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Total field approach

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seogi
2014-02-20 17:29:08 -08:00
parent 37bca3b3e9
commit 3bc66134aa
3 changed files with 1034 additions and 164 deletions
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simpegPF/notebooks/Boundary_conditions.ipynb
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simpegPF/notebooks/MagForward_total.ipynb
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simpegPF/notebooks/test_boundary.py
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from SimPEG.Utils.sputils import kron3, speye, sdiag
from SimPEG import *
import numpy as np
import scipy.sparse as sp
def ddxFaceDivBC(n, bc):
ij = (np.array([0, n-1]),np.array([0, 1]))
vals = np.zeros(2)
ij = (np.array([0, n-1]),np.array([0, 1]))
vals = np.zeros(2)
# Set the first side
if(bc[0] == 'dirichlet'):
vals[0] = 0
elif(bc[0] == 'neumann'):
vals[0] = -1
# Set the second side
if(bc[1] == 'dirichlet'):
vals[1] = 0
elif(bc[1] == 'neumann'):
vals[1] = 1
D = sp.csr_matrix((vals, ij), shape=(n,2))
return D
# Set the first side
if(bc[0] == 'dirichlet'):
vals[0] = 0
elif(bc[0] == 'neumann'):
vals[0] = -1
# Set the second side
if(bc[1] == 'dirichlet'):
vals[1] = 0
elif(bc[1] == 'neumann'):
vals[1] = 1
D = sp.csr_matrix((vals, ij), shape=(n,2))
return D
def faceDivBC(mesh, BC, ind):
"""
The facd divergence boundary condtion matrix
"""
The facd divergence boundary condtion matrix
"""
# The number of cell centers in each direction
n = mesh.nCv
# Compute faceDivergence operator on faces
if(mesh.dim == 1):
D = ddxFaceDivBC(n[0], BC[0])
elif(mesh.dim == 2):
D1 = sp.kron(speye(n[1]), ddxFaceDivBC(n[0]), BC[0])
D2 = sp.kron(ddxFaceDivBC(n[1], BC[1]), speye(n[0]))
D = sp.hstack((D1, D2), format="csr")
elif(mesh.dim == 3):
D1 = kron3(speye(n[2]), speye(n[1]), ddxFaceDivBC(n[0], BC[0]))
D2 = kron3(speye(n[2]), ddxFaceDivBC(n[1], BC[1]), speye(n[0]))
D3 = kron3(ddxFaceDivBC(n[2], BC[2]), speye(n[1]), speye(n[0]))
D = sp.hstack((D1, D2, D3), format="csr")
# Compute areas of cell faces & volumes
S = mesh.area[ind]
V = mesh.vol
mesh._faceDiv = sdiag(1/V)*D*sdiag(S)
.. math::
return mesh._faceDiv
"""
# The number of cell centers in each direction
n = mesh.nCv
# Compute faceDivergence operator on faces
if(mesh.dim == 1):
D = ddxFaceDivBC(n[0], BC[0])
elif(mesh.dim == 2):
D1 = sp.kron(speye(n[1]), ddxFaceDivBC(n[0]), BC[0])
D2 = sp.kron(ddxFaceDivBC(n[1], BC[1]), speye(n[0]))
D = sp.hstack((D1, D2), format="csr")
elif(mesh.dim == 3):
D1 = kron3(speye(n[2]), speye(n[1]), ddxFaceDivBC(n[0], BC[0]))
D2 = kron3(speye(n[2]), ddxFaceDivBC(n[1], BC[1]), speye(n[0]))
D3 = kron3(ddxFaceDivBC(n[2], BC[2]), speye(n[1]), speye(n[0]))
D = sp.hstack((D1, D2, D3), format="csr")
# Compute areas of cell faces & volumes
S = mesh.area[ind]
V = mesh.vol
mesh._faceDiv = sdiag(1/V)*D*sdiag(S)
return mesh._faceDiv
def faceBCind(mesh):
"""
Find indices of boundary faces in each direction
"""
Find indices of boundary faces in each direction
"""
if(mesh.dim==1):
indxd = (mesh.gridFx[:,0]==min(mesh.gridFx[:,0]))
indxu = (mesh.gridFx[:,0]==max(mesh.gridFx[:,0]))
return indxd, indxu
elif(mesh.dim==1):
indxd = (mesh.gridFx[:,0]==min(mesh.gridFx[:,0]))
indxu = (mesh.gridFx[:,0]==max(mesh.gridFx[:,0]))
indyd = (mesh.gridFy[:,1]==min(mesh.gridFy[:,1]))
indyu = (mesh.gridFy[:,1]==max(mesh.gridFy[:,1]))
return indxd, indxu, indyd, indyu
elif(mesh.dim==3):
indxd = (mesh.gridFx[:,0]==min(mesh.gridFx[:,0]))
indxu = (mesh.gridFx[:,0]==max(mesh.gridFx[:,0]))
indyd = (mesh.gridFy[:,1]==min(mesh.gridFy[:,1]))
indyu = (mesh.gridFy[:,1]==max(mesh.gridFy[:,1]))
indzd = (mesh.gridFz[:,2]==min(mesh.gridFz[:,2]))
indzu = (mesh.gridFz[:,2]==max(mesh.gridFz[:,2]))
return indxd, indxu, indyd, indyu, indzd, indzu
"""
if(mesh.dim==1):
indxd = (mesh.gridFx[:,0]==min(mesh.gridFx[:,0]))
indxu = (mesh.gridFx[:,0]==max(mesh.gridFx[:,0]))
return indxd, indxu
elif(mesh.dim==1):
indxd = (mesh.gridFx[:,0]==min(mesh.gridFx[:,0]))
indxu = (mesh.gridFx[:,0]==max(mesh.gridFx[:,0]))
indyd = (mesh.gridFy[:,1]==min(mesh.gridFy[:,1]))
indyu = (mesh.gridFy[:,1]==max(mesh.gridFy[:,1]))
return indxd, indxu, indyd, indyu
elif(mesh.dim==3):
indxd = (mesh.gridFx[:,0]==min(mesh.gridFx[:,0]))
indxu = (mesh.gridFx[:,0]==max(mesh.gridFx[:,0]))
indyd = (mesh.gridFy[:,1]==min(mesh.gridFy[:,1]))
indyu = (mesh.gridFy[:,1]==max(mesh.gridFy[:,1]))
indzd = (mesh.gridFz[:,2]==min(mesh.gridFz[:,2]))
indzu = (mesh.gridFz[:,2]==max(mesh.gridFz[:,2]))
return indxd, indxu, indyd, indyu, indzd, indzu
def spheremodel(mesh, x0, y0, z0, r):
"""
Generate model indicies for sphere
- (x0, y0, z0 ): is the center location of sphere
- r: is the radius of the sphere
- it returns logical indicies of cell-center model
"""
ind = np.sqrt((mesh.gridCC[:,0]-x0)**2+(mesh.gridCC[:,1]-y0)**2+(mesh.gridCC[:,2]-z0)**2 ) < r
return ind
def MagSphereAnalFun(x, y, z, R, x0, y0, z0, mu1, mu2, H0, flag):
"""
Analytic function for Magnetics problem. The set up here is
magnetic sphere in whole-space.
- (x0,y0,z0)
- (x0, y0, z0 ): is the center location of sphere
- r: is the radius of the sphere
.. math::
\mathbf{H}^p = H_0\hat{x}
"""
if (~np.size(x)==np.size(y)==np.size(z)):
print "Specify same size of x, y, z"
return
dim = x.shape
x = Utils.mkvc(x)
y = Utils.mkvc(y)
z = Utils.mkvc(z)
ind = np.sqrt((x-x0)**2+(y-y0)**2+(z-z0)**2 ) < R
r = Utils.mkvc(np.sqrt((x-x0)**2+(y-y0)**2+(z-z0)**2 ))
Bx = np.zeros(x.size)
By = np.zeros(x.size)
Bz = np.zeros(x.size)
# Inside of the sphere
rf2 = 3*mu1/(mu2+2*mu1)
if (flag == 'total'):
Bx[ind] = mu2*H0*(rf2)
elif (flag == 'secondary'):
Bx[ind] = mu2*H0*(rf2)-mu1*H0
By[ind] = 0.
Bz[ind] = 0.
# Outside of the sphere
rf1 = (mu2-mu1)/(mu2+2*mu1)
if (flag == 'total'):
Bx[~ind] = mu1*(H0+H0/r[~ind]**5*(R**3)*rf1*(2*x[~ind]**2-y[~ind]**2-z[~ind]**2))
elif (flag == 'secondary'):
Bx[~ind] = mu1*(H0/r[~ind]**5*(R**3)*rf1*(2*x[~ind]**2-y[~ind]**2-z[~ind]**2))
By[~ind] = mu1*(H0/r[~ind]**5*(R**3)*rf1*(3*x[~ind]*y[~ind]))
Bz[~ind] = mu1*(H0/r[~ind]**5*(R**3)*rf1*(3*x[~ind]*z[~ind]))
return np.reshape(Bx, x.shape, order='F'), np.reshape(By, x.shape, order='F'), np.reshape(Bz, x.shape, order='F')