mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-28 09:13:21 +08:00
seogi
229 lines
7.8 KiB
Python
229 lines
7.8 KiB
Python
from scipy.constants import mu_0
|
|
from SimPEG import *
|
|
from SimPEG.Utils import kron3, speye, sdiag
|
|
import matplotlib.pyplot as plt
|
|
|
|
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}_0 = 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')
|
|
|
|
|
|
def CongruousMagBC(mesh, Bo, chi):
|
|
"""
|
|
Computing boundary condition using Congrous sphere method.
|
|
This is designed for secondary field formulation.
|
|
|
|
>> Input
|
|
|
|
* mesh: Mesh class
|
|
* Bo: np.array([Box, Boy, Boz]): Primary magnetic flux
|
|
* chi: susceptibility at cell volume
|
|
|
|
.. math::
|
|
|
|
\\vec{B}(r) = \\frac{\mu_0}{4\pi} \\frac{m}{ \| \\vec{r} - \\vec{r}_0\|^3}[3\hat{m}\cdot\hat{r}-\hat{m}]
|
|
|
|
"""
|
|
|
|
ind = chi > 0.
|
|
V = mesh.vol[ind].sum()
|
|
|
|
gamma = 1/V*(chi*mesh.vol).sum() # like a mass!
|
|
|
|
Bot = np.sqrt(sum(Bo**2))
|
|
mx = Bo[0]/Bot
|
|
my = Bo[1]/Bot
|
|
mz = Bo[2]/Bot
|
|
|
|
mom = 1/mu_0*Bot*gamma*V/(1+gamma/3)
|
|
xc = sum(chi[ind]*mesh.gridCC[:,0][ind])/sum(chi[ind])
|
|
yc = sum(chi[ind]*mesh.gridCC[:,1][ind])/sum(chi[ind])
|
|
zc = sum(chi[ind]*mesh.gridCC[:,2][ind])/sum(chi[ind])
|
|
|
|
indxd, indxu, indyd, indyu, indzd, indzu = mesh.faceBoundaryInd
|
|
|
|
const = mu_0/(4*np.pi)*mom
|
|
rfun = lambda x: np.sqrt((x[:,0]-xc)**2 + (x[:,1]-yc)**2 + (x[:,2]-zc)**2)
|
|
|
|
mdotrx = (mx*(mesh.gridFx[(indxd|indxu),0]-xc)/rfun(mesh.gridFx[(indxd|indxu),:]) +
|
|
my*(mesh.gridFx[(indxd|indxu),1]-yc)/rfun(mesh.gridFx[(indxd|indxu),:]) +
|
|
mz*(mesh.gridFx[(indxd|indxu),2]-zc)/rfun(mesh.gridFx[(indxd|indxu),:]))
|
|
|
|
Bbcx = const/(rfun(mesh.gridFx[(indxd|indxu),:])**3)*(3*mdotrx*(mesh.gridFx[(indxd|indxu),0]-xc)/rfun(mesh.gridFx[(indxd|indxu),:])-mx)
|
|
|
|
mdotry = (mx*(mesh.gridFy[(indyd|indyu),0]-xc)/rfun(mesh.gridFy[(indyd|indyu),:]) +
|
|
my*(mesh.gridFy[(indyd|indyu),1]-yc)/rfun(mesh.gridFy[(indyd|indyu),:]) +
|
|
mz*(mesh.gridFy[(indyd|indyu),2]-zc)/rfun(mesh.gridFy[(indyd|indyu),:]))
|
|
|
|
Bbcy = const/(rfun(mesh.gridFy[(indyd|indyu),:])**3)*(3*mdotry*(mesh.gridFy[(indyd|indyu),1]-yc)/rfun(mesh.gridFy[(indyd|indyu),:])-my)
|
|
|
|
mdotrz = (mx*(mesh.gridFz[(indzd|indzu),0]-xc)/rfun(mesh.gridFz[(indzd|indzu),:]) +
|
|
my*(mesh.gridFz[(indzd|indzu),1]-yc)/rfun(mesh.gridFz[(indzd|indzu),:]) +
|
|
mz*(mesh.gridFz[(indzd|indzu),2]-zc)/rfun(mesh.gridFz[(indzd|indzu),:]))
|
|
|
|
Bbcz = const/(rfun(mesh.gridFz[(indzd|indzu),:])**3)*(3*mdotrz*(mesh.gridFz[(indzd|indzu),2]-zc)/rfun(mesh.gridFz[(indzd|indzu),:])-mz)
|
|
|
|
return np.r_[Bbcx, Bbcy, Bbcz], (1/gamma-1/(3+gamma))*1/V
|
|
|
|
|
|
def MagSphereAnalFunA(x, y, z, R, xc, yc, zc, chi, Bo, flag):
|
|
"""
|
|
Computing boundary condition using Congrous sphere method.
|
|
This is designed for secondary field formulation.
|
|
>> Input
|
|
mesh: Mesh class
|
|
Bo: np.array([Box, Boy, Boz]): Primary magnetic flux
|
|
Chi: susceptibility at cell volume
|
|
|
|
.. math::
|
|
|
|
\\vec{B}(r) = \\frac{\mu_0}{4\pi}\\frac{m}{\| \\vec{r}-\\vec{r}_0\|^3}[3\hat{m}\cdot\hat{r}-\hat{m}]
|
|
|
|
"""
|
|
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)
|
|
|
|
Bot = np.sqrt(sum(Bo**2))
|
|
mx = Bo[0]/Bot
|
|
my = Bo[1]/Bot
|
|
mz = Bo[2]/Bot
|
|
|
|
ind = np.sqrt((x-xc)**2+(y-yc)**2+(z-zc)**2 ) < R
|
|
|
|
Bx = np.zeros(x.size)
|
|
By = np.zeros(x.size)
|
|
Bz = np.zeros(x.size)
|
|
|
|
# Inside of the sphere
|
|
rf2 = 3/(chi+3)*(1+chi)
|
|
if (flag == 'total'):
|
|
Bx[ind] = Bo[0]*(rf2)
|
|
By[ind] = Bo[1]*(rf2)
|
|
Bz[ind] = Bo[2]*(rf2)
|
|
elif (flag == 'secondary'):
|
|
Bx[ind] = Bo[0]*(rf2)-Bo[0]
|
|
By[ind] = Bo[1]*(rf2)-Bo[1]
|
|
Bz[ind] = Bo[2]*(rf2)-Bo[2]
|
|
|
|
r = Utils.mkvc(np.sqrt((x-xc)**2+(y-yc)**2+(z-zc)**2 ))
|
|
V = 4*np.pi*R**3/3
|
|
mom = Bot/mu_0*chi/(1+chi/3)*V
|
|
const = mu_0/(4*np.pi)*mom
|
|
mdotr = (mx*(x[~ind]-xc)/r[~ind] + my*(y[~ind]-yc)/r[~ind] + mz*(z[~ind]-zc)/r[~ind])
|
|
Bx[~ind] = const/(r[~ind]**3)*(3*mdotr*(x[~ind]-xc)/r[~ind]-mx)
|
|
By[~ind] = const/(r[~ind]**3)*(3*mdotr*(y[~ind]-yc)/r[~ind]-my)
|
|
Bz[~ind] = const/(r[~ind]**3)*(3*mdotr*(z[~ind]-zc)/r[~ind]-mz)
|
|
|
|
|
|
return Bx, By, Bz
|
|
|
|
def IDTtoxyz(Inc, Dec, Btot):
|
|
"""
|
|
Convert from Inclination, Declination, Total intensity of earth field to x, y, z
|
|
"""
|
|
Bx = Btot*np.cos(Inc/180.*np.pi)*np.sin(Dec/180.*np.pi)
|
|
By = Btot*np.cos(Inc/180.*np.pi)*np.cos(Dec/180.*np.pi)
|
|
Bz = -Btot*np.sin(Inc/180.*np.pi)
|
|
|
|
return np.r_[Bx, By, Bz]
|
|
|
|
if __name__ == '__main__':
|
|
|
|
hxind = ((0,25,1.3),(21, 12.5),(0,25,1.3))
|
|
hyind = ((0,25,1.3),(21, 12.5),(0,25,1.3))
|
|
hzind = ((0,25,1.3),(20, 12.5),(0,25,1.3))
|
|
hx, hy, hz = Utils.meshTensors(hxind, hyind, hzind)
|
|
M3 = Mesh.TensorMesh([hx, hy, hz], [-sum(hx)/2,-sum(hy)/2,-sum(hz)/2])
|
|
indxd, indxu, indyd, indyu, indzd, indzu = M3.faceBoundaryInd
|
|
mu0 = 4*np.pi*1e-7
|
|
chibkg = 0.
|
|
chiblk = 0.01
|
|
chi = np.ones(M3.nC)*chibkg
|
|
sph_ind = spheremodel(M3, 0, 0, 0, 100)
|
|
chi[sph_ind] = chiblk
|
|
mu = (1.+chi)*mu0
|
|
Bbc, const = CongruousMagBC(M3, np.array([1., 0., 0.]), chi)
|
|
|
|
flag = 'secondary'
|
|
Box = 1.
|
|
H0 = Box/mu_0
|
|
Bbcxx, Bbcxy, Bbcxz = MagSphereAnalFun(M3.gridFx[(indxd|indxu),0], M3.gridFx[(indxd|indxu),1], M3.gridFx[(indxd|indxu),2], 100, 0., 0., 0., mu_0, mu_0*(1+chiblk), H0, flag)
|
|
Bbcyx, Bbcyy, Bbcyz = MagSphereAnalFun(M3.gridFy[(indyd|indyu),0], M3.gridFy[(indyd|indyu),1], M3.gridFy[(indyd|indyu),2], 100, 0., 0., 0., mu_0, mu_0*(1+chiblk), H0, flag)
|
|
Bbczx, Bbczy, Bbczz = MagSphereAnalFun(M3.gridFz[(indzd|indzu),0], M3.gridFz[(indzd|indzu),1], M3.gridFz[(indzd|indzu),2], 100, 0., 0., 0., mu_0, mu_0*(1+chiblk), H0, flag)
|
|
Bbc_anal = np.r_[Bbcxx, Bbcyy, Bbczz]
|
|
|
|
fig, ax = plt.subplots(1,1, figsize = (10, 10))
|
|
ax.plot(Bbc_anal)
|
|
ax.plot(Bbc)
|
|
plt.show()
|
|
err = np.linalg.norm(Bbc-Bbc_anal)/np.linalg.norm(Bbc_anal)
|
|
|
|
if err < 0.1:
|
|
print 'Mag Boundary computation is valid, err = ', err
|
|
else:
|
|
print 'Mag Boundary computation is wrong!!, err = ', err
|
|
|
|
pass
|