本文將採用有限差分法中的虛擬邊界法於非交錯性直角座標網格系統，模擬不規則形狀物體之熱傳導以及金屬材料透過模具成型之問題。使用此方法在進行求解時，不需要配合物體的複雜幾何形狀做網格產生以及進行不同的網格座標轉換，如此一來能使計算速度大幅增加，並且保持答案的準確性。
從不規則形狀物體之熱傳導的模擬結果中可以發現利用此方法所計算出的溫度場具有相當高的準確性。而雖然金屬成型的模擬結果有所錯誤，但並不是此方法出現問題，而是在應力分析時缺少應力波方程式才導致這樣的結果。

In this study, we apply virtual boundary method of finite difference method with non-staggered coordinate grid system to simulate heat conduction of the irregularly shaped object and the metal forming problem. This method doesn't need to match the complex geometry of the object to do the grid generation and the conversion in different grid coordinates, so that the calculating time can be reduced and keep the accuracy at the same time.
From the simulation results of the heat conduction of irregularly shaped object, the answer calculated by this method is very accurate. While the simulation results of metal forming are wrong, this is not a problem with this method, but rather the lack of stress wave equation in stress analysis causes this result.

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