simpeg/notebooks/DC forward.ipynb

In [1]:

from SimPEG import *

In [6]:

%pylab inline

Populating the interactive namespace from numpy and matplotlib

WARNING: pylab import has clobbered these variables: ['linalg']
`%matplotlib` prevents importing * from pylab and numpy

In [69]:

cs = 25.
hx = [(cs,7, -1.3),(cs,21),(cs,7, 1.3)]
hy = [(cs,7, -1.3),(cs,21),(cs,7, 1.3)]
hz = [(cs,7, -1.3),(cs,20)]

In [72]:

mesh = Mesh.TensorMesh([hx, hy, hz], "CCN")
sigma = np.ones(mesh.nC)

In [79]:

print mesh

  ---- 3-D TensorMesh ----  
   x0: -833.94
   y0: -833.94
   z0: -1071.44
  nCx: 35
  nCy: 35
  nCz: 27
   hx: 156.87, 120.67, 92.82, 71.40, 54.93, 42.25, 32.50, 21*25.00, 32.50, 42.25, 54.93, 71.40, 92.82, 120.67, 156.87
   hy: 156.87, 120.67, 92.82, 71.40, 54.93, 42.25, 32.50, 21*25.00, 32.50, 42.25, 54.93, 71.40, 92.82, 120.67, 156.87
   hz: 156.87, 120.67, 92.82, 71.40, 54.93, 42.25, 32.50, 20*25.00

In [81]:

mesh.nC

Out [81]:

33075

In [82]:

Div = mesh.faceDiv

In [83]:

mesh.setCellGradBC("neumann")

Out [83]:

[['neumann', 'neumann'], ['neumann', 'neumann'], ['neumann', 'neumann']]

In [84]:

Grad = mesh.cellGrad

In [101]:

Afc = mesh.aveF2CC
Msig = Utils.sdiag(1./(Afc.T*(1./sigma)))

In [102]:

A = Div*Msig*Grad

In [103]:

# A[-1, -1] / mesh.vol[-1]

In [104]:

A[0,0] /= mesh.vol[0]

In [105]:

inds = Utils.closestPoints(mesh, np.r_[0., 0., 0.])

In [106]:

q = np.zeros(mesh.nC)
q[inds] = 1.

In [109]:

from pymatsolver import MumpsSolver

In [110]:

Ainv = MumpsSolver(A)

In [111]:

phi = Ainv*q

In [115]:

mesh.vectorCCz.shape

Out [115]:

(27,)

In [117]:

mesh.plotSlice(phi,ind=26, grid=True)

Out [117]:

(<matplotlib.collections.QuadMesh at 0x10e663790>,
 <matplotlib.lines.Line2D at 0x10e663c10>)

In [120]:

xyzM = Utils.ndgrid(mesh.vectorCCx+5., mesh.vectorCCy, np.r_[0.])
xyzN = Utils.ndgrid(mesh.vectorCCx-5., mesh.vectorCCy, np.r_[0.])

In [123]:

PM = mesh.getInterpolationMat(xyzM, "CC")
PN = mesh.getInterpolationMat(xyzN, "CC")

In [ ]:

PM = mesh.getInterpolationMat

In [124]:

data = PM*phi-PN*phi

In [126]:

plt.imshow(data.reshape(mesh.nCx, mesh.nCy))

Out [126]:

<matplotlib.image.AxesImage at 0x108812c10>

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