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A fast hp-FEA program for the membrane Poisson equation

c(Δu) = -f 

using variable order triangle elements (orders 1-20) with heterogeneous p-refinement.


Use the package manager pip to install PlanarPy.

pip install planarpy


The Mesh object requires a list of point tuples, pts = [(x0,y0), (x1,y1), ...], a list triangle node tuples, cells = [(0,1,2), (2,5,6), ...], and a base power, pow = 2, to initialize.

Define groups using boolean functions. Always use both coordinates x,y for all function definitions. Groups are used to define Dirichlet boundary conditions and may also be used to set volume forces on part of the domain. If no group is chosen when setting a volume force, a default group is used.

from planarpy import Mesh, Dom, sin, cos

# it is up to the user to define points and cells
# either manually or by using a foreign library.
# here the domain is assumed to be [-10, 10]x[-10, 10]
# enable the reverse Cuthill Mckee algorithm (rcm) for 
# increased memory alignment 
mesh = Mesh(pts, cells, 1, rcm=True)

# define groups
outer = mesh.def_group(lambda x, y: x == -10. or x == 10. or y == -10. or y == 10.)
left_half = mesh.def_group(lambda x, y: x <= 0.)

# p-refinement 
mesh.adapt_p(left_half, 10)

# domain setup
dom = Dom(mesh)

# define Dirichlet boundary
# get the amount of free and constrained degrees of freedom
pos_dofs, neg_dofs = dom.dofs()
# set material constant c
# set boundary condition, default is 0
dom.embed_bcond(lambda x, y: [sin(x) + cos(y)], outer)
# set force in the domain
dom.set_force(lambda x, y: [sin(x) + cos(y)])

# solve

# measure error with an exact solution
err = dom.err(lambda x, y: [sin(x) + cos(y)])


PlanarPy offers three functions in order to extract graphical data in the form of lines

# mesh plot
sys = dom.plot_sys()
# displacement plot with 5 segments per line
disp = dom.plot_disp()
# displacement plot with a given 
# number of segments per line
smooth = dom.plot_smooth(50)

The functions return three lists, x, y, z, for line coordinates.


Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.

Please make sure to update tests as appropriate.


PlanarPy is licensed under GNU LGPLv3.

This software relies on the PyO3 library under the Apache-2.0 license for ffi and on the rayon crate under the MIT and Apache-2.0 licenses for parallelism.

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