Loading [MathJax]/extensions/TeX/boldsymbol.js
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\halfi}{{1/2}}
\newcommand{\xpoint}{\boldsymbol{x}}
\newcommand{\normalvec}{\boldsymbol{n}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
\newcommand{\Ix}{\mathcal{I}_x}
\newcommand{\Iy}{\mathcal{I}_y}
\newcommand{\It}{\mathcal{I}_t}
\newcommand{\setb}[1]{#1^0} % set begin
\newcommand{\sete}[1]{#1^{-1}} % set end
\newcommand{\setl}[1]{#1^-}
\newcommand{\setr}[1]{#1^+}
\newcommand{\seti}[1]{#1^i}
\newcommand{\Real}{\mathbb{R}}
Vectorized computations: mesh coordinates
Mesh with 30\times 30 cells: vectorization reduces the CPU
time by a factor of 70 (!).
Need special coordinate arrays xv and yv such that I(x,y)
and f(x,y,t) can be vectorized:
from numpy import newaxis
xv = x[:,newaxis]
yv = y[newaxis,:]
u_1[:,:] = I(xv, yv)
f_a[:,:] = f(xv, yv, t)
