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adding example mesh creation notebook #6

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5a63523
adding example mesh creation notebook
briandrawert Apr 23, 2018
20b9113
Updated example mesh creation notebook
Jun 26, 2018
b6558e1
Merge branch 'master' of github.com:briandrawert/MOLNS_notebooks
Jun 26, 2018
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269 changes: 269 additions & 0 deletions Example_Mesh_Creation.ipynb
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Notes on Spatial Information for StochSS\n",
"\n",
"When setting up a spatial problem in StochSS information about the geometry needs to be provided through two files: a\n",
"file containing the mesh information in DOLFIN XML format and a text file containing information about subdomains. The\n",
"file with subdomain information is optional in general (if it is not provided the entire mesh will belong to one subdomain).\n",
"Below is a tutorial on how to provide that information in a variety of cases.\n",
"\n",
"## Mesh Library \n",
"\n",
"The first and simpilest scenario is using one of the default built­in meshes provided by StochSS in the Mesh Library.\n",
"These include simple example mesh and subdomain combinations that are common in biological modeling. For example\n",
"there is a unit sphere with a membrane (i.e. the volume is one subdomain and the surface is another), a unit cube witha\n",
"membrane, a cylinder with the two ends being different subdomains among others. If for a given problem these are not\n",
"sufficient then mesh and subdomain information can be provided by attaching files. One simple case where creating and\n",
"attaching a file may be necessary could involve using the DOLFIN built in meshes but with different subdomains than\n",
"provided in the Mesh Library. This can be done as follows.\n",
"## Using DOLFIN Built-In Geometry with Subdomains Outside of Mesh\n",
"Library\n",
"For example consider a sphere with three different subdomains: the top half of the membrane, the bottom half of the\n",
"membrane and the volume. This can be done using pyurdme as follows (pyurdme and FEniCS are software packages\n",
"that are automatically installed during the StochSS installation and DOLFIN is a library within FEniCS).\n",
"First the appropriate libraries need to be imported:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"FILENAME = \"sphere_top_bot_mesh.xml\"\n",
"SD_FILENAME = \"sphere_top_botsubdomains.txt\""
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import dolfin\n",
"import mshr\n",
"import os\n",
"import pyurdme"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"class top_half_membrane(dolfin.SubDomain):\n",
" def inside(self,x,on_boundary):\n",
" return on_boundary and x[2]>=0\n",
"class bottom_half_membrane(dolfin.SubDomain):\n",
" def inside(self,x,on_boundary):\n",
" return on_boundary and x[2]<=0"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"class sphere_top_bot(pyurdme.URDMEModel):\n",
" def __init__(self,model_name=\"polarization\"):\n",
" pyurdme.URDMEModel.__init__(self,model_name)\n",
" #DefineGeometry\n",
" sphere=mshr.Sphere(dolfin.Point(0.0,0.0,0.0),1.0)\n",
" self.mesh=pyurdme.URDMEMesh(mesh=mshr.generate_mesh(sphere,10))\n",
" cell_function=dolfin.CellFunction(\"size_t\",self.mesh)\n",
"\n",
" self.add_subdomain(top_half_membrane(),2)\n",
" self.add_subdomain(bottom_half_membrane(),3)\n",
" #Defineinitialpopulations\n",
" self.set_initial_condition_scatter({},[1])"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"model=sphere_top_bot()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"sd=model.get_subdomain_vector()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"#This is a dolfin xml file with mesh information\n",
"dolfin.File(FILENAME) << model.mesh"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import base64\n",
"import IPython.display\n",
"with open(FILENAME) as fd:\n",
" b64 = base64.b64encode(fd.read())\n",
" payload = b64.decode()\n",
" html = '<H1><a download=\"{filename}\" href=\"data:text/csv;base64,{payload}\" target=\"_blank\">{title}</a></H1>'\n",
" html = html.format(payload=payload,title=\"Click here to Download Mesh\",filename=FILENAME)\n",
"IPython.display.HTML(html)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"#This is the file to capture information about subdomains\n",
"with open(SD_FILENAME,'w') as sfd:\n",
" for ndx,val in enumerate(sd):\n",
" sfd.write(\"{0},{1}\\n\".format(ndx,val))\n",
"import base64\n",
"import IPython.display\n",
"with open(SD_FILENAME) as fd:\n",
" b64 = base64.b64encode(fd.read())\n",
" payload = b64.decode()\n",
" html = '<H1><a download=\"{filename}\" href=\"data:text/csv;base64,{payload}\" target=\"_blank\">{title}</a></H1>'\n",
" html = html.format(payload=payload,title=\"Click here to Download SD file\",filename=SD_FILENAME)\n",
"IPython.display.HTML(html)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# IF you want to visualize your mesh, execute the following two cells"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Code to setup javascript display libraries\n",
"import os.path\n",
"import IPython.display\n",
"with open(os.path.join(os.path.dirname(pyurdme.__file__),'data/three.js_templates/js/three.js')) as fd:\n",
" bufa = fd.read()\n",
"with open(os.path.join(os.path.dirname(pyurdme.__file__),'data/three.js_templates/js/render.js')) as fd:\n",
" bufb = fd.read()\n",
"with open(os.path.join(os.path.dirname(pyurdme.__file__),'data/three.js_templates/js/OrbitControls.js')) as fd:\n",
" bufc = fd.read()\n",
"IPython.display.display(IPython.display.HTML('<script>'+bufa+bufc+bufb+'</script>'))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"model.mesh"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 1
}