FElupe documentation#
FElupe is a Python 3.8+ 🐍 finite element analysis package 📦 focussing on the formulation and numerical solution of nonlinear problems in continuum mechanics 🔧 of solid bodies 🚂. Its name is a combination of FE (finite element) and the german word Lupe 🔍 (magnifying glass) as a synonym for getting an insight 📖 how a finite element analysis code 🧮 looks like under the hood 🕳️.
Highlights
high-level finite-element-analysis API
flexible building blocks for finite element assembly
hyperelastic
integral (weak) forms
straight-forward definition of
mixed-fields
Installation#
Install Python, fire up 🔥 a terminal and run 🏃
pip install felupe[all]
where [all]
is a combination of [io,parallel,plot,progress,view]
and installs all optional dependencies. FElupe has minimal requirements, all available at PyPI supporting all platforms.
numpy for array operations
scipy for sparse matrices
tensortrax for automatic differentiation
In order to make use of all features of FElupe 💎💰💍👑💎, it is suggested to install all optional dependencies.
Extension Packages#
The capabilities of FElupe may be enhanced with extension packages created by the community.
Package |
Description |
---|---|
Constitutive hyperelastic material formulations |
|
Material Definition with Automatic Differentiation (AD) |
|
Math on Hyper-Dual Tensors with Trailing Axes (bundled with FElupe) |
|
A visualization tool for FElupe |
Performance#
This is a simple benchmark to compare assembly times for linear elasticity and hyperelasticity on tetrahedrons.
Analysis |
DOF/s |
---|---|
Linear-Elastic |
136193 +/-22916 |
Hyperelastic |
100613 +/-18702 |
Tested on: Windows 10, Python 3.11, Intel® Core™ i7-11850H @ 2.50GHz, 32GB RAM.
from timeit import timeit
import matplotlib.pyplot as plt
import numpy as np
import felupe as fem
def pre_linear_elastic(n, **kwargs):
mesh = fem.Cube(n=n).triangulate()
region = fem.RegionTetra(mesh)
field = fem.FieldContainer([fem.Field(region, dim=3)])
umat = fem.LinearElastic(E=1, nu=0.3)
solid = fem.SolidBody(umat, field)
return mesh, solid
def pre_hyperelastic(n, **kwargs):
mesh = fem.Cube(n=n).triangulate()
region = fem.RegionTetra(mesh)
field = fem.FieldContainer([fem.Field(region, dim=3)])
umat = fem.NeoHookeCompressible(mu=1.0, lmbda=2.0)
solid = fem.SolidBody(umat, field)
return mesh, solid
print("# Assembly Runtimes")
print("")
print("| DOF | Linear-Elastic in s | Hyperelastic in s |")
print("| ------- | ------------------- | ----------------- |")
points_per_axis = np.round((np.logspace(3, 5, 6) / 3)**(1 / 3)).astype(int)
number = 3
parallel = False
runtimes = np.zeros((len(points_per_axis), 2))
for i, n in enumerate(points_per_axis):
mesh, solid = pre_linear_elastic(n)
matrix = solid.assemble.matrix(parallel=parallel)
time_linear_elastic = (
timeit(lambda: solid.assemble.matrix(parallel=parallel), number=number) / number
)
mesh, solid = pre_hyperelastic(n)
matrix = solid.assemble.matrix(parallel=parallel)
time_hyperelastic = (
timeit(lambda: solid.assemble.matrix(parallel=parallel), number=number) / number
)
runtimes[i] = time_linear_elastic, time_hyperelastic
print(
f"| {mesh.points.size:7d} | {runtimes[i][0]:19.2f} | {runtimes[i][1]:17.2f} |"
)
dofs_le = points_per_axis ** 3 * 3 / runtimes[:, 0]
dofs_he = points_per_axis ** 3 * 3 / runtimes[:, 1]
print("")
print("| Analysis | DOF/s |")
print("| -------------- | ----------------- |")
print(
f"| Linear-Elastic | {np.mean(dofs_le):5.0f} +/-{np.std(dofs_le):5.0f} |"
)
print(f"| Hyperelastic | {np.mean(dofs_he):5.0f} +/-{np.std(dofs_he):5.0f} |")
plt.figure()
plt.loglog(
points_per_axis ** 3 * 3,
runtimes[:, 1],
"C0",
label=r"Stiffness Matrix (Hyperelastic)",
)
plt.loglog(
points_per_axis ** 3 * 3,
runtimes[:, 0],
"C1--",
label=r"Stiffness Matrix (Linear-Elastic)",
)
plt.xlabel(r"Number of degrees of freedom $\longrightarrow$")
plt.ylabel(r"Runtime in s $\longrightarrow$")
plt.legend()
plt.tight_layout()
plt.savefig("benchmark.png")
License#
FElupe - Finite Element Analysis (C) 2021-2024 Andreas Dutzler, Graz (Austria).
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program. If not, see https://www.gnu.org/licenses/.