectively when expressed in the form of complex variables. This effectiveness is generally attributed to the powerful techniques of complex analysis and the richness of complex function theory. In view of this, the present thesis is aimed to extend the techniques to n-dimensional problems of boundary integral equations (BIEs) for harmonic field variables. Regarding usefulness for practical purposes, we derive singular and hypersingular BIEs not only for points on smooth boundaries but also for corner boundary points. The relations of real, complex, quaternion, and Clifford valued BIEs are explored. In Clifford valued BIEs, the three types of functions of are treated. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-14T16:46:12Z (GMT). No. of bitstreams: 1 ntu-97-R95521230-1.pdf: 1629997 bytes, checksum: f07193c7e99f5e252731ce429c97ec2d (MD5) Previous issue date: 2008 | en |
| dc.description.tableofcontents | Acknowledgements i
Abstract(Chinese) ii Abstract(English) iii Contents iv List of figures vi 1 Introduction 1 1.1 Motivation 1 1.2 Literature reviews 1 1.3 Framework 3 2 Boundary integral equations in R 5 2.1 Singular BIE 5 2.2 Hypersingular BIE 9 2.3 Summary 12 3 Boundary integral equations in C 13 3.1 Complex differential operators 13 3.2 Singular BIE from Borel-Pompeiu formula 14 3.3 Hypersingular BIE from Borel-Pompeiu formula 17 3.4 Real variable BIEs from complex variable BIEs 20 3.4.1 Singular BIE 20 3.4.2 Hypersingular BIE 21 3.5 Summary 23 4 Quaternionic algebra H and quaternionic analysis 24 4.1 Real quaternion 24 4.2 Complex quaternion 25 4.3 Pure quaternion 25 4.4 Reduced quaternion 26 4.5 Summary 27 5 Boundary integral equation in C`0,n 28 5.1 Clifford algebra and Clifford analysis in C`0,n 28 5.2 Singular BIE 30 5.3 Relations of BIEs 32 5.3.1 C`0,1 32 5.3.2 C`0,2 33 5.3.3 C`0,3 34 5.4 Summary 34 6 Boundary integral equation in C`n 35 6.1 Clifford algebra and Clifford analysis in C`n 35 6.2 Singular BIE 36 6.3 Relations of BIEs 39 6.3.1 C`1 39 6.3.2 C`2 39 6.3.3 C`3 40 6.4 C`0,n, C`n and C`0,n−1 41 6.5 Summary 42 7 Application 43 7.1 Physical problem 43 8 Conclusion and future work 45 8.1 Conclusion 45 8.2 Future work 46 References 47 | |
| dc.language.iso | en | |
| dc.subject | 超奇異邊界積分方程式 | zh_TW |
| dc.subject | 奇異邊界積分方程式 | zh_TW |
| dc.subject | 拉普拉斯方程式 | zh_TW |
| dc.subject | 狄氏方程式 | zh_TW |
| dc.subject | 複變分析 | zh_TW |
| dc.subject | 克氏分析 | zh_TW |
| dc.subject | Laplace equation | en |
| dc.subject | Dirac equation | en |
| dc.subject | complex analysis | en |
| dc.subject | singular boundary integral equation | en |
| dc.subject | hypersingular boundary integral equation | en |
| dc.subject | Clifford analysis | en |
| dc.title | 克氏分析之邊界積分方程式 | zh_TW |
| dc.title | Boundary Integral Equations in Clifford Analysis | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 96-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 楊德良,黃燦輝,陳正宗 | |
| dc.subject.keyword | 奇異邊界積分方程式,超奇異邊界積分方程式,拉普拉斯方程式,狄氏方程式,複變分析,克氏分析, | zh_TW |
| dc.subject.keyword | singular boundary integral equation,hypersingular boundary integral equation,Laplace equation,Dirac equation,complex analysis,Clifford analysis, | en |
| dc.relation.page | 49 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2008-07-31 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 土木工程學研究所 | zh_TW |
| 顯示於系所單位： | 土木工程學系 | |
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