臺灣博碩士論文加值系統

在工業工程及食品製造業中管子穩定狀態的熱傳導與一個包含孔洞的無限平面相關。這裡探討許多在特定形狀的孔洞假設下的理論研究。

然而，平面上孔洞的一般形狀的解必須使用數值方法。拉普拉斯方程(Laplace’s equation)的解由緊緻的電荷密度可以得到基函數及電荷密度相乘的積分。基於均勻網格離散化及泰勒級數展開，所提出的數值方法具有二階精度，通過解析位能密度在廣義麥克勞林(Maclaurin)圓盤的驗證。

在快速傅里葉變換(FFT)的幫助下，數值計算複雜度從O(N2)降低到O(N log2 N)，其中N是一維區域的數量。最後，我們將其數值方法應用於多個圓形孔洞的現實中的工程問題上。

An infinite plane containing holes are related to steady state heat conduction of tube in engineering industry and food manufacturing industry. There many theoretical studies under the assumption of particular shapes of the holes are
explored.

However, the solutions of the plane of general shapes of holes have to employ the numerical approach. The solutions of Laplace’s equation given by the charge density of compact supported can be obtained by the integration of the product of the fundamental function and charge density. Based on the uniform grid discretization and Taylor series expansion, the proposed numerical method has the accuracy of second order verified by the analytic potential-density pair, the generalized Maclaurin disks.

With the help of fast Fourier transform, the numerical computation complexity is reduced from O(N2) to O(N log2 N), where N the total number of grid zones. Finally, we apply the numerical approach in the reality engineering problems of multiple circular holes.

1 Introduction.............................1
2 Potential and its calculation............2
3 Numerical Simulations....................8
4 Applications............................17
4.1 One hole..............................17
4.2 Multiple holes........................18
4.3 Two circles...........................22
5 Conclusion..............................23

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