本研究專為離散元素法(Discrete Element Method)建立一套離散元素法之模擬架構，並且應用繪圖處理器(Graphic processors)於離散元素法的計算上。
　　在計算方面，因離散元素法的計算時間除了受元素的數量影響之外，其時間步程數(Time step)的數量也是影響離散元素法計算時間的一項重要因素，也因此離散元素法在計算上將可能花費大量的時間。在本研究中，一方面除了需要挑選適當的碰撞搜尋演算法來減少搜尋離散元素的時間之外，亦可以選擇利用平行運算的方式，降低程式的執行運算時間。有鑑於此，本研究將初步探討並應用GPGPU(General-Purpose computing on graphics processing units)技術於離散元素法的計算之中。
　　本研究 1) 利用物件導向程式設計的概念並融合物件導向設計模式(Design Pattern)的方式，建立一套離散元素法的模擬架構；2) 結合離散元素法的物件導向架構與CUDA(Compute Unified Device Architecture)架構所發展出來的GPGPU程式，並將對於 1) 運算效能、2) 不同碰撞偵測結果，以及3) 不同浮點數精確度進行探討，且將在最後的結論一併探討本研究中，GPU的總體執行效能因何不如CPU的總體執行效能。

　　Discrete-element method (DEM) is a simulation method that has many potential applications in civil-engineering such as rock-fall, sand behaviors, etc. However, DEM currently has little practical applications due to its computational requirements. Realistic DEM simulations often involves thousands of discrete objects and requires many time increments. Therefore, in order to reduce overall computation time for DEM simulations, a object-oriented code written in C++ is developed in this work to incorporate graphics processing units (GPU) in discrete-element simulations. GPUs are specialized processors for graphics-processing, but has been adopted for general-purpose computing in recent years for their superior floating-point calculation capabilities than general-purpose central processing units.
　　In this study, in order to ensure the developed code can be extended and maintained easily, design patters in object-oriented programming are utilized to develop a DEM software framework. The developed software framework is then implemented using C++ programming language, and then performance-profiled to identify the bottleneck in a DEM simulation. The identified bottleneck code is then modified to incorporate GPU computation using CUDA. Finally, by using the developed code, the 1) performance, 2) results between different contact-detection methods or using different processors, and 3) single-precision versus double-precision were evaluated. Finally, some recommendations on using GPU for DEM simulations were discussed.

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