Coarse Grained Molecular Dynamics (CGMD) 為分子動力學(MD)的一種延伸方法。此法能夠藉由擷取一團原子群重要特徵之方式，來達到以較少的節點數取代多數原子做運算之目的。因此CGMD不但能夠比MD節省運算時間，在多尺度的模擬上(multi-scale simulation)，更能針對其物理特性的不同，靈活的對系統做適當的尺度變換。

　　CGMD法簡化粒子數的方式主要是源自於有限元素法概念，其運動方程式的推導乃是由MD法經由統計力學之處理所求得，所以CGMD在處理多尺度問題時，由於系統內不同尺度仍處於相同的理論基礎，因此能夠成功解決跨尺度模擬時在接合面所產生之不連續問題。

　　儘管CGMD 擁有簡化粒子數與變換尺度之優點，但此法之發展仍處於萌芽階段，尤其是在勢能函數的處理上，尚有諸多限制存在。因此在本文中，除了對CGMD法做更完整的理論推導外，更將針對勢能函數由原子至節點之轉換，探討以下兩種近似法：第一種近似法是利用泰勒展開式的方式來對勢能做轉換；第二種方法則是藉由尋找新的材料參數的方式來對原子勢能做模擬轉換。此兩種方法，均能在CGMD法做平衡態模擬時有良好的模擬結果，然而對於材料之拉伸、壓縮、扭轉等之力學試驗中，若要正確的模擬，在勢能的處理上仍有諸多限制需要克服。因此針對此部分，本文亦將由理論及模擬結果兩方面切入，進一步探討其發生原因及改善之方向。

　　綜合以上所述，尋找適當方法來正確描述節點勢能將是解決CGMD法限制之關鍵。因此，如果能夠找到一組參數能夠適用到所有之力學行為，或找到恰當的勢能函數來對節點勢能做模擬，那麼就能夠成功的將原子間的運算轉換至節點。如此一來，CGMD法不單只是一種MD的簡化法，更是一個能夠跨足微觀與介觀尺度模擬之有效方法。

　Coarse Grained Molecular Dynamics (CGMD) is a technique for simulation extended from Molecular Dynamics (MD). It captures the important atomistic effects with fewer nodes instead of atoms so that CGMD can not only effectively save more computational cost than MD but it also can vary its scale to describe the system more appropriate in multi-scales simulation.

　The concept of CGMD utilizes Finite Element Method (FEM) to reduce the number of atoms. And the equations of motion are derived directly from MD through a statistical coarse graining procedure so that the different scales are run concurrently with the same model in multi-scale simulation. Therefore, this allows a seamless coupling of length scales.

　Despite its having above advantages, CGMD model is still in its infant. Especially in dealing with the potential function, it still exist some limitations. Therefore, except developing the CGMD theory, two approaches for atom/node transformation of potential function will be discussed in this thesis. First approach is taking advantage of Taylor series to describe the model; and second is describing the model by finding the “new parameters of material”. As the results of simulation, all of these two approaches have good performance in equilibrium state. However, considering the tension, torsion, and compression case, it still has some limitations in CGMD method. Therefore, this paper will explore the cause of limitation and discuss the way to improve the simulation base on theory and results of simulation as well.

　In conclusion, the determination of appropriate potential function for describing the CGMD model is the key to solve the limitations. As long as the potential function can well describe the behavior of node, CGMD can transform the calculations from atoms to nodes successfully. Therefore, CGMD will not only have the ability to simplify the MD but it also can accurate describe specific materials on length scales spanning from the microscopic to mesoscopic scale.

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