def get1DEfields(m1d, sigma, freq, sourceAmp=1.0):
"""Function to get 1D electrical fields"""
# Get the gradient
G = m1d.nodalGrad
# Mass matrices
# Magnetic permeability
Mmu = simpeg.Utils.sdiag(m1d.vol * (1.0 / mu_0))
# Conductivity
Msig = m1d.getFaceInnerProduct(sigma)
# Set up the solution matrix
A = G.T * Mmu * G + 1j * 2. * np.pi * freq * Msig
# Define the inner part of the solution matrix
Aii = A[1:-1, 1:-1]
# Define the outer part of the solution matrix
Aio = A[1:-1, [0, -1]]
# Set the boundary conditions
Ed, Eu, Hd, Hu = getEHfields(m1d, sigma, freq, m1d.vectorNx)
Etot = (Ed + Eu)
if sourceAmp is not None:
Etot = ((Etot / Etot[-1]) * sourceAmp
) # Scale the fields to be equal to sourceAmp at the top
## Note: The analytic solution is derived with e^iwt
bc = np.r_[Etot[0], Etot[-1]]
# The right hand side
rhs = Aio * bc
# Solve the system
Aii_inv = simpeg.Solver(Aii)
eii = Aii_inv * rhs
# Assign the boundary conditions
e = np.r_[bc[0], eii, bc[1]]
# Return the electrical fields
return e
