mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-27 22:08:38 +08:00
Lindsey Heagy
204 lines
7.3 KiB
Python
204 lines
7.3 KiB
Python
from SimPEG import *
|
|
from scipy.special import ellipk, ellipe
|
|
from scipy.constants import mu_0, pi
|
|
|
|
def MagneticDipoleVectorPotential(srcLoc, obsLoc, component, moment=1., dipoleMoment=(0., 0., 1.), mu = mu_0):
|
|
"""
|
|
Calculate the vector potential of a set of magnetic dipoles
|
|
at given locations 'ref. <http://en.wikipedia.org/wiki/Dipole#Magnetic_vector_potential>'
|
|
|
|
:param numpy.ndarray srcLoc: Location of the source(s) (x, y, z)
|
|
:param numpy.ndarray,SimPEG.Mesh obsLoc: Where the potentials will be calculated (x, y, z) or a SimPEG Mesh
|
|
:param str,list component: The component to calculate - 'x', 'y', or 'z' if an array, or grid type if mesh, can be a list
|
|
:param numpy.ndarray dipoleMoment: The vector dipole moment
|
|
:rtype: numpy.ndarray
|
|
:return: The vector potential each dipole at each observation location
|
|
"""
|
|
#TODO: break this out!
|
|
|
|
if type(component) in [list, tuple]:
|
|
out = range(len(component))
|
|
for i, comp in enumerate(component):
|
|
out[i] = MagneticDipoleVectorPotential(srcLoc, obsLoc, comp, dipoleMoment=dipoleMoment)
|
|
return np.concatenate(out)
|
|
|
|
if isinstance(obsLoc, Mesh.BaseMesh):
|
|
mesh = obsLoc
|
|
assert component in ['Ex','Ey','Ez','Fx','Fy','Fz'], "Components must be in: ['Ex','Ey','Ez','Fx','Fy','Fz']"
|
|
return MagneticDipoleVectorPotential(srcLoc, getattr(mesh,'grid'+component), component[1], dipoleMoment=dipoleMoment)
|
|
|
|
if component == 'x':
|
|
dimInd = 0
|
|
elif component == 'y':
|
|
dimInd = 1
|
|
elif component == 'z':
|
|
dimInd = 2
|
|
else:
|
|
raise ValueError('Invalid component')
|
|
|
|
srcLoc = np.atleast_2d(srcLoc)
|
|
obsLoc = np.atleast_2d(obsLoc)
|
|
dipoleMoment = np.atleast_2d(dipoleMoment)
|
|
|
|
nEdges = obsLoc.shape[0]
|
|
nSrc = srcLoc.shape[0]
|
|
|
|
m = np.array(dipoleMoment).repeat(nEdges, axis=0)
|
|
A = np.empty((nEdges, nSrc))
|
|
for i in range(nSrc):
|
|
dR = obsLoc - srcLoc[i, np.newaxis].repeat(nEdges, axis=0)
|
|
mCr = np.cross(m, dR)
|
|
r = np.sqrt((dR**2).sum(axis=1))
|
|
A[:, i] = +(mu/(4*pi)) * mCr[:,dimInd]/(r**3)
|
|
if nSrc == 1:
|
|
return A.flatten()
|
|
return A
|
|
|
|
|
|
def MagneticDipoleFields(srcLoc, obsLoc, component, moment=1., mu = mu_0):
|
|
"""
|
|
Calculate the vector potential of a set of magnetic dipoles
|
|
at given locations 'ref. <http://en.wikipedia.org/wiki/Dipole#Magnetic_vector_potential>'
|
|
|
|
:param numpy.ndarray srcLoc: Location of the source(s) (x, y, z)
|
|
:param numpy.ndarray obsLoc: Where the potentials will be calculated (x, y, z)
|
|
:param str component: The component to calculate - 'x', 'y', or 'z'
|
|
:param numpy.ndarray moment: The vector dipole moment (vertical)
|
|
:rtype: numpy.ndarray
|
|
:return: The vector potential each dipole at each observation location
|
|
"""
|
|
|
|
if component=='x':
|
|
dimInd = 0
|
|
elif component=='y':
|
|
dimInd = 1
|
|
elif component=='z':
|
|
dimInd = 2
|
|
else:
|
|
raise ValueError('Invalid component')
|
|
|
|
srcLoc = np.atleast_2d(srcLoc)
|
|
obsLoc = np.atleast_2d(obsLoc)
|
|
moment = np.atleast_2d(moment)
|
|
|
|
nFaces = obsLoc.shape[0]
|
|
nSrc = srcLoc.shape[0]
|
|
|
|
m = np.array(moment).repeat(nFaces, axis=0)
|
|
B = np.empty((nFaces, nSrc))
|
|
for i in range(nSrc):
|
|
dR = obsLoc - srcLoc[i, np.newaxis].repeat(nFaces, axis=0)
|
|
r = np.sqrt((dR**2).sum(axis=1))
|
|
if dimInd == 0:
|
|
B[:, i] = +(mu/(4*pi)) /(r**3) * (3*dR[:,2]*dR[:,0]/r**2)
|
|
elif dimInd == 1:
|
|
B[:, i] = +(mu/(4*pi)) /(r**3) * (3*dR[:,2]*dR[:,1]/r**2)
|
|
elif dimInd == 2:
|
|
B[:, i] = +(mu/(4*pi)) /(r**3) * (3*dR[:,2]**2/r**2-1)
|
|
else:
|
|
raise Exception("Not Implemented")
|
|
if nSrc == 1:
|
|
return B.flatten()
|
|
return B
|
|
|
|
|
|
|
|
def MagneticLoopVectorPotential(srcLoc, obsLoc, component, radius, mu=mu_0):
|
|
"""
|
|
Calculate the vector potential of horizontal circular loop
|
|
at given locations
|
|
|
|
:param numpy.ndarray srcLoc: Location of the source(s) (x, y, z)
|
|
:param numpy.ndarray,SimPEG.Mesh obsLoc: Where the potentials will be calculated (x, y, z) or a SimPEG Mesh
|
|
:param str,list component: The component to calculate - 'x', 'y', or 'z' if an array, or grid type if mesh, can be a list
|
|
:param numpy.ndarray I: Input current of the loop
|
|
:param numpy.ndarray radius: radius of the loop
|
|
:rtype: numpy.ndarray
|
|
:return: The vector potential each dipole at each observation location
|
|
"""
|
|
|
|
if type(component) in [list, tuple]:
|
|
out = range(len(component))
|
|
for i, comp in enumerate(component):
|
|
out[i] = MagneticLoopVectorPotential(srcLoc, obsLoc, comp, radius, mu)
|
|
return np.concatenate(out)
|
|
|
|
if isinstance(obsLoc, Mesh.BaseMesh):
|
|
mesh = obsLoc
|
|
assert component in ['Ex','Ey','Ez','Fx','Fy','Fz'], "Components must be in: ['Ex','Ey','Ez','Fx','Fy','Fz']"
|
|
return MagneticLoopVectorPotential(srcLoc, getattr(mesh,'grid'+component), component[1], radius, mu)
|
|
|
|
srcLoc = np.atleast_2d(srcLoc)
|
|
obsLoc = np.atleast_2d(obsLoc)
|
|
|
|
n = obsLoc.shape[0]
|
|
nSrc = srcLoc.shape[0]
|
|
|
|
if component=='z':
|
|
A = np.zeros((n, nSrc))
|
|
if nSrc ==1:
|
|
return A.flatten()
|
|
return A
|
|
|
|
else:
|
|
|
|
A = np.zeros((n, nSrc))
|
|
for i in range (nSrc):
|
|
x = obsLoc[:, 0] - srcLoc[i, 0]
|
|
y = obsLoc[:, 1] - srcLoc[i, 1]
|
|
z = obsLoc[:, 2] - srcLoc[i, 2]
|
|
r = np.sqrt(x**2 + y**2)
|
|
m = (4 * radius * r) / ((radius + r)**2 + z**2)
|
|
m[m > 1.] = 1.
|
|
# m might be slightly larger than 1 due to rounding errors
|
|
# but ellipke requires 0 <= m <= 1
|
|
K = ellipk(m)
|
|
E = ellipe(m)
|
|
ind = (r > 0) & (m < 1)
|
|
# % 1/r singular at r = 0 and K(m) singular at m = 1
|
|
Aphi = np.zeros(n)
|
|
# % Common factor is (mu * I) / pi with I = 1 and mu = 4e-7 * pi.
|
|
Aphi[ind] = 4e-7 / np.sqrt(m[ind]) * np.sqrt(radius / r[ind]) *((1. - m[ind] / 2.) * K[ind] - E[ind])
|
|
if component == 'x':
|
|
A[ind, i] = Aphi[ind] * (-y[ind] / r[ind] )
|
|
elif component == 'y':
|
|
A[ind, i] = Aphi[ind] * ( x[ind] / r[ind] )
|
|
else:
|
|
raise ValueError('Invalid component')
|
|
|
|
if nSrc == 1:
|
|
return A.flatten()
|
|
return A
|
|
|
|
if __name__ == '__main__':
|
|
from SimPEG import Mesh
|
|
import matplotlib.pyplot as plt
|
|
cs = 20
|
|
ncx, ncy, ncz = 41, 41, 40
|
|
hx = np.ones(ncx)*cs
|
|
hy = np.ones(ncy)*cs
|
|
hz = np.ones(ncz)*cs
|
|
mesh = Mesh.TensorMesh([hx, hy, hz], 'CCC')
|
|
srcLoc = np.r_[0., 0., 0.]
|
|
Ax = MagneticLoopVectorPotential(srcLoc, mesh.gridEx, 'x', 200)
|
|
Ay = MagneticLoopVectorPotential(srcLoc, mesh.gridEy, 'y', 200)
|
|
Az = MagneticLoopVectorPotential(srcLoc, mesh.gridEz, 'z', 200)
|
|
A = np.r_[Ax, Ay, Az]
|
|
B0 = mesh.edgeCurl*A
|
|
J0 = mesh.edgeCurl.T*B0
|
|
|
|
# mesh.plotImage(A, vType = 'Ex')
|
|
# mesh.plotImage(A, vType = 'Ey')
|
|
|
|
mesh.plotImage(B0, vType = 'Fx')
|
|
mesh.plotImage(B0, vType = 'Fy')
|
|
mesh.plotImage(B0, vType = 'Fz')
|
|
|
|
# # mesh.plotImage(J0, vType = 'Ex')
|
|
# mesh.plotImage(J0, vType = 'Ey')
|
|
# mesh.plotImage(J0, vType = 'Ez')
|
|
|
|
plt.show()
|
|
|
|
|