Super-geometric Convergence of Trefftz Method for Helmholtz Equation
碩士 === 國立中山大學 === 應用數學系研究所 === 100 === In literature Trefftz method normally has geometric (exponential) convergence. Recently many scholars have found that spectral method in some cases can converge faster than exponential, which is called super-geometric convergence. Since Trefftz method can be re...
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| Format: | Others |
| Language: | en_US |
| Published: |
2012
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| Online Access: | http://ndltd.ncl.edu.tw/handle/37809285399032168039 |
| Summary: | 碩士 === 國立中山大學 === 應用數學系研究所 === 100 === In literature Trefftz method normally has geometric (exponential) convergence. Recently many scholars have found that spectral method in some cases can converge faster than exponential, which is called super-geometric convergence. Since Trefftz method can be regarded as a kind of spectral method, we expect it might possess super-geometric convergence too. In this thesis, we classify all types of super-geometric convergence and compare their speeds. We develop a method to decide the convergent type of given error data. Finally we can observe in many numerical experiments the super-geometric convergence of Trefftz method to solve Helmholtz boundary value problems.
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