平行架構與快速演算法應用於麻田散鐵與磁性材料微結構之研究

Abstract

本文(1)以開發平行架構從事形狀記憶合金微結構之數值模擬研究；(2)以發展快速傅立葉轉換計算鐵磁材料磁力耦合之數值模擬研究。 在形狀記憶合金中，本文以之前所發展之新式相場法為雛型，再利用MPI將整體改寫為平行版。所考量之問題為具有兩個方向之兄弟晶微結構材料，利用所開發之平行架構進行分析模擬，除得到正確的微結構分佈外，數值模擬效率亦大幅提昇。 在鐵磁材料中，本文以之前所發展之磁力互動模型為基本，再利用快速傅立葉轉換計算有界物體其應力引發之等效磁場，並配合九點高斯積分增加其準確度。所考量之問題為具大磁致伸縮應變之鐵磁薄膜，利用所開發之快速傅立葉轉換進行微磁域分析模擬，除得到正確的微磁域分佈外，所能劃分之網格數亦大幅提昇。

The goal of the present thesis has two folds. First, we develop an algorithm to simulate microstructure in shape-memory alloys with parallel computation. Second, we develop a fast algorithm (FFT) to compute magnetoelastic stress in ferromagnetic materials. For shape-memory alloys, a new MPI numerical structure is implemented in the code which was developed based on the novel phase-field method. The material in the present consideration has two variants. The results provide not only an accurate distribution of martensitic variants, but also show a significant reduction in time needed for simulation. For ferromagnetic materials, a fast algorithm is developed to compute the stress-induced magnetic field in a finite body. It is based on the Fast Fourier Transform and 9-point Gaussian integration. The material in the present consideration has large magnetostriction. The results provide not only an accurate distribution of magnetic domains, but also show a significant increase in simulation scales.