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
Installation:
The fc_hypermesh Python package is available from the Python Package Index, so to install/upgrade simply do
pip install fc_hypermesh -U
Thereafter, it's possible to run one of the demo functions
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:
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
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()
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:
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
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()
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:
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
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()
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:
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
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()
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:
import fc_hypermesh fc_hypermesh.demos.demo01()
Benchmarking:
Bench of the OrthMesh constructor for a 3-dimensional orthotope tessellated with (order 1) simplices.
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 1.679Bench of the OrthMesh constructor for a 3-dimensional orthotope tessellated with 3-order simplices.
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 0.733Bench of the OrthMesh constructor for a 5-dimensional orthotope tessellated with (order 1) orthotopes.
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