wassname/simpeg
1
0
Fork 0
mirror of https://github.com/wassname/simpeg.git synced 2026-06-30 23:29:21 +08:00
Code Issues Packages Projects Releases Wiki Activity

Start of analytical dipole in a whole-space. Not yet tested

Browse Source
This commit is contained in:
Lindsey Heagy
2014-10-06 19:37:26 -07:00
parent dd766a3ce3
commit cf2a9688c3
1 changed files with 48 additions and 1 deletions
Download Patch File Download Diff File Expand all files Collapse all files
simpegEM/Analytics/FEM.py
+48 -1
View File
@@ -1,6 +1,7 @@
import numpy as np
from scipy.constants import mu_0, pi
from scipy.special import erf
import matplotlib.pyplot as plt
def hzAnalyticDipoleF(r, freq, sigma, secondary=True):
"""
@@ -22,7 +23,7 @@ def hzAnalyticDipoleF(r, freq, sigma, secondary=True):
"""
r = np.abs(r)
k = np.sqrt(-1j*2.*np.pi*freq*mu_0*sigma)
k = np.sqrt(-1j*2.*np.pi*f*mu_0*sigma)
m = 1
front = m / (2. * np.pi * (k**2) * (r**5) )
@@ -35,4 +36,50 @@ def hzAnalyticDipoleF(r, freq, sigma, secondary=True):
return hz
def AnalyticDipoleH(x,y,z,sig,f,xs=0.,ys=0.,zs=0.,m=1.,orientation='X'):
"""
Analytical solution for a dipole in a whole-space.
Equation 2.57 of Ward and Hohmann
"""
dx = x-xs
dy = y-ys
dz = z-zs
r = np.sqrt( dx**2. + dy**2. + dz**2.)
k = np.sqrt(-1j*2.*np.pi*f*mu_0*sig)
kr = k*r
front = m / (4.*pi * r**3.) * np.exp(-1j*kr)
mid = -kr**2. + 3.*1j*kr + 3.
if orientation.upper() == 'X':
Hx = front*( (dx/r)**2. * mid + (kr**2. - 1j*kr - 1.) )
Hy = front*( (dx*dy/r**2.) * mid )
Hz = front*( (dx*dz/r**2.) * mid )
elif orientation.upper() == 'Y':
Hx = front*( (dy*dx/r**2.) * mid )
Hy = front*( (dy/r)**2. * mid + (kr**2. - 1j*kr - 1.) )
Hz = front*( (dy*dz/r**2.) * mid )
elif orientation.upper() == 'Z':
Hx = front*( (dx*dz/r**2.) * mid )
Hy = front*( (dy*dz/r**2.) * mid )
Hz = front*( (dz/r)**2. * mid + (kr**2. - 1j*kr - 1.) )
return Hx, Hy, Hz
if __name__ == '__main__':
x = np.arange(-100.,102.,2.)
y = 50.
z = 0.
sig = 1.
f = 1.
Hx, Hy, Hz = AnalyticDipoleH(x,y,z,sig,f)