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1
2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3 % Copyright (c) 2003-2012 by University of Queensland
4 % http://www.uq.edu.au
5 %
6 % Primary Business: Queensland, Australia
7 % Licensed under the Open Software License version 3.0
8 % http://www.opensource.org/licenses/osl-3.0.php
9 %
10 % Development until 2012 by Earth Systems Science Computational Center (ESSCC)
11 % Development since 2012 by School of Earth Sciences
12 %
13 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
14
15 \section{3D pycad}
16 \sslist{example09m.py}
17 This example explains how to build a 3D layered domain using pycad. As
18 simple as this example sounds, there are a few import concepts that one must
19 remember so that the model will function correctly.
20 \begin{itemize}
21 \item There must be no duplication of any geometric features whether they are
22 points, lines, loops, surfaces or volumes.
23 \item All objects with dimensions greater then a line have a normal defined by
24 the right hand rule (RHR). It is important to consider which direction a
25 normal is oriented when combining primitives to form higher order shapes.
26 \end{itemize}
27
28 The first step as always is to import the external modules. To build a 3D model
29 and mesh we will need pycad, some GMesh interfaces, the Finley domain builder
30 and some additional tools.
31 \begin{python}
32 #######################################################EXTERNAL MODULES
33 from esys.pycad import * #domain constructor
34 from esys.pycad.gmsh import Design #Finite Element meshing package
35 from esys.finley import MakeDomain #Converter for escript
36 from esys.escript import mkDir, getMPISizeWorld
37 import os
38 \end{python}
39 After carrying out some routine checks and setting the \verb!save_path! we then
40 specify the parameters of the model. This model will be 2000 by 2000 meters on
41 the surface and extend to a depth of 500 meters. An interface or boundary
42 between two layers will be created at half the total depth or 250 meters. This
43 type of model is known as a horizontally layered model or a layer cake model.
44 \begin{python}
45 ################################################ESTABLISHING PARAMETERS
46 #Model Parameters
47 xwidth=2000.0*m #x width of model
48 ywidth=2000.0*m #y width of model
49 depth=500.0*m #depth of model
50 intf=depth/2. #Depth of the interface.
51 \end{python}
52 We now start to specify the components of our model starting with the vertexes
53 using the \verb!Point! primitive. These are then joined by lines in a regular
54 manner taking note of the right hand rule. Finally, the lines are turned into
55 loops and then planar surfaces.
56 \footnote{Some code has been emmitted here for
57 simlpicity. For the full script please refer to the script referenced at the beginning of
58 this section.}
59 \begin{python}
60 ####################################################DOMAIN CONSTRUCTION
61 # Domain Corners
62 p0=Point(0.0, 0.0, 0.0)
63 #..etc..
64 l45=Line(p4, p5)
65
66 # Join line segments to create domain boundaries and then surfaces
67 ctop=CurveLoop(l01, l12, l23, l30); stop=PlaneSurface(ctop)
68 cbot=CurveLoop(-l67, -l56, -l45, -l74); sbot=PlaneSurface(cbot)
69 \end{python}
70 With the top and bottom of the domain taken care of, it is now time to focus on
71 the interface. Again the vertexes of the planar interface are created. With
72 these, vertical and horizontal lines (edges) are created joining the interface
73 with itself and the top and bottom surfaces.
74 \begin{python}
75 # for each side
76 ip0=Point(0.0, 0.0, intf)
77 #..etc..
78 linte_ar=[]; #lines for vertical edges
79 linhe_ar=[]; #lines for horizontal edges
80 linte_ar.append(Line(p0,ip0))
81 #..etc..
82 linhe_ar.append(Line(ip3,ip0))
83 \end{python}
84 Consider now the sides of the domain. One could specify the whole side using the
85 points first defined for the top and bottom layer. This would define the whole
86 domain as one volume. However, there is an interface and we wish to define each
87 layer individually. Therefore, there will be 8 surfaces on the sides of our
88 domain. We can do this operation quite simply using the points and lines that we
89 had defined previously. First loops are created and then surfaces making sure to
90 keep a normal for each layer which is consistent with upper and lower surfaces
91 of the layer. For example, all surface normals must face outwards from or
92 inwards towards the centre of the volume.
93 \begin{python}
94 cintfa_ar=[]; cintfb_ar=[] #curveloops for above and below interface on sides
95 cintfa_ar.append(CurveLoop(linte_ar[0],linhe_ar[0],-linte_ar[2],-l01))
96 #..etc..
97 cintfb_ar.append(CurveLoop(linte_ar[7],l45,-linte_ar[1],-linhe_ar[3]))
98
99 sintfa_ar=[PlaneSurface(cintfa_ar[i]) for i in range(0,4)]
100 sintfb_ar=[PlaneSurface(cintfb_ar[i]) for i in range(0,4)]
101
102 sintf=PlaneSurface(CurveLoop(*tuple(linhe_ar)))
103 \end{python}
104 Assuming all is well with the normals, the volumes can be created from our
105 surface arrays. Note the use here of the \verb!*tuple! function. This allows us
106 to pass an list array as an argument list to a function. It must be placed at
107 the end of the function arguments and there cannot be more than one per function
108 call.
109 \begin{python}
110 vintfa=Volume(SurfaceLoop(stop,-sintf,*tuple(sintfa_ar)))
111 vintfb=Volume(SurfaceLoop(sbot,sintf,*tuple(sintfb_ar)))
112
113 # Create the volume.
114 #sloop=SurfaceLoop(stop,sbot,*tuple(sintfa_ar+sintfb_ar))
115 #model=Volume(sloop)
116 \end{python}
117 The final steps are designing the mesh, tagging the volumes and the interface
118 and outputting the data to file so it can be imported by an \esc solution
119 script.
120 \begin{python}
121 #############################################EXPORTING MESH FOR ESCRIPT
122 # Create a Design which can make the mesh
123 d=Design(dim=3, element_size=5.0*m)
124 d.addItems(PropertySet('vintfa',vintfa))
125 d.addItems(PropertySet('vintfb',vintfb))
126 d.addItems(sintf)
127
128 d.setScriptFileName(os.path.join(save_path,"example09m.geo"))
129
130 d.setMeshFileName(os.path.join(save_path,"example09m.msh"))
131 #
132 # make the finley domain:
133 #
134 domain=MakeDomain(d)
135 # Create a file that can be read back in to python with
136 # mesh=ReadMesh(fileName)
137 domain.write(os.path.join(save_path,"example09m.fly"))
138 \end{python}
139
140 \begin{figure}[htp]
141 \begin{center}
142 \begin{subfigure}[Gmesh view of geometry only.]
143 {\label{fig:gmsh3dgeo}
144 \includegraphics[width=3.5in]{figures/gmsh-example09m.png}}
145 \end{subfigure}
146 \begin{subfigure}[Gmesh view of a 200m 2D mesh on the domain surfaces.]
147 {\label{fig:gmsh3dmsh}
148 \includegraphics[width=3.5in]{figures/gmsh-example09msh2d.png}}
149 \end{subfigure}
150 \begin{subfigure}[Gmesh view of a 200m 3D mesh on the domain volumes.]
151 {\label{fig:gmsh3dmsh}
152 \includegraphics[width=3.5in]{figures/gmsh-example09msh3d.png}}
153 \end{subfigure}
154 \end{center}
155 \end{figure}
156 \clearpage
157
158 \section{Layer Cake Models}
159 Whilst this type of model seems simple enough to construct for two layers,
160 specifying multiple layers can become cumbersome. A function exists to generate
161 layer cake models called \verb!layer_cake!. A detailed description of its
162 arguments and returns is available in the API and the function can be imported
163 from the pycad.extras module.
164 \begin{python}
165 from esys.pycad.extras import layer_cake
166 intfaces=[10,30,50,55,80,100,200,250,400,500]
167
168 domaindes=Design(dim=3,element_size=element_size,order=2)
169 cmplx_domain=layer_cake(domaindes,xwidth,ywidth,intfaces)
170 cmplx_domain.setScriptFileName(os.path.join(save_path,"example09lc.geo"))
171 cmplx_domain.setMeshFileName(os.path.join(save_path,"example09lc.msh"))
172 dcmplx=MakeDomain(cmplx_domain)
173 dcmplx.write(os.path.join(save_path,"example09lc.fly"))
174 \end{python}
175
176 \begin{figure}[ht]
177 \begin{center}
178 \includegraphics[width=5in]{figures/gmsh-example09lc.png}
179 \caption{Example geometry using layer cake function.}
180 \label{fig:gmsh3dlc}
181 \end{center}
182 \end{figure}
183 \clearpage
184 \section{Troubleshooting Pycad}
185 There are some techniques which can be useful when trying to troubleshoot
186 problems with pycad. As mentioned earlier it is important to ensure the correct
187 directionality of your primitives when constructing more complicated domains. If
188 it remains too difficult to establish the tangent of a line or curveloop, or
189 the normal of a surface, these values can be checked by importing the geometry
190 to gmesh and applying the appropriate visualisation options.
191
192 \section{3D Seismic Wave Propagation}
193 Adding an extra dimension to our wave equation solution script should be
194 relatively simple. Apart from the changes to the domain and therefore the
195 parameters of the model, there are only a few minor things which must be
196 modified to make the solution appropriate for 3d modelling.
197
198 \section{Applying a function to a domain tag}
199 \sslist{example09a.py}
200 To apply a function or data object to a domain requires a two step process. The
201 first step is to create a data object with an on/off mask based upon the tagged
202 value. This is quite simple and can be achieved by using a scalar data object
203 based upon the domain. In this case we are using the \verb!FunctionOnBoundary!
204 function space because the tagged value \verb!'stop'! is effectively a specific
205 subsurface of the boundary of the whole domain.
206 \begin{python}
207 stop=Scalar(0.0,FunctionOnBoundary(domain))
208 stop.setTaggedValue("stop",1.0)
209 \end{python}
210 Now the data object \verb|stop| has the value 1.0 on the surface
211 \verb!'stop'! and zero everywhere else.
212 %
213 To apply our function to the boundary only on \verb|stop| we now
214 mulitply it by \verb|stop|
215 \begin{python}
216 xb=FunctionOnBoundary(domain).getX()
217 yx=(cos(length(xb-xc)*3.1415/src_length)+1)*whereNegative(length(xb-xc)-src_length)
218 src_dir=numpy.array([0.,0.,1.0]) # defines direction of point source as down
219 mypde.setValue(y=source[0]*yx*src_dir*stop) #set the source as a function on the boundary
220 \end{python}
221
222 \section{Mayavi2 with 3D data.}
223 There are a variety of visualisation options available when using VTK data. The
224 types of visualisation are often data and interpretation specific and thus
225 consideration must be given to the type of output saved to file. Whether that is
226 scalar, vector or tensor data.
227
228 \begin{figure}[htp]
229 \centering
230 \begin{subfigure}[Example 9 at time step 201.]
231 {\label{fig:ex9b 201}
232 \includegraphics[width=0.45\textwidth]{figures/ex09b00201.png}}
233 \end{subfigure}
234 \begin{subfigure}[Example 9 at time step 341.]
235 {\label{fig:ex9b 201}
236 \includegraphics[width=0.45\textwidth]{figures/ex09b00341.png}}
237 \end{subfigure}\\
238 \begin{subfigure}[Example 9 at time step 440.]
239 {\label{fig:ex9b 201}
240 \includegraphics[width=0.45\textwidth]{figures/ex09b00440.png}}
241 \end{subfigure}
242 \end{figure}

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