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

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Revision 1673 - (hide annotations)
Thu Jul 24 22:28:50 2008 UTC (11 years, 7 months ago) by gross
File MIME type: text/x-python
File size: 13490 byte(s)
more algorithms for level set
1 gross 1473 from esys.escript import *
2 gross 1659 from esys.escript.linearPDEs import LinearPDE, TransportPDE
3 gross 1473 from esys.escript.pdetools import Projector
4     from esys import finley
5     import math
6    
7    
8    
9     class LevelSet(object):
10 gross 1659 def __init__(self,phi,reinitialization_steps_max=10,reinitialization_each=2,relative_smoothing_width=2.):
11 gross 1473 """
12     initialize model
13     """
14 gross 1659 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 gross 1661 self.__h = sup(Function(self.__domain).getSize())
22 gross 1659 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 gross 1473
29 gross 1659 #==================================================
30 gross 1673 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 gross 1659
43     #=======================================
44 gross 1673 self.__reinitFC=False
45     if self.__reinitFC:
46     self.__reinitfc=TransportPDE(self.__domain,num_equations=1,theta=1.)
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-8)
56     # self.__reinitPde.setSolverMethod(preconditioner=LinearPDE.ILU0)
57 gross 1659 #=======================================
58 gross 1661 self.__updateInterface()
59     print "phi range:",inf(phi), sup(phi)
60 gross 1473
61 gross 1661 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 gross 1473
66 gross 1673 def getH(self):
67     return self.__h
68 gross 1473 def getDomain(self):
69 gross 1659 return self.__domain
70 gross 1473
71 gross 1659 def getTimeStepSize(self,velocity):
72     """
73     returns a new dt for a given velocity using the courant coundition
74     """
75     self.velocity=velocity
76 gross 1673 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 gross 1659 return dt
82    
83     def getLevelSetFunction(self):
84     """
85     returns the level set function
86     """
87     return self.__phi
88    
89 gross 1661 def __updateInterface(self):
90     self.__smoothed_char=self.__makeInterface(self.__phi)
91    
92     def __makeInterface(self,phi,smoothing_width=1.):
93 gross 1659 """
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 gross 1473 s=smoothing_width*self.__h
98 gross 1661 phi_on_h=interpolate(phi,Function(self.__domain))
99 gross 1473 mask_neg = whereNonNegative(-s-phi_on_h)
100     mask_pos = whereNonNegative(phi_on_h-s)
101     mask_interface = 1.-mask_neg-mask_pos
102 gross 1661 # 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 gross 1473 return - mask_neg + mask_pos + mask_interface * interface
105    
106 gross 1661 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 gross 1473 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 gross 1673 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 gross 1659 self.__update_count += 1
131 gross 1473 if self.__update_count%self.__reinitialization_each == 0:
132 gross 1661 self.__phi=self.__reinitialise(self.__phi)
133 gross 1673 if self.__FC:
134     self.__fc.setInitialSolution(self.__phi+self.__diam)
135 gross 1661 self.__updateInterface()
136 gross 1473
137 gross 1659 def setTolerance(self,tolerance=1e-3):
138 gross 1673 if self.__FC:
139     self.__fc.setTolerance(tolerance)
140 gross 1473
141 gross 1659 def __reinitialise(self,phi):
142     print "reintialization started:"
143 gross 1673 s=self.__makeInterface(phi,1.5)
144 gross 1659 g=grad(phi)
145     w = s*g/(length(g)+EPSILON)
146 gross 1673 if self.__reinitFC:
147     self.__reinitfc.setValue(C=-w,Y=s)
148     self.__reinitfc.setInitialSolution(phi+self.__diam)
149     # dtau=self.__reinitfc.getSafeTimeStepSize()
150     dtau = 0.5*inf(Function(self.__domain).getSize())
151     else:
152     dtau = 0.5*inf(Function(self.__domain).getSize())
153     print "step size: dt = ",dtau,inf(abs(phi.interpolate(Function(self.__domain)))/abs(s-inner(w,grad(phi))))
154 gross 1659 iter =0
155 gross 1673 # self.__reinitPde.setValue(q=whereNegative(abs(phi)-2*self.__h), r=phi)
156 gross 1661 # self.__reinitPde.setValue(r=phi)
157 gross 1659 while (iter<=self.__reinitialization_steps_max):
158     phi_old=phi
159 gross 1673 if self.__reinitFC:
160     phi = self.__reinitfc.solve(dtau)-self.__diam
161     else:
162     self.__reinitPde.setValue(Y = phi+(dtau/2.)*(s-inner(w,grad(phi))))
163     phi_half = self.__reinitPde.getSolution()
164     self.__reinitPde.setValue(Y = phi+dtau*(s-inner(w,grad(phi_half))))
165     # g=grad(phi)
166     # S=inner(w,grad(phi))
167     # self.__reinitPde.setValue(Y = phi+dtau*(s-S),X=dtau**2/2*w*(s-S))
168     phi = self.__reinitPde.getSolution()
169 gross 1659 change = Lsup(phi-phi_old)/self.__diam
170     print "phi range:",inf(phi), sup(phi)
171     print "iteration :", iter, " error:", change
172     iter +=1
173     print "reintialization completed."
174     return phi
175 gross 1473
176 gross 1661 def createParameter(self,value_negative=-1.,value_positive=1):
177     out = (value_negative+value_positive)/2. + self.__smoothed_char * ((value_positive-value_negative)/2.)
178     return out
179 gross 1473
180 gross 1661
181 gross 1659 #================ things from here onwards are not used nor tested: ==========================================
182    
183    
184     def getCharacteristicFunction(self):
185     return self.__smoothed_char
186    
187    
188    
189    
190 gross 1473 def RK2(self,L):
191     k0=L(phi)
192     phi_1=phi+dt*k0
193     k1=L(phi_1)
194     phi=phi+dt/2*(k0+k1)
195     def RK3(self,L):
196     k0=L(phi)
197     phi_1=phi+dt*L(phi)
198     k1=L(phi_1)
199     phi_2=phi+dt/4*(k0+k1)
200     k2=L(phi_2)
201     phi=phi+dt/6*(k0+4*k2+K1)
202     def TG(self,L):
203     k0=L(phi)
204     phi_1=phi+dt/2*k0
205     k1=L(phi_1)
206     phi=phi+dt*k1
207    
208    
209 gross 1659 def __reinitialise_old(self):
210 gross 1473 #=============================================
211     f=0.1
212     f2=0.3
213     h=self.__h
214     fs=h.getFunctionSpace()
215     vol=self.getVolumeOfNegativeDomain()
216     self.__reinitPde.setValue(D=1.0)
217     #============
218     grad_phi=grad(self.__phi,fs)
219     len_grad_phi=length(grad_phi)
220     w=grad_phi/len_grad_phi
221    
222     # s=wherePositive(self. __makeInterface(2.))-whereNegative(self. __makeInterface(2.))
223     s=self. __makeInterface(2.)
224     # s2=whereNegative(len_grad_phi-f2)*(1-(1-len_grad_phi/f2)**2)+(1-whereNegative(len_grad_phi-f2))
225     s2=1.
226     s=s*s2
227     dtau=f*inf(h/abs(s))
228    
229     #========================
230     diff=1.
231     d=1.
232     c =0
233     #==============================================
234     TVD=integrate(length(grad_phi))
235     print "initial range ",inf(self.__phi),sup(self.__phi),"error:",Lsup(1.-len_grad_phi),"volume =",vol,TVD
236     # saveVTK("test.%s.xml"%c,l=length(grad(self.__phi,fs))-1,s=s,phi=self.__phi)
237    
238     dtau=f*inf(h/abs(s))
239     while c < self.__reinitialization_steps_max: # and abs(diff) >= 0.01:
240     #
241     grad_phi=grad(self.__phi,fs)
242     len_grad_phi=length(grad_phi)
243     #
244     # s=self.__makeInterface(1.)
245     # s2=whereNegative(len_grad_phi-f2)*(1-(1-len_grad_phi/f2)**2)+(1-whereNegative(len_grad_phi-f2))
246     # s=s*s2
247     # phi_on_h=interpolate(self.__phi,fs)
248     # self.__reinitPde.setValue(Y =self.__phi+dtau/2*s*(1.-len_grad_phi))
249     # phi_half=self.__reinitPde.getSolution()
250     # self.__reinitPde.setValue(Y =self.__phi+dtau*s*(1.-length(grad(phi_half,fs))))
251 gross 1659 # self.__reinitPde.setValue(Y =self.__phi, Y_reduced=dtau*s*(1.-inner(w,grad(phi_half,ReducedFunction(self.__domain)))))
252 gross 1473 # self.__reinitPde.setValue(Y =self.__phi+dtau*(s-inner(w,grad_phi)),X=dtau/2*h*(s-inner(w,grad_phi))*w)
253     # self.__reinitPde.setValue(Y =self.__phi+dtau*s*(1.-len_grad_phi),X=-dtau/2*h*s**2*grad_phi)
254     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)
255    
256     # 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)
257     self.__phi, previous = self.__reinitPde.getSolution(), self.__phi
258 gross 1661 # self.__updateInterface()
259 gross 1473
260     vol,vol_old=self.getVolumeOfNegativeDomain(),vol
261     diff=(vol-vol_old)
262     r=Lsup(length(grad(self.__phi))-1.)
263     TVD=integrate(length(grad(self.__phi,fs)))
264     print "iteration :", c, "range ",inf(self.__phi),sup(self.__phi),"error :",r,"volume change:",diff,TVD
265     # saveVTK("test.%s.xml"%(c+1),l=length(grad(self.__phi,fs)),s=s,phi=self.__phi,v=grad(self.__phi,fs))
266     c += 1
267     return
268     #==============================================
269     f2=0.7
270     h=self.__h
271     fs=h.getFunctionSpace()
272     vol=self.getVolumeOfNegativeDomain()
273     s=abs(self. __makeInterface(2.))
274     grad_phi=grad(self.__phi,fs)
275     len_grad_phi=length(grad_phi)
276    
277     #----
278     # aphi_on_h=abs(interpolate(self.__phi,self.__h.getFunctionSpace()))
279     # q=2*self.__h
280     # mask_neg = whereNegative(aphi_on_h-q)
281     # mask_pos = wherePositive(aphi_on_h-q-self.__h)
282     # mask_interface = 1.-mask_neg-mask_pos
283     # s2=mask_neg + mask_interface * (q+self.__h-aphi_on_h)/self.__h
284     #----
285     m=whereNonPositive(len_grad_phi-f2)
286     s2=m*len_grad_phi/f2+(1.-m)
287     #----
288     # s2=1.
289     #----
290     self.__reinitPde.setValue(D=(1-s)/h**2,Y=(1-s)/h**2*self.__phi)
291     self.__reinitPde.setValue(A=(s2*len_grad_phi+(1.-s2))*kronecker(3),X=grad_phi)
292     # self.__reinitPde.setValue(A=(len_grad_phi-1)/len_grad_phi*kronecker(3))
293     # self.__reinitPde.setValue(A=kronecker(3), X=grad_phi/len_grad_phi)
294     self.__phi = self.__reinitPde.getSolution()
295     r=Lsup(length(grad(self.__phi))-1.)
296     vol,vol_old=self.getVolumeOfNegativeDomain(),vol
297     diff=(vol-vol_old)/vol
298     print "iteration :", inf(self.__phi),sup(self.__phi),r,diff
299     # saveVTK("test.%s.xml"%0,l=length(grad(self.__phi,fs)),s=s,phi=self.__phi,v=grad(self.__phi,fs),s2=s2)
300     return
301     #=============================================
302    
303     #============
304    
305    
306     def getVolumeOfNegativeDomain(self):
307     """
308     return the current volume of domain with phi<0.
309     """
310     return integrate((1.-self.__makeInterface(1.))/2.)
311    
312    
313     def getBoundingBoxOfNegativeDomain(self):
314     """
315     get the height of the region with phi<0
316     """
317     fs=self.__h.getFunctionSpace()
318     mask_phi1=wherePositive(interpolate(self.__phi,fs))
319     mask_phi2=wherePositive(self.__phi)
320     x1=fs.getX()
321 gross 1659 x2=self.__domain.getX()
322 gross 1473 out=[]
323     for i in range(fs.getDim()):
324     x1_i=x1[i]
325     x2_i=x2[i]
326     d=2*(sup(x2_i)-inf(x2_i))
327     offset1=d*mask_phi1
328     offset2=d*mask_phi2
329     out.append((min(inf(x1_i+offset1),inf(x2_i+offset2)),max(sup(x1_i-offset1),sup(x2_i-offset2))))
330     return tuple(out)
331    

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