PyCUDA在熱傳導方程的應用

Abstract

在本篇論文中，我們將呈現解擴散方程的交替分組法(Alternating group method)，對於傳統前向差分法(Explicit Forward Method(、後向差分法(Implicit Backward Method)、克蘭克-尼科爾森法(Crank-Nicolson method)來說，交替分組法的精確度比較好，並且具有平行化的特性。當資料量放大時，傳統方法將會需要較長的計算時間，因此交替分組法在平行計算時間上可以明顯的縮短計算時間。本論文將透過PyCUDA平行化套件將此方法實現在GPU計算上，藉此取得在計算時間上的優勢。雖然GPU的單位計算精度較CPU的單位計算精度差，然而在最後的數值計算誤差比較上，交替分組法的CPU版本與GPU版本之間的誤差幾乎相同。若此問題擴展到二維或三維，其計算量更是龐大，因此交替分組法的GPU平行化經驗在數值計算上是必要的。

In this paper, we will present an alternating group method for solving diffusion equation. The alternating group method is more precise than the Explicit forward Euler method, the Implicit backward Euler method and Crank-Nicolson method. Moreover, the alternating group method can be easily implement to the parallel version. When the computational system become huge, the serial computing methods take more time than the parallel computing methods. Hence, the parallel alternating group method will take the adventage in computational time. We will demonstrate the GPU version of alternating group method by the PyCUDA packge in this thesis. Although the precision of the GPU hardware is worse than CPU, the numerical results between GPU and CPU have almost no difference. Because the computational cost of 2D or 3D problem is much higher than the 1D problem, the experience of GPU version of alternating group method is very important in this field.