/[escript]/trunk/escript/py_src/levelset.py
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Contents of /trunk/escript/py_src/levelset.py

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Revision 1716 - (show annotations)
Thu Aug 21 05:03:49 2008 UTC (11 years, 1 month ago) by gross
File MIME type: text/x-python
File size: 14966 byte(s)
getListOfTags method added to FunctionSpace class
1 from esys.escript import *
2 from esys.escript.linearPDEs import LinearPDE, TransportPDE
3 from esys.escript.pdetools import Projector
4 from esys import finley
5 import math
6
7
8
9 class LevelSet(object):
10 def __init__(self,phi,reinitialization_steps_max=10,reinitialization_each=2,relative_smoothing_width=2.):
11 """
12 initialize model
13 """
14 self.__domain = phi.getDomain()
15 x=self.__domain.getX()
16 diam=0
17 for i in range(self.__domain.getDim()):
18 xi=x[i]
19 diam+=(inf(xi)-sup(xi))**2
20 self.__diam=sqrt(diam)
21 self.__h = sup(Function(self.__domain).getSize())
22 self.__reinitialization_each=reinitialization_each
23 self.__reinitialization_steps_max = reinitialization_steps_max
24 self.__relative_smoothing_width = relative_smoothing_width
25 self.__phi = phi
26 self.__update_count=0
27 self.velocity = None
28
29 #==================================================
30 self.__FC=True
31 if self.__FC:
32 self.__fc=TransportPDE(self.__domain,num_equations=1,theta=0.5)
33 # self.__fc.setReducedOrderOn()
34 self.__fc.setValue(M=Scalar(1.,Function(self.__domain)))
35 self.__fc.setInitialSolution(phi+self.__diam)
36 else:
37 self.__fcpde = LinearPDE(self.__domain,numEquations=1, numSolutions=1)
38 self.__fcpde.setSolverMethod(solver=LinearPDE.LUMPING)
39 self.__fcpde.setReducedOrderOn()
40 self.__fcpde.setSymmetryOn()
41 self.__fcpde.setValue(D=1.)
42
43 #=======================================
44 self.__reinitFC=False
45 if self.__reinitFC:
46 self.__reinitfc=TransportPDE(self.__domain,num_equations=1,theta=1.0)
47 self.__reinitfc.setValue(M=Scalar(1.,Function(self.__domain)))
48 self.__reinitfc.setTolerance(1.e-5)
49 else:
50 self.__reinitPde = LinearPDE(self.__domain,numEquations=1, numSolutions=1)
51 # self.__reinitPde.setSolverMethod(solver=LinearPDE.LUMPING)
52 self.__reinitPde.setReducedOrderOn()
53 self.__reinitPde.setSymmetryOn()
54 self.__reinitPde.setValue(D=1.)
55 self.__reinitPde.setTolerance(1.e-2)
56 # self.__reinitPde.setSolverMethod(preconditioner=LinearPDE.ILU0)
57 #=======================================
58 self.__updateInterface()
59 print "phi range:",inf(phi), sup(phi)
60
61 def setFixedRegion(self,mask,contour=0):
62 q=whereNonPositive(abs(self.__phi-contour)-self.__h)*mask
63 # self.__fc.setValue(q=q)
64 self.__reinitPde.setValue(q=q)
65
66 def getH(self):
67 return self.__h
68 def getDomain(self):
69 return self.__domain
70
71 def getTimeStepSize(self,velocity):
72 """
73 returns a new dt for a given velocity using the courant coundition
74 """
75 self.velocity=velocity
76 if self.__FC:
77 self.__fc.setValue(C=-interpolate(velocity,Function(self.__domain)))
78 dt=self.__fc.getSafeTimeStepSize()
79 else:
80 dt=0.5*self.__h/sup(length(velocity))
81 return dt
82
83 def getLevelSetFunction(self):
84 """
85 returns the level set function
86 """
87 return self.__phi
88
89 def __updateInterface(self):
90 self.__smoothed_char=self.__makeInterface(self.__phi)
91
92 def __makeInterface(self,phi,smoothing_width=1.):
93 """
94 creates a very smooth interface from -1 to 1 over the length 2*h*smoothing_width where -1 is used where the level set is negative
95 and 1 where the level set is 1
96 """
97 s=smoothing_width*self.__h
98 phi_on_h=interpolate(phi,Function(self.__domain))
99 mask_neg = whereNonNegative(-s-phi_on_h)
100 mask_pos = whereNonNegative(phi_on_h-s)
101 mask_interface = 1.-mask_neg-mask_pos
102 # interface=1.-(phi_on_h-s)**2/(2.*s**3)*(phi_on_h+2*s) # function f with f(s)=1, f'(s)=0, f(-s)=-1, f'(-s)=0, f(0)=0, f'(0)=
103 interface=phi_on_h/s
104 return - mask_neg + mask_pos + mask_interface * interface
105
106 def makeCharacteristicFunction(self, contour=0, positiveSide=True, smoothing_width=1.):
107 return self.makeCharacteristicFunctionFromExternalLevelSetFunction(self.__phi,contour,positiveSide,smoothing_width)
108
109 def makeCharacteristicFunctionFromExternalLevelSetFunction(self,phi,contour=0, positiveSide=True, smoothing_width=1.):
110 s=self.__makeInterface(phi-contour,smoothing_width)
111 if positiveSide:
112 return (1+s)/2
113 else:
114 return (1-s)/2
115
116
117 def update(self,dt):
118 """
119 sets a new velocity and updates the level set fuction
120
121 @param dt: time step forward
122 """
123 if self.__FC:
124 self.__phi=self.__fc.solve(dt, verbose=False)-self.__diam
125 else:
126 self.__fcpde.setValue(Y = self.__phi-(dt/2.)*inner(self.velocity,grad(self.__phi)))
127 phi_half = self.__fcpde.getSolution()
128 self.__fcpde.setValue(Y = self.__phi-dt*inner(self.velocity,grad(phi_half)))
129 self.__phi= self.__fcpde.getSolution()
130 self.__update_count += 1
131 if self.__update_count%self.__reinitialization_each == 0:
132 self.__phi=self.__reinitialise(self.__phi)
133 if self.__FC:
134 self.__fc.setInitialSolution(self.__phi+self.__diam)
135 self.__updateInterface()
136
137 def setTolerance(self,tolerance=1e-3):
138 if self.__FC:
139 self.__fc.setTolerance(tolerance)
140
141 def __reinitialise(self,phi):
142 print "reintialization started:"
143 s=self.__makeInterface(phi,1.)
144 print "phi range:",inf(phi), sup(phi)
145 g=grad(phi)
146 w=s*g/(length(g)+EPSILON)
147 #=======================================================
148 # # positive part:
149 # phi_p=wherePositive(phi)*phi
150 # self.__reinitfc.setInitialSolution(phi_p)
151 # self.__reinitfc.setValue(C=-wherePositive(s)*w,Y=wherePositive(s)*s,q=whereNonPositive(phi))
152 # dtau=self.__h
153 # print "step size: dt (pos)= ",dtau
154 # print "phi_p range:",inf(phi_p), sup(phi_p)
155 # iter=0
156 # while (iter<=self.__reinitialization_steps_max):
157 # phi_p=self.__reinitfc.solve(dtau)
158 # print "phi_p range:",inf(phi_p), sup(phi_p)
159 # iter+=1
160 # # negative part:
161 # phi_n=-whereNegative(phi)*phi
162 # self.__reinitfc.setInitialSolution(phi_n)
163 # self.__reinitfc.setValue(C=-whereNegative(s)*w,Y=-whereNegative(s)*s,q=whereNonNegative(phi))
164 # # dtau=self.__reinitfc.getSafeTimeStepSize()
165 # dtau=self.__h
166 # print "step size: dt (neg)= ",dtau
167 # print "phi_n range:",inf(phi_n), sup(phi_n)
168 # iter=0
169 # while (iter<=self.__reinitialization_steps_max):
170 # phi_n=self.__reinitfc.solve(dtau)
171 # print "phi_n range:",inf(phi_n), sup(phi_n)
172 # iter+=1
173 # phi=phi_p-phi_n
174 # print "phi range:",inf(phi), sup(phi)
175 # print "reintialization completed."
176 # return phi
177
178 #=======================================================
179 if self.__reinitFC:
180 self.__reinitfc.setValue(C=-w,Y=s)
181 self.__reinitfc.setInitialSolution(phi+self.__diam)
182 dtau=self.__reinitfc.getSafeTimeStepSize()
183 # dtau = 0.5*inf(Function(self.__domain).getSize())
184 else:
185 dtau = 0.5*inf(Function(self.__domain).getSize())
186 print "step size: dt = ",dtau,inf(abs(phi.interpolate(Function(self.__domain)))/abs(s-inner(w,grad(phi))))
187 iter =0
188 # self.__reinitPde.setValue(q=whereNegative(abs(phi)-2*self.__h), r=phi)
189 # self.__reinitPde.setValue(r=phi)
190 while (iter<=self.__reinitialization_steps_max):
191 phi_old=phi
192 if self.__reinitFC:
193 phi = self.__reinitfc.solve(dtau)-self.__diam
194 else:
195 self.__reinitPde.setValue(Y = phi+(dtau/2.)*(s-inner(w,grad(phi))))
196 phi_half = self.__reinitPde.getSolution()
197 self.__reinitPde.setValue(Y = phi+dtau*(s-inner(w,grad(phi_half))))
198 # g=grad(phi)
199 # S=inner(w,grad(phi))
200 # self.__reinitPde.setValue(Y = phi+dtau*(s-S),X=dtau**2/2*w*(s-S))
201 phi = self.__reinitPde.getSolution()
202 change = Lsup(phi-phi_old)/self.__diam
203 print "phi range:",inf(phi), sup(phi)
204 print "iteration :", iter, " change:", change
205 iter +=1
206 print "reintialization completed."
207 return phi
208
209 def createParameter(self,value_negative=-1.,value_positive=1):
210 out = (value_negative+value_positive)/2. + self.__smoothed_char * ((value_positive-value_negative)/2.)
211 return out
212
213
214 #================ things from here onwards are not used nor tested: ==========================================
215
216
217 def getCharacteristicFunction(self):
218 return self.__smoothed_char
219
220
221
222
223 def RK2(self,L):
224 k0=L(phi)
225 phi_1=phi+dt*k0
226 k1=L(phi_1)
227 phi=phi+dt/2*(k0+k1)
228 def RK3(self,L):
229 k0=L(phi)
230 phi_1=phi+dt*L(phi)
231 k1=L(phi_1)
232 phi_2=phi+dt/4*(k0+k1)
233 k2=L(phi_2)
234 phi=phi+dt/6*(k0+4*k2+K1)
235 def TG(self,L):
236 k0=L(phi)
237 phi_1=phi+dt/2*k0
238 k1=L(phi_1)
239 phi=phi+dt*k1
240
241
242 def __reinitialise_old(self):
243 #=============================================
244 f=0.1
245 f2=0.3
246 h=self.__h
247 fs=h.getFunctionSpace()
248 vol=self.getVolumeOfNegativeDomain()
249 self.__reinitPde.setValue(D=1.0)
250 #============
251 grad_phi=grad(self.__phi,fs)
252 len_grad_phi=length(grad_phi)
253 w=grad_phi/len_grad_phi
254
255 # s=wherePositive(self. __makeInterface(2.))-whereNegative(self. __makeInterface(2.))
256 s=self. __makeInterface(2.)
257 # s2=whereNegative(len_grad_phi-f2)*(1-(1-len_grad_phi/f2)**2)+(1-whereNegative(len_grad_phi-f2))
258 s2=1.
259 s=s*s2
260 dtau=f*inf(h/abs(s))
261
262 #========================
263 diff=1.
264 d=1.
265 c =0
266 #==============================================
267 TVD=integrate(length(grad_phi))
268 print "initial range ",inf(self.__phi),sup(self.__phi),"error:",Lsup(1.-len_grad_phi),"volume =",vol,TVD
269 # saveVTK("test.%s.xml"%c,l=length(grad(self.__phi,fs))-1,s=s,phi=self.__phi)
270
271 dtau=f*inf(h/abs(s))
272 while c < self.__reinitialization_steps_max: # and abs(diff) >= 0.01:
273 #
274 grad_phi=grad(self.__phi,fs)
275 len_grad_phi=length(grad_phi)
276 #
277 # s=self.__makeInterface(1.)
278 # s2=whereNegative(len_grad_phi-f2)*(1-(1-len_grad_phi/f2)**2)+(1-whereNegative(len_grad_phi-f2))
279 # s=s*s2
280 # phi_on_h=interpolate(self.__phi,fs)
281 # self.__reinitPde.setValue(Y =self.__phi+dtau/2*s*(1.-len_grad_phi))
282 # phi_half=self.__reinitPde.getSolution()
283 # self.__reinitPde.setValue(Y =self.__phi+dtau*s*(1.-length(grad(phi_half,fs))))
284 # self.__reinitPde.setValue(Y =self.__phi, Y_reduced=dtau*s*(1.-inner(w,grad(phi_half,ReducedFunction(self.__domain)))))
285 # self.__reinitPde.setValue(Y =self.__phi+dtau*(s-inner(w,grad_phi)),X=dtau/2*h*(s-inner(w,grad_phi))*w)
286 # self.__reinitPde.setValue(Y =self.__phi+dtau*s*(1.-len_grad_phi),X=-dtau/2*h*s**2*grad_phi)
287 self.__reinitPde.setValue(Y=self.__phi+dtau*s*(1.-len_grad_phi),X=f*dtau/2*h*abs(s)*(1.-len_grad_phi)*grad_phi/len_grad_phi)
288
289 # self.__reinitPde.setValue(Y=self.__phi+dtau*s*(1.-len_grad_phi),X=f*dtau/2*h*abs(s)*(1.-len_grad_phi)*grad_phi/len_grad_phi)
290 self.__phi, previous = self.__reinitPde.getSolution(), self.__phi
291 # self.__updateInterface()
292
293 vol,vol_old=self.getVolumeOfNegativeDomain(),vol
294 diff=(vol-vol_old)
295 r=Lsup(length(grad(self.__phi))-1.)
296 TVD=integrate(length(grad(self.__phi,fs)))
297 print "iteration :", c, "range ",inf(self.__phi),sup(self.__phi),"error :",r,"volume change:",diff,TVD
298 # saveVTK("test.%s.xml"%(c+1),l=length(grad(self.__phi,fs)),s=s,phi=self.__phi,v=grad(self.__phi,fs))
299 c += 1
300 return
301 #==============================================
302 f2=0.7
303 h=self.__h
304 fs=h.getFunctionSpace()
305 vol=self.getVolumeOfNegativeDomain()
306 s=abs(self. __makeInterface(2.))
307 grad_phi=grad(self.__phi,fs)
308 len_grad_phi=length(grad_phi)
309
310 #----
311 # aphi_on_h=abs(interpolate(self.__phi,self.__h.getFunctionSpace()))
312 # q=2*self.__h
313 # mask_neg = whereNegative(aphi_on_h-q)
314 # mask_pos = wherePositive(aphi_on_h-q-self.__h)
315 # mask_interface = 1.-mask_neg-mask_pos
316 # s2=mask_neg + mask_interface * (q+self.__h-aphi_on_h)/self.__h
317 #----
318 m=whereNonPositive(len_grad_phi-f2)
319 s2=m*len_grad_phi/f2+(1.-m)
320 #----
321 # s2=1.
322 #----
323 self.__reinitPde.setValue(D=(1-s)/h**2,Y=(1-s)/h**2*self.__phi)
324 self.__reinitPde.setValue(A=(s2*len_grad_phi+(1.-s2))*kronecker(3),X=grad_phi)
325 # self.__reinitPde.setValue(A=(len_grad_phi-1)/len_grad_phi*kronecker(3))
326 # self.__reinitPde.setValue(A=kronecker(3), X=grad_phi/len_grad_phi)
327 self.__phi = self.__reinitPde.getSolution()
328 r=Lsup(length(grad(self.__phi))-1.)
329 vol,vol_old=self.getVolumeOfNegativeDomain(),vol
330 diff=(vol-vol_old)/vol
331 print "iteration :", inf(self.__phi),sup(self.__phi),r,diff
332 # saveVTK("test.%s.xml"%0,l=length(grad(self.__phi,fs)),s=s,phi=self.__phi,v=grad(self.__phi,fs),s2=s2)
333 return
334 #=============================================
335
336 #============
337
338
339 def getVolumeOfNegativeDomain(self):
340 """
341 return the current volume of domain with phi<0.
342 """
343 return integrate((1.-self.__makeInterface(1.))/2.)
344
345
346 def getBoundingBoxOfNegativeDomain(self):
347 """
348 get the height of the region with phi<0
349 """
350 fs=self.__h.getFunctionSpace()
351 mask_phi1=wherePositive(interpolate(self.__phi,fs))
352 mask_phi2=wherePositive(self.__phi)
353 x1=fs.getX()
354 x2=self.__domain.getX()
355 out=[]
356 for i in range(fs.getDim()):
357 x1_i=x1[i]
358 x2_i=x2[i]
359 d=2*(sup(x2_i)-inf(x2_i))
360 offset1=d*mask_phi1
361 offset2=d*mask_phi2
362 out.append((min(inf(x1_i+offset1),inf(x2_i+offset2)),max(sup(x1_i-offset1),sup(x2_i-offset2))))
363 return tuple(out)
364

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