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

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Revision 1661 - (show annotations)
Mon Jul 21 22:08:27 2008 UTC (11 years, 3 months ago) by gross
File MIME type: text/x-python
File size: 11649 byte(s)
some improvements on level set
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=TransportPDE(self.__domain,num_equations=1,theta=0.5)
31 # self.__fc.setReducedOrderOn()
32 self.__fc.setValue(M=Scalar(1.,Function(self.__domain)))
33 self.__fc.setInitialSolution(phi+self.__diam)
34
35 #=======================================
36 self.__reinitPde = LinearPDE(self.__domain,numEquations=1, numSolutions=1)
37 self.__reinitPde.setSolverMethod(solver=LinearPDE.LUMPING)
38 self.__reinitPde.setReducedOrderOn()
39 self.__reinitPde.setSymmetryOn()
40 self.__reinitPde.setValue(D=1.)
41 # self.__reinitPde.setTolerance(1.e-8)
42 # self.__reinitPde.setSolverMethod(preconditioner=LinearPDE.ILU0)
43 #=======================================
44 self.__updateInterface()
45 print "phi range:",inf(phi), sup(phi)
46
47 def setFixedRegion(self,mask,contour=0):
48 q=whereNonPositive(abs(self.__phi-contour)-self.__h)*mask
49 # self.__fc.setValue(q=q)
50 self.__reinitPde.setValue(q=q)
51
52 def getDomain(self):
53 return self.__domain
54
55 def getTimeStepSize(self,velocity):
56 """
57 returns a new dt for a given velocity using the courant coundition
58 """
59 self.velocity=velocity
60 self.__fc.setValue(C=-interpolate(velocity,Function(self.__domain)))
61 dt=self.__fc.getSafeTimeStepSize()
62 return dt
63
64 def getLevelSetFunction(self):
65 """
66 returns the level set function
67 """
68 return self.__phi
69
70 def __updateInterface(self):
71 self.__smoothed_char=self.__makeInterface(self.__phi)
72
73 def __makeInterface(self,phi,smoothing_width=1.):
74 """
75 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
76 and 1 where the level set is 1
77 """
78 s=smoothing_width*self.__h
79 phi_on_h=interpolate(phi,Function(self.__domain))
80 mask_neg = whereNonNegative(-s-phi_on_h)
81 mask_pos = whereNonNegative(phi_on_h-s)
82 mask_interface = 1.-mask_neg-mask_pos
83 # 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)=
84 interface=phi_on_h/s
85 return - mask_neg + mask_pos + mask_interface * interface
86
87 def makeCharacteristicFunction(self, contour=0, positiveSide=True, smoothing_width=1.):
88 return self.makeCharacteristicFunctionFromExternalLevelSetFunction(self.__phi,contour,positiveSide,smoothing_width)
89
90 def makeCharacteristicFunctionFromExternalLevelSetFunction(self,phi,contour=0, positiveSide=True, smoothing_width=1.):
91 s=self.__makeInterface(phi-contour,smoothing_width)
92 if positiveSide:
93 return (1+s)/2
94 else:
95 return (1-s)/2
96
97
98 def update(self,dt):
99 """
100 sets a new velocity and updates the level set fuction
101
102 @param dt: time step forward
103 """
104 self.__phi=self.__fc.solve(dt, verbose=False)-self.__diam
105 self.__update_count += 1
106 if self.__update_count%self.__reinitialization_each == 0:
107 self.__phi=self.__reinitialise(self.__phi)
108 self.__fc.setInitialSolution(self.__phi+self.__diam)
109 self.__updateInterface()
110
111 def setTolerance(self,tolerance=1e-3):
112 self.__fc.setTolerance(tolerance)
113
114 def __reinitialise(self,phi):
115 print "reintialization started:"
116 s=self.__makeInterface(phi,1.)
117 g=grad(phi)
118 w = s*g/(length(g)+EPSILON)
119 dtau = 0.5*inf(Function(self.__domain).getSize())
120 print "step size: dt = ",dtau
121 iter =0
122 # self.__reinitPde.setValue(q=whereNegative(abs(phi)-self.__h), r=phi)
123 # self.__reinitPde.setValue(r=phi)
124 while (iter<=self.__reinitialization_steps_max):
125 phi_old=phi
126 self.__reinitPde.setValue(Y = phi+(dtau/2.)*(s-inner(w,grad(phi))))
127 phi_half = self.__reinitPde.getSolution()
128 self.__reinitPde.setValue(Y = phi+dtau*(s-inner(w,grad(phi_half))))
129 phi = self.__reinitPde.getSolution()
130 change = Lsup(phi-phi_old)/self.__diam
131 print "phi range:",inf(phi), sup(phi)
132 print "iteration :", iter, " error:", change
133 iter +=1
134 print "reintialization completed."
135 return phi
136
137 def createParameter(self,value_negative=-1.,value_positive=1):
138 out = (value_negative+value_positive)/2. + self.__smoothed_char * ((value_positive-value_negative)/2.)
139 return out
140
141
142 #================ things from here onwards are not used nor tested: ==========================================
143
144
145 def getCharacteristicFunction(self):
146 return self.__smoothed_char
147
148
149
150
151 def RK2(self,L):
152 k0=L(phi)
153 phi_1=phi+dt*k0
154 k1=L(phi_1)
155 phi=phi+dt/2*(k0+k1)
156 def RK3(self,L):
157 k0=L(phi)
158 phi_1=phi+dt*L(phi)
159 k1=L(phi_1)
160 phi_2=phi+dt/4*(k0+k1)
161 k2=L(phi_2)
162 phi=phi+dt/6*(k0+4*k2+K1)
163 def TG(self,L):
164 k0=L(phi)
165 phi_1=phi+dt/2*k0
166 k1=L(phi_1)
167 phi=phi+dt*k1
168
169
170 def __reinitialise_old(self):
171 #=============================================
172 f=0.1
173 f2=0.3
174 h=self.__h
175 fs=h.getFunctionSpace()
176 vol=self.getVolumeOfNegativeDomain()
177 self.__reinitPde.setValue(D=1.0)
178 #============
179 grad_phi=grad(self.__phi,fs)
180 len_grad_phi=length(grad_phi)
181 w=grad_phi/len_grad_phi
182
183 # s=wherePositive(self. __makeInterface(2.))-whereNegative(self. __makeInterface(2.))
184 s=self. __makeInterface(2.)
185 # s2=whereNegative(len_grad_phi-f2)*(1-(1-len_grad_phi/f2)**2)+(1-whereNegative(len_grad_phi-f2))
186 s2=1.
187 s=s*s2
188 dtau=f*inf(h/abs(s))
189
190 #========================
191 diff=1.
192 d=1.
193 c =0
194 #==============================================
195 TVD=integrate(length(grad_phi))
196 print "initial range ",inf(self.__phi),sup(self.__phi),"error:",Lsup(1.-len_grad_phi),"volume =",vol,TVD
197 # saveVTK("test.%s.xml"%c,l=length(grad(self.__phi,fs))-1,s=s,phi=self.__phi)
198
199 dtau=f*inf(h/abs(s))
200 while c < self.__reinitialization_steps_max: # and abs(diff) >= 0.01:
201 #
202 grad_phi=grad(self.__phi,fs)
203 len_grad_phi=length(grad_phi)
204 #
205 # s=self.__makeInterface(1.)
206 # s2=whereNegative(len_grad_phi-f2)*(1-(1-len_grad_phi/f2)**2)+(1-whereNegative(len_grad_phi-f2))
207 # s=s*s2
208 # phi_on_h=interpolate(self.__phi,fs)
209 # self.__reinitPde.setValue(Y =self.__phi+dtau/2*s*(1.-len_grad_phi))
210 # phi_half=self.__reinitPde.getSolution()
211 # self.__reinitPde.setValue(Y =self.__phi+dtau*s*(1.-length(grad(phi_half,fs))))
212 # self.__reinitPde.setValue(Y =self.__phi, Y_reduced=dtau*s*(1.-inner(w,grad(phi_half,ReducedFunction(self.__domain)))))
213 # self.__reinitPde.setValue(Y =self.__phi+dtau*(s-inner(w,grad_phi)),X=dtau/2*h*(s-inner(w,grad_phi))*w)
214 # self.__reinitPde.setValue(Y =self.__phi+dtau*s*(1.-len_grad_phi),X=-dtau/2*h*s**2*grad_phi)
215 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)
216
217 # 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)
218 self.__phi, previous = self.__reinitPde.getSolution(), self.__phi
219 # self.__updateInterface()
220
221 vol,vol_old=self.getVolumeOfNegativeDomain(),vol
222 diff=(vol-vol_old)
223 r=Lsup(length(grad(self.__phi))-1.)
224 TVD=integrate(length(grad(self.__phi,fs)))
225 print "iteration :", c, "range ",inf(self.__phi),sup(self.__phi),"error :",r,"volume change:",diff,TVD
226 # saveVTK("test.%s.xml"%(c+1),l=length(grad(self.__phi,fs)),s=s,phi=self.__phi,v=grad(self.__phi,fs))
227 c += 1
228 return
229 #==============================================
230 f2=0.7
231 h=self.__h
232 fs=h.getFunctionSpace()
233 vol=self.getVolumeOfNegativeDomain()
234 s=abs(self. __makeInterface(2.))
235 grad_phi=grad(self.__phi,fs)
236 len_grad_phi=length(grad_phi)
237
238 #----
239 # aphi_on_h=abs(interpolate(self.__phi,self.__h.getFunctionSpace()))
240 # q=2*self.__h
241 # mask_neg = whereNegative(aphi_on_h-q)
242 # mask_pos = wherePositive(aphi_on_h-q-self.__h)
243 # mask_interface = 1.-mask_neg-mask_pos
244 # s2=mask_neg + mask_interface * (q+self.__h-aphi_on_h)/self.__h
245 #----
246 m=whereNonPositive(len_grad_phi-f2)
247 s2=m*len_grad_phi/f2+(1.-m)
248 #----
249 # s2=1.
250 #----
251 self.__reinitPde.setValue(D=(1-s)/h**2,Y=(1-s)/h**2*self.__phi)
252 self.__reinitPde.setValue(A=(s2*len_grad_phi+(1.-s2))*kronecker(3),X=grad_phi)
253 # self.__reinitPde.setValue(A=(len_grad_phi-1)/len_grad_phi*kronecker(3))
254 # self.__reinitPde.setValue(A=kronecker(3), X=grad_phi/len_grad_phi)
255 self.__phi = self.__reinitPde.getSolution()
256 r=Lsup(length(grad(self.__phi))-1.)
257 vol,vol_old=self.getVolumeOfNegativeDomain(),vol
258 diff=(vol-vol_old)/vol
259 print "iteration :", inf(self.__phi),sup(self.__phi),r,diff
260 # saveVTK("test.%s.xml"%0,l=length(grad(self.__phi,fs)),s=s,phi=self.__phi,v=grad(self.__phi,fs),s2=s2)
261 return
262 #=============================================
263
264 #============
265
266
267 def getVolumeOfNegativeDomain(self):
268 """
269 return the current volume of domain with phi<0.
270 """
271 return integrate((1.-self.__makeInterface(1.))/2.)
272
273
274 def getBoundingBoxOfNegativeDomain(self):
275 """
276 get the height of the region with phi<0
277 """
278 fs=self.__h.getFunctionSpace()
279 mask_phi1=wherePositive(interpolate(self.__phi,fs))
280 mask_phi2=wherePositive(self.__phi)
281 x1=fs.getX()
282 x2=self.__domain.getX()
283 out=[]
284 for i in range(fs.getDim()):
285 x1_i=x1[i]
286 x2_i=x2[i]
287 d=2*(sup(x2_i)-inf(x2_i))
288 offset1=d*mask_phi1
289 offset2=d*mask_phi2
290 out.append((min(inf(x1_i+offset1),inf(x2_i+offset2)),max(sup(x1_i-offset1),sup(x2_i-offset2))))
291 return tuple(out)
292

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