这是一份andrews圣安德鲁斯大学 MT2507作业代写的成功案例
The coordinates of four boundary faces generated in two dimensions, with the help of adaptation methods, can be written in vector form as:
$$
\begin{array}{ll}
\mathbf{a}{l}(\eta)=\mathbf{r}\left(\xi{l}, \eta\right), & l=1,2 \
\mathbf{b}{l}(\xi)=\mathbf{r}\left(\xi, \eta{l}\right), & l=1,2
\end{array}
$$
where the coordinates of the transformed computational coordinate system, $\xi$ and $\eta$, are:
$\xi=\frac{(i-1)}{(I-1)}$ and $\eta=\frac{(j-1)}{(J-1)}$
$i$ and $j$ denote point numbers in physical coordinates while $I$ and $J$ are the overall number of points on these coordinates. As defined by the transfinite mapping method, the coordinates of the interior points are given as:
MT2507 COURSE NOTES ：
The simplest method of obtaining blending functions is by Lagrange interpolation:
$$
\begin{array}{ll}
\alpha_{1}(\xi)=1-\xi & \alpha_{2}(\xi)=\xi \
\beta_{1}(\eta)=1-\eta & \beta_{2}(\eta)=\eta
\end{array}
$$
Applying (3.37) to equation (3.36) gives the inner mesh points as:
$$
\begin{aligned}
&x(\xi, \eta)=(1-\xi) X_{1}(\xi, \eta)+\xi X_{2}(\xi, \eta) \
&y(\xi, \eta)=(1-\eta) Y_{1}(\xi, \eta)+\eta Y_{2}(\xi, \eta)
\end{aligned}
$$