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fc-hypermesh-0.1.1
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مشاهده بیشترتوضیحات
Generate conforming meshes of hypercubes, hyperrectangles or of any d-orthotopes by simplices or orthotopes with their m-faces
| ویژگی | مقدار |
|---|---|
| سیستم عامل | - |
| نام فایل | fc-hypermesh-0.1.1 |
| نام | fc-hypermesh |
| نسخه کتابخانه | 0.1.1 |
| نگهدارنده | [] |
| ایمیل نگهدارنده | [] |
| نویسنده | Francois Cuvelier |
| ایمیل نویسنده | cuvelier@math.univ-paris13.fr |
| آدرس صفحه اصلی | http://www.math.univ-paris13.fr/~cuvelier/software |
| آدرس اینترنتی | https://pypi.org/project/fc-hypermesh/ |
| مجوز | BSD |
.. _fc-hypermesh: http://www.math.univ-paris13.fr/~cuvelier/software/Python/fc-hypermesh.html
.. _www.python.org: http://www.python.org/
.. _Miniconda: https://conda.io/miniconda.html
.. _Anaconda: https://www.anaconda.com
.. _Canopy: https://www.enthought.com/product/canopy/
.. _Mayavi: http://docs.enthought.com/mayavi/mayavi/
.. _Matplotlib: https://matplotlib.org/
.. _hypermesh-report: https://hal.archives-ouvertes.fr/hal-01638329/file/hypermesh_0.1.1%20%281%29.pdf
.. image:: http://www.math.univ-paris13.fr/~cuvelier/software/codes/Python/fc-hypermesh/pyfc-hypermesh_400.png
:width: 400px
:align: center
The **fc\_hypermesh** Python package allows to generate conforming meshes
of hypercubes, hyperrectangles or of any d-orthotopes by p-order simplices or orthotopes with their m-faces
Introduction:
-------------
__ hypermesh-report_
.. image:: http://www.math.univ-paris13.fr/~cuvelier/images/icons/HALv3_78x78.png
:target: https://hal.archives-ouvertes.fr/hal-01638329
:align: left
:alt: sysfs line plot
:width: 55px
This implements `Vectorized algorithms for regular and conforming tessellations of d-orthotopes and their faces with high-order orthotopes or simplicial elements, Cuvelier F., 2019`__
.. _fc\_hypermesh Python package: http://www.math.univ-paris13.fr/~cuvelier/software/fc-hypermesh-Python.html
More documentation is available on `fc\_hypermesh Python package`_ dedicated web page.
Installation:
-------------
The **fc\_hypermesh** Python package is available from the Python Package Index, so to install/upgrade simply do
.. code::
pip install fc_hypermesh -U
Thereafter, it's possible to run one of the demo functions
.. code:: python
import fc_hypermesh
fc_hypermesh.demos.demo01()
Examples usage:
---------------
- Meshing the rectangle [-1,1]x[0,1] by simplices with 12+1 points in
x-axis and 5+1 points in y-axis:
.. code:: python
from fc_hypermesh import OrthMesh
oTh=OrthMesh(2,[12,5],type='simplex',box=[[-1,1],[0,1]])
print(oTh)
The output of the ``print(oTh)`` command is::
OrthMesh object
d : 2
order : 1
box : [[-1.0, 1.0], [0.0, 1.0]]
mapping : None
Mesh (order,type,nq,nme) : (1,simplex,78,120)
Number of 1-faces : 4
[ 0] (order,type,nq,nme) : (1,simplex,6,5)
[ 1] (order,type,nq,nme) : (1,simplex,6,5)
[ 2] (order,type,nq,nme) : (1,simplex,13,12)
[ 3] (order,type,nq,nme) : (1,simplex,13,12)
Number of 0-faces : 4
[ 0] (order,type,nq,nme) : (1,simplex,1,1)
[ 1] (order,type,nq,nme) : (1,simplex,1,1)
[ 2] (order,type,nq,nme) : (1,simplex,1,1)
[ 3] (order,type,nq,nme) : (1,simplex,1,1)
If ``matplotlib`` package is installed one can represent the mesh
.. code:: python
from fc_tools.graphics import set_axes_equal
import matplotlib.pyplot as plt
plt.ion()
plt.figure(1)
oTh.plotmesh(legend=True)
plt.figure(2)
oTh.plotmesh(m=1,legend=True,linewidth=3)
plt.axis('off')
set_axes_equal()
.. |OrthMesh_2D_simplicial_fig1| image:: http://www.math.univ-paris13.fr/~cuvelier/software/codes/Python/fc-hypermesh/snapshots/OrthMesh_2D_simplicial_fig1_Python374.png
:width: 300
:align: middle
.. |OrthMesh_2D_simplicial_fig2| image:: http://www.math.univ-paris13.fr/~cuvelier/software/codes/Python/fc-hypermesh/snapshots/OrthMesh_2D_simplicial_fig2_Python374.png
:width: 300
:align: middle
+-------------------------------+-------------------------------+
| |OrthMesh_2D_simplicial_fig1| | |OrthMesh_2D_simplicial_fig2| |
+-------------------------------+-------------------------------+
- Meshing the rectangular cuboid [-1,1]x[0,1]x[0,2] by simplices with 11+1 points in
x-axis, 5+1 points in y-axis and 10+1 points in z-axis:
.. code:: python
from fc_hypermesh import OrthMesh
oTh=OrthMesh(3,[10,5,10],box=[[-1,1],[0,1],[0,2]])
If ``matplotlib`` package is installed one can represent the mesh
.. code:: python
from fc_tools.graphics import set_axes_equal
import matplotlib.pyplot as plt
plt.ion()
plt.figure(1)
oTh.plotmesh(legend=True,linewidth=0.5)
set_axes_equal()
plt.figure(2)
oTh.plotmesh(m=2,legend=True,edgecolor=[0,0,0])
plt.axis('off')
set_axes_equal()
.. |OrthMesh_3D_simplicial_fig1| image:: http://www.math.univ-paris13.fr/~cuvelier/software/codes/Python/fc-hypermesh/snapshots/OrthMesh_3D_simplicial_fig1_Python374.png
:width: 300
:align: middle
.. |OrthMesh_3D_simplicial_fig2| image:: http://www.math.univ-paris13.fr/~cuvelier/software/codes/Python/fc-hypermesh/snapshots/OrthMesh_3D_simplicial_fig2_Python374.png
:width: 300
:align: middle
+-------------------------------+-------------------------------+
| |OrthMesh_3D_simplicial_fig1| | |OrthMesh_3D_simplicial_fig2| |
+-------------------------------+-------------------------------+
- Meshing the rectangle [-1,1]x[0,1] by orthotopes with 12+1 points in
x-axis, 5+1 points in y-axis and 10+1 points in z-axis:
.. code:: python
from fc_hypermesh import OrthMesh
oTh=OrthMesh(2,[12,5],type='orthotope',box=[[-1,1],[0,1]])
If ``matplotlib`` package is installed one can represent the mesh
.. code:: python
from fc_tools.graphics import set_axes_equal
import matplotlib.pyplot as plt
plt.ion()
plt.figure(1)
oTh.plotmesh(legend=True)
set_axes_equal()
plt.figure(2)
oTh.plotmesh(m=1,legend=True,linewidth=3)
plt.axis('off')
set_axes_equal()
.. |OrthMesh_2D_orthotope_fig1| image:: http://www.math.univ-paris13.fr/~cuvelier/software/codes/Python/fc-hypermesh/snapshots/OrthMesh_2D_orthotope_fig1_Python374.png
:width: 300
:align: middle
.. |OrthMesh_2D_orthotope_fig2| image:: http://www.math.univ-paris13.fr/~cuvelier/software/codes/Python/fc-hypermesh/snapshots/OrthMesh_2D_orthotope_fig2_Python374.png
:width: 300
:align: middle
+------------------------------+------------------------------+
| |OrthMesh_2D_orthotope_fig1| | |OrthMesh_2D_orthotope_fig2| |
+------------------------------+------------------------------+
- Meshing the rectangular cuboid [-1,1]x[0,1]x[0,2] by orthotopes with 11+1 points in
x-axis, 5+1 points in y-axis and 10+1 points in z-axis:
.. code:: python
from fc_hypermesh import OrthMesh
oTh=OrthMesh(3,[10,5,10],type='orthotope', box=[[-1,1],[0,1],[0,2]])
If ``matplotlib`` package is installed one can represent the mesh
.. code:: python
from fc_tools.graphics import set_axes_equal
import matplotlib.pyplot as plt
plt.ion()
plt.figure(1)
oTh.plotmesh(legend=True,linewidth=0.5)
set_axes_equal()
plt.figure(2)
oTh.plotmesh(m=2,legend=True,edgecolor=[0,0,0])
plt.axis('off')
set_axes_equal()
.. |OrthMesh_3D_orthotope_fig1| image:: http://www.math.univ-paris13.fr/~cuvelier/software/codes/Python/fc-hypermesh/snapshots/OrthMesh_3D_orthotope_fig1_Python374.png
:width: 300
:align: middle
.. |OrthMesh_3D_orthotope_fig2| image:: http://www.math.univ-paris13.fr/~cuvelier/software/codes/Python/fc-hypermesh/snapshots/OrthMesh_3D_orthotope_fig2_Python374.png
:width: 300
:align: middle
+------------------------------+------------------------------+
| |OrthMesh_3D_orthotope_fig1| | |OrthMesh_3D_orthotope_fig2| |
+------------------------------+------------------------------+
Testing :
---------
There are eight demos functions in the ``fc_hypermesh.demos`` module named ``demo01`` to ``demo08``.
The source code is in module ``demos.py``.
For example, run the following code under Python:
.. code:: python
import fc_hypermesh
fc_hypermesh.demos.demo01()
Benchmarking:
-------------
- Bench of the ``OrthMesh`` constructor for a 3-dimensional orthotope tessellated with (order 1) simplices.
.. code:: python
import fc_hypermesh
fc_hypermesh.bench(3,range(20,170,20),type='simplex',box=[[-1,1],[-1,1],[-1,1]])
The output of this code is::
#---------------------------------------------------------------------------
# computer: zbook17
# system: Ubuntu 18.04.3 LTS (x86_64)
# processor: Intel(R) Core(TM) i7-4800MQ CPU @ 2.70GHz
# (1 procs/4 cores by proc/2 threads by core)
# RAM: 31.3 Go
# software: Python
# release: 3.7.6
#---------------------------------------------------------------------------
# fc_hypermesh.OrthMesh constructor with
# d =3
# type =simplex
# order =1
# box =[[-1, 1], [-1, 1], [-1, 1]]
# mapping=None
#---------------------------------------------------------------------------
#date:2019-12-29_14-13-35
#nbruns:5
#numpy: i8 i8 i8 f8
#format: {:>7d} {:>10d} {:>10d} {:11.3f}
#labels: N nq nme OrthMesh(s)
20 9261 48000 0.196
40 68921 384000 0.209
60 226981 1296000 0.302
80 531441 3072000 0.411
100 1030301 6000000 0.576
120 1771561 10368000 0.840
140 2803221 16464000 1.197
160 4173281 24576000 1.679
- Bench of the ``OrthMesh`` constructor for a 3-dimensional orthotope tessellated with 3-order simplices.
.. code:: python
import fc_hypermesh
fc_hypermesh.bench(3,range(10,61,10),order=3,type='simplex',box=[[-1,1],[-1,1],[-1,1]])
The output of this code is::
#---------------------------------------------------------------------------
# computer: zbook17
# system: Ubuntu 18.04.3 LTS (x86_64)
# processor: Intel(R) Core(TM) i7-4800MQ CPU @ 2.70GHz
# (1 procs/4 cores by proc/2 threads by core)
# RAM: 31.3 Go
# software: Python
# release: 3.7.6
#---------------------------------------------------------------------------
# fc_hypermesh.OrthMesh constructor with
# d =3
# type =simplex
# order =3
# box =[[-1, 1], [-1, 1], [-1, 1]]
# mapping=None
#---------------------------------------------------------------------------
#date:2019-12-29_14-26-34
#nbruns:5
#numpy: i8 i8 i8 f8
#format: {:>7d} {:>10d} {:>10d} {:11.3f}
#labels: N nq nme OrthMesh(s)
10 29791 6000 0.143
20 226981 48000 0.222
30 753571 162000 0.269
40 1771561 384000 0.357
50 3442951 750000 0.500
60 5929741 1296000 0.733
- Bench of the ``OrthMesh`` constructor for a 5-dimensional orthotope tessellated with (order 1) orthotopes.
.. code:: python
import fc_hypermesh
fc_hypermesh.bench(5,[5,10,15,20,25,27],type='orthotope',box=[[-1,1],[-1,1],[-1,1],[-1,1],[-1,1]])
The output of this code is::
#---------------------------------------------------------------------------
# computer: zbook17
# system: Ubuntu 18.04.3 LTS (x86_64)
# processor: Intel(R) Core(TM) i7-4800MQ CPU @ 2.70GHz
# (1 procs/4 cores by proc/2 threads by core)
# RAM: 31.3 Go
# software: Python
# release: 3.7.6
#---------------------------------------------------------------------------
# fc_hypermesh.OrthMesh constructor with
# d =5
# type =orthotope
# order =1
# box =[[-1, 1], [-1, 1], [-1, 1], [-1, 1], [-1, 1]]
# mapping=None
#---------------------------------------------------------------------------
#date:2019-12-29_14-18-30
#nbruns:5
#numpy: i8 i8 i8 f8
#format: {:>7d} {:>10d} {:>10d} {:11.3f}
#labels: N nq nme OrthMesh(s)
5 7776 3125 0.427
10 161051 100000 0.529
15 1048576 759375 0.844
20 4084101 3200000 1.789
25 11881376 9765625 4.296
27 17210368 14348907 5.958
نحوه نصب
نصب پکیج whl fc-hypermesh-0.1.1:
pip install fc-hypermesh-0.1.1.whl
نصب پکیج tar.gz fc-hypermesh-0.1.1:
pip install fc-hypermesh-0.1.1.tar.gz