本文以等參幾何分析(IGA)方法為基礎，以非均勻有理B樣條(NURBS)為形狀函數近似物理場，利用NURBS在引入權重後能完美近似無理函數的特性，使近似出的物理量完整重建物理場。在電腦輔助設計中，NURBS調整權重後可以準確描述幾何形狀，例如圓形。因此權重是NURBS更有彈性描述幾何的關鍵變數。一般有限元素法近似物理場時是求解離散點上的物理量，在等參幾何法中分析物理問題時通常是在固定權重下的NURBS形狀函數以控制值作為變量求解。最佳化等參幾何法則以控制值及權重作為變數，計算權重後讓近似解更完整重建物理場。最佳化等參幾何法以最小二乘法及非線性迭代方法計算權重，並利用NURBS特性，使用曲線擬合邊界條件，計算邊界權重，讓邊界誤差最小化。以二維帕松方程式測試權重計算結果，最後將最佳化等參幾何法套用在穩態熱傳問題，最佳化結果能以較少的離散點數得到更精確的近似解。

This research is based on the iso-geometric analysis (IGA) method, which uses non-uniform rational B-splines (NURBS) as a shape function multiplied by control values to approximate physical fields. The NURBS function is a combination of B-splines and weights. In computer-aided design, NURBS can accurately describe geometric shapes, such as circles, because of introducing the weights which are used to describe irrational functions. Therefore, weights are one of the key variables in making NURBS more flexible in describing geometry. In general, the finite element method approximates physical fields by solving physical quantities at discrete points, while in IGA method, the weights are fixed as geometric weights and the control values are used as variables for solving physical problems. However, geometric fields are not necessarily related to physical fields. Therefore, in this research, we introduce the optimization method, which treat both control values and weights as nodal variables, to obtain better physical solution. The weights are calculated using least squares and non-linear iterative methods to allow a more complete reconstruction of the physical field. In addition, when dealing with irrational essential boundary conditions, we use curve fitting to fit the irrational boundary conditions and calculate the boundary weights to minimize the boundary error. Finally, the results of the weight calculation are tested against the two-dimensional Poisson's equation and the optimization of iso-geometric analysis method is applied to the steady-state heat transfer problem. The optimization results show that a more accurate approximate solution can be obtained with fewer discrete points.