利用繪圖處理器平行運算技術計算電子電洞交換能

Abstract

本論文主要探討繪圖處理器平行運算技術計算電子電洞交換能，將庫侖交互作用積分式子離散化後程式中實質上是六重迴圈，因此我們將研究繪圖處理器對迴圈增快的速率。而後會介紹一些有關繪圖處理器的每個核心是如何運行的，以及記憶體的分配與傳遞方式，進而了解每個細節對迴圈增快的效益，使我們能更進一步了解程式碼在程式中執行的方式，讓程式的撰寫更順利。 程式中所使用的理論則是利用量子點 單能帶模型和有效質量近似法的激子系統計算庫侖交互作用，而庫侖交互作用分為直接庫侖作用與交換能。直接庫侖作用的計算則是引用建智學長論文[1]中的程式，將程式修改成使用繪圖處理器作程式平行運算即可；對於交換能而言，先前使用中央處理器單核心計算需耗費大量的時間，一直無法驗證程式的正確性，而後使用繪圖處理器計算時，相對於單核中央處理器時間減少10倍以上，因此我們將能驗證此程式的正確性並討論數值解與解析解的誤差，對於將來要計算庫侖矩陣以及交換能矩陣時，能計算的更迅速。

This thesis theoretically investigates GPU’s parallel computing technology for the computation of electron-hole exchange interaction energy, the Coulomb’s integration in the program is essentially the six loops, we will study the rate is accelerated by the GPU loop. Accelerated rate in order to study, will find some relevant information to understand, and thus to understand every detail of the loop to increase the amount of fast effective help when we write code, to further understand the code in the Fortran program is how to perform. When it calculates the Coulomb’s interaction, we are based on theory’s single-band model and effective mass approximation method of exciton’s system in the quantum dot to calculate, the Coulomb’s interaction divide into direct coulomb and exchange energy. Direct coulomb’s part have been calculated via Chien-Chih senior’s thesis[1], so long as the original program have to modify the GPU who can run the program；exchange energy’s part have been unable to verify the correctness of the program, the reason is that the program’s execution time is very long. When using the GPU run the program, it will speed up to 10 times than single-core CPU, so we will be able to verify the correctness of this program in short time(error less than 5%), calculating Coulomb’s matrix and exchange energy’s matrix in second quantization in the future can calculate more quickly.