/[escript]/branches/symbolic_from_3470/ripley/test/python/gravity_gamma.py
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Contents of /branches/symbolic_from_3470/ripley/test/python/gravity_gamma.py

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Revision 3877 - (show annotations)
Mon Mar 19 00:52:00 2012 UTC (6 years, 11 months ago) by gross
File MIME type: text/x-python
File size: 4254 byte(s)
underrelaxtion fixed.
1 from esys.escript import *
2 from esys.escript.linearPDEs import LinearPDE, LinearSinglePDE
3 from esys.escript.nonlinearPDE import *
4 from esys.finley import Rectangle,Brick
5 from math import pi
6 import os
7 import esys.escript.unitsSI as U
8 #import numpy as np
9 #import scipy.optimize as so
10
11 #DIM=3
12 #NE=10
13
14 DIM=2
15 NE=80
16
17
18 class RockFeature(object):
19 def __init__(self, lx, ly, lz, x=0, y=0, depth=0, rho=0):
20 self.x=x
21 self.y=y
22 self.lx=lx
23 self.ly=ly
24 self.lz=lz
25 self.depth=depth
26 self.rho=rho
27 def getMask(self, x):
28 DIM=x.getDomain().getDim()
29 m=whereNonPositive(x[DIM-1]+self.depth) * whereNonNegative(x[DIM-1]+(self.depth+self.lz)) \
30 *whereNonNegative(x[0]-(self.x-self.lx/2)) * whereNonPositive(x[0]-(self.x+self.lx/2))
31 if DIM>2:
32 m*=whereNonNegative(x[1]-(self.y-self.ly/2)) * whereNonPositive(x[1]-(self.y+self.ly/2))
33 return m
34
35
36 H=20*U.km
37 L=60*U.km
38 L0=0
39 L1=0
40 H_earth=10.*U.km
41
42
43 rho_rock=2300*U.kg/U.m**3
44 rho_air=0.
45 feastures = [ RockFeature(lx=10.*U.km, ly=10.*U.km, lz=1.*U.km, x= L/2-10.*U.km, y=L/2-10.*U.km, depth=1.*U.km, rho=rho_rock*0.1),
46 RockFeature(lx=10.*U.km, ly=10.*U.km, lz=1.*U.km, x= L/2+10.*U.km, y=L/2+10.*U.km, depth=5.*U.km, rho=rho_rock*0.1) ]
47
48
49
50
51 # generate Domain:
52 NE_H=NE
53 NE_L=int((L/H)*NE+0.5)
54 if DIM==2:
55 domain = Rectangle(NE_L,NE_H,l0=L,l1=H)
56 x_cord=domain.getX()-[L0, H_earth]
57 else:
58 domain = Brick(NE_L,NE_L,NE_H,l0=L,l1=L,l2=H)
59 x_cord=domain.getX()-[L0, L1, H_earth]
60 LL=max(L,H)
61
62 m_psi=whereZero(x_cord[DIM-1]-inf(x_cord[DIM-1])) + whereZero(x_cord[DIM-1]-sup(x_cord[DIM-1]))
63 for i in range(DIM-1):
64 m_psi= m_psi + whereZero(x_cord[i]-inf(x_cord[i])) + whereZero(x_cord[i]-sup(x_cord[i]))
65 #m_rho=wherePositive(domain.getX()[DIM-1]-H_earth)
66 #m_rho=whereZero(x_cord[DIM-1]-inf(x_cord[DIM-1])) + whereZero(x_cord[DIM-1]-sup(x_cord[DIM-1]))
67 m_rho=wherePositive(domain.getX()[DIM-1]-H_earth) + whereZero(x_cord[DIM-1]-inf(x_cord[DIM-1])) + whereZero(x_cord[DIM-1]-sup(x_cord[DIM-1]))
68 #m_rho=whereZero(x_cord[DIM-1]-sup(x_cord[DIM-1]))
69
70
71 # create test density:
72 rho_ref= 0
73 for f in feastures:
74 m=f.getMask(x_cord)
75 rho_ref = rho_ref * (1-m) + f.rho * m
76
77 #rho_ref=sup(x_cord[DIM-1])-x_cord[DIM-1] for testing!
78
79 # get the reference potential:
80 pde=LinearSinglePDE(domain)
81 pde.setValue(A=kronecker(domain), Y=4*pi*rho_ref, q=m_psi)
82 pde.getSolverOptions().setVerbosityOn()
83 pde.setSymmetryOn()
84 #pde.getSolverOptions().setSolverMethod(pde.getSolverOptions().DIRECT)
85 psi_ref=pde.getSolution()
86 del pde
87 d_obs=kronecker(DIM)[DIM-1]
88 g_hat=grad(psi_ref)[DIM-1]
89 beta=1/1000000.
90 #beta=1/100.
91 #
92 # where do we know the gravity:
93 #
94 chi=1.
95 x=Function(domain).getX()
96 dz=H/NE_H
97 H_earth=int(H_earth/dz)*dz # lock to grid
98 chi=whereNegative(abs(x[DIM-1]-(H_earth+dz/2))-dz/2)
99 #
100 # normalize g_hat (data):
101 #
102 g0=Lsup(chi * g_hat)
103 if not g0 > 0: g0=1.
104 g_hat*=1./g0
105 print "Data normalization factor = %e"%g0
106
107 #=========== This is the same with the variational class ===================================
108 print "====== Use variational problem ============================================="
109 psi_s=Symbol("psi", (), dim=DIM)
110 rho_s=Symbol("rho", (), dim=DIM)
111 gamma_s=Symbol("gamma", (), dim=DIM)
112 gamma_s=0.5
113 gamma_s=0.6
114 #g=Symbol("g", (), dim=DIM)
115
116 v=VariationalProblem(domain, u=psi_s,p=rho_s, debug=VariationalProblem.DEBUG3)
117 v.setValue( H = 0.5*chi*(grad(psi_s)[DIM-1]-g_hat)**2 + beta/gamma_s * (length(grad(rho_s))**2 + EPSILON**2)**gamma_s,
118 X=grad(psi_s), Y=-4*pi*rho_s/LL**2,
119 qp=m_rho, q=m_psi)
120 v.getNonlinearPDE().getLinearSolverOptions().setSolverMethod(v.getNonlinearPDE().getLinearSolverOptions().DIRECT)
121
122 rho_v, psi_v, lag=v.getSolution(psi=0, rho=1, gamma=2) # gamma=0.5 is the interesting case!
123 print "rho =",rho_v
124 print "rho_ref =",rho_ref*g0
125 print "psi =",psi_v
126 print "lambda =",lag
127
128 print "Differences to Data :"
129 print "rho =",Lsup(rho_ref-rho_v*g0/LL**2)/Lsup(rho_ref)
130 print "psi =",Lsup(psi_ref-psi_v*g0)/Lsup(psi_ref)
131 print "g =",Lsup(chi*grad(psi_ref-psi_v*g0)[DIM-1])/Lsup(chi*grad(psi_ref)[DIM-1])
132
133
134
135 #saveVTK("u.vtu", rho_ref=rho_ref, psi_ref=psi_ref, g=grad(psi_ref)[DIM-1], rho=rho_v, psi=psi_v, chi=chi)

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