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| 研究生： |
周成芳 Chou, Cheng-Fang |
|---|---|
| 論文名稱： |
使用有安德森加速的不連續有限元素法求解具奇異性的p-拉普拉斯方程 Numerical solution of p-Laplace equations with singularity using local discontinuous Galerkin method with Anderson acceleration |
| 指導教授： |
陳旻宏
Chen, Min-Hung |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系應用數學碩博士班 Department of Mathematics |
| 論文出版年： | 2025 |
| 畢業學年度： | 113 |
| 語文別： | 英文 |
| 論文頁數： | 60 |
| 中文關鍵詞： | p-拉普拉斯 、不連續有限元素法 、安德森加速 |
| 外文關鍵詞： | p-Laplace, Local discontinuous Galerkin method, Anderson acceleration |
| 相關次數： | 點閱：21 下載：0 |
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本文旨在研究源於淺冰架近似的 p-拉普拉斯問題，由於淺冰架近似可轉為具有奇異性的 p-拉普拉斯方程，我們引入正則化參數來處理奇異點。我們使用不連續有限元素法求解此方程，並加入安德森加速方法來加速收斂。數值實驗顯示，在光滑問題中，該方法具有良好的收斂性；即使在具有奇異性的情況下，亦展現出穩定的結果。
This thesis focuses on the numerical study of the p-Laplace problem arising from the Shallow Shelf Approximation (SSA) in glacier modeling. The SSA model can be reformulated as a p-Laplace system, which naturally gives rise to singularities when the gradient vanishes. To handle these singularities, a regularization parameter δ is introduced. We aim to develop an efficient numerical method to solve the p-Laplace equations. We employ the Local Discontinuous Galerkin (LDG) method to solve the system and adopt the Anderson acceleration to speed up. Numerical experiments demonstrate convergent behavior in smooth problems and show that the method remains effective in the presence of singularities.
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校內：2026-08-31公開校外：2026-08-31公開