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研究生: 謝博宇
Shieh, Po-Yu
論文名稱: 顯卡加速技術於時變波方程不連續有限元方法之應用
GPU Acceleration on the RKDG methods for Time dependent Wave Equations
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: 2011
畢業學年度: 99
語文別: 中文
論文頁數: 37
中文關鍵詞: 高階數值方法不連續有限元素法波動方程GPU加速CUDA
外文關鍵詞: High-order method, Discontinuous Galerkin method, Elastic wave equations, GPU, CUDA
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  • 本文中,將使用高階不連續有限元素法解決波動方程及其相關的模型問題。
    同時使用GPU來提升計算速度,而為了提高計算上的效能,將設定網格為平行四邊形。
    計算結果將會看到當計算量足夠大的時候,GPU將可以有效的提高計算速度達20倍以上的效能。

    In this work, we develop a high-order Runge-Kutta Discontinuous Galerkin (RKDG) method to solve the two-dimensional time-dependent wave equations and use GPU to speedup the computation.

    1 簡介 1 2 二維傳輸方程式 3 2.1 模型與穩定性分析 3 2.2 數值計算格式及穩定性 4 3 二維波動方程式 7 3.1 模型介紹 7 3.2 數值計算格式及穩定性 8 4 二維彈性波方程式 10 4.1 模型介紹 10 4.2 數值計算格式 11 5 時間迭代與基底函數 13 5.1 SSP-RK方法 13 5.2 Legendre多項式 14 6 GPU-CUDA介紹及網格設定 15 6.1 GPU-CUDA介紹 15 6.2 CUDA在DG計算上的想法 17 6.3 平行四邊形網格設定 18 7 數值結果 21 7.1 誤差及收斂階數計算 22 7.2 二維傳輸方程 23 7.3 二維波動方程 26 7.4 二維彈性波方程 28 8 結論 31 參考文獻 32

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