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The Method of Fundamental Solutions for 2D Helmholtz Equation

In the thesis, the error and stability analysis is made for the 2D Helmholtz equation by the method of fundamental solutions (MFS) using both Bessel and Neumann functions. The bounds of errors in bounded simply-connected domains are derived, while the bounds of condition number are derived only for disk domains. The MFS using Bessel functions is more efficient than the MFS using Neumann functions. Interestingly, for the MFS using Bessel functions, the radius R of the source points is not necessarily larger than the maximal radius r_max of the solution domain. This is against the traditional condition: r_max < R for MFS. Numerical experiments are carried out to support the analysis and conclusions made.

Identiferoai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0620108-143959
Date20 June 2008
CreatorsLo, Lin-Feng
ContributorsZi-Cai Li, Tzon-Tzer Lu, Jeng-Tzong Chen, Der-Liang Young, Chien-Sen Huang
PublisherNSYSU
Source SetsNSYSU Electronic Thesis and Dissertation Archive
LanguageEnglish
Detected LanguageEnglish
Typetext
Formatapplication/pdf
Sourcehttp://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0620108-143959
Rightsoff_campus_withheld, Copyright information available at source archive

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