The following is a quick start guide to running your first Nutils simulation in three simple steps. Afterward, be sure to read the installation guide for extra installation instructions, study the tutorial to familiarize yourself with Nutils' concepts and syntax, and explore the examples for inspiration.
With Python version 3.7 or newer installed, Nutils and Matplotlib can be installed via the Python Package Index using the pip package installer. In a terminal window:
python -m pip install --user nutils matplotlib
Note that Nutils depends on Numpy, Treelog and Stringly, which means that these modules are pulled in automatically if they were not installed prior. Though most Nutils applications will require Matplotlib for visualization, it is not a dependency for Nutils itself, and is therefore installed explicitly.
Open a text editor and create a file
poisson.py with the following contents:
from nutils import mesh, function, solver, export, cli def main(nelems: int = 10, etype: str = 'square'): domain, x = mesh.unitsquare(nelems, etype) u = function.dotarg('udofs', domain.basis('std', degree=1)) g = u.grad(x) J = function.J(x) cons = solver.optimize('udofs', domain.boundary.integral(u**2 * J, degree=2), droptol=1e-12) udofs = solver.optimize('udofs', domain.integral((g @ g / 2 - u) * J, degree=1), constrain=cons) bezier = domain.sample('bezier', 3) x, u = bezier.eval([x, u], udofs=udofs) export.triplot('u.png', x, u, tri=bezier.tri, hull=bezier.hull) cli.run(main)
Note that while we could make the script even shorter by avoiding the main
cli.run, the above structure is preferred as it automatically
sets up a logging environment, activates a matrix backend and handles command
Back in the terminal, the simulation can now be started by running:
This should produce the following output:
nutils v7.0 optimize > constrained 40/121 dofs optimize > optimum value 0.00e+00 optimize > solve > solving 81 dof system to machine precision using arnoldi solver optimize > solve > solver returned with residual 6e-17 optimize > optimum value -1.75e-02 u.png log written to file:///home/myusername/public_html/poisson.py/log.html
If the terminal is reasonably modern (Windows users may want to install the new Windows Terminal) then the messages are coloured for extra clarity. The last line of the log shows the location of the simultaneously generated html file that holds the same log, as well as a link to the generated image.
To run the same simulation on a mesh that is finer and made up or triangles instead of squares, arguments can be provided on the command line:
python poisson.py nelems=20 etype=triangle