def mixedBC(self, boundary, userData):
"""Apply mixed boundary conditions."""
if boundary.marker() != pg.MARKER_BOUND_MIXED:
return 0
sourcePos = pg.center(userData['sourcePos'])
k = userData['k']
r1 = boundary.center() - sourcePos
# Mirror on surface at depth=0
r2 = boundary.center() - pg.RVector3(1.0, -1.0, 1.0) * sourcePos
r1A = r1.abs()
r2A = r2.abs()
rho = 1.
if self.resistivity is not None:
rho = self.resistivity[boundary.leftCell().id()]
n = boundary.norm()
if r1A > 1e-12 and r2A > 1e-12:
if (pg.besselK0(r1A * k) + pg.besselK0(r2A * k)) > 1e-12:
return 1./rho * k * (r1.dot(n) / r1A * pg.besselK1(r1A * k) +
r2.dot(n) / r2A * pg.besselK1(r2A * k)) /\
(pg.besselK0(r1A * k) + pg.besselK0(r2A * k))
else:
return 0.
else:
return 0.
def uAnalytical(p, sourcePos, k):
"""Calculates the analytical solution for the 2.5D geoelectrical problem.
Solves the 2.5D geoelectrical problem for one wave number k.
It calculates the normalized (for injection current 1 A and sigma=1 S/m)
potential at position p for a current injection at position sourcePos.
Injection at the subsurface is recognized via mirror sources along the
surface at depth=0.
Parameters
----------
p : pg.Pos
Position for the sought potential
sourcePos : pg.Pos
Current injection position.
k : float
Wave number
Returns
-------
u : float
Solution u(p)
"""
r1A = (p - sourcePos).abs()
# Mirror on surface at depth=0
r2A = (p - pg.RVector3(1.0, -1.0, 1.0) * sourcePos).abs()
if r1A > 1e-12 and r2A > 1e-12:
return (pg.besselK0(r1A * k) + pg.besselK0(r2A * k)) / (2.0 * np.pi)
else:
return 0.
def uAnalytical(p, sourcePos, k):
"""Calculates the analytical solution for the 2.5D geoelectrical problem.
Solves the 2.5D geoelectrical problem for one wave number k.
It calculates the normalized (for injection current 1 A and sigma=1 S/m)
potential at position p for a current injection at position sourcePos.
Injection at the subsurface is recognized via mirror sources along the
surface at depth=0.
Parameters
----------
p : pg.Pos
Position for the sought potential
sourcePos : pg.Pos
Current injection position.
k : float
Wave number
Returns
-------
u : float
Solution u(p)
"""
r1A = (p - sourcePos).abs()
# Mirror on surface at depth=0
r2A = (p - pg.RVector3(1.0, -1.0, 1.0) * sourcePos).abs()
if r1A > 1e-12 and r2A > 1e-12:
return (pg.besselK0(r1A * k) + pg.besselK0(r2A * k)) / (2.0 * np.pi)
else:
return 0.
def mixedBC(self, boundary, userData):
"""Apply mixed boundary conditions."""
if boundary.marker() != pg.MARKER_BOUND_MIXED:
return 0
sourcePos = pg.center(userData['sourcePos'])
k = userData['k']
r1 = boundary.center() - sourcePos
# Mirror on surface at depth=0
r2 = boundary.center() - pg.RVector3(1.0, -1.0, 1.0) * sourcePos
r1A = r1.abs()
r2A = r2.abs()
rho = 1.
if self.resistivity is not None:
rho = self.resistivity[boundary.leftCell().id()]
n = boundary.norm()
if r1A > 1e-12 and r2A > 1e-12:
if (pg.besselK0(r1A * k) + pg.besselK0(r2A * k)) > 1e-12:
return 1./rho * k * (r1.dot(n) / r1A * pg.besselK1(r1A * k) +
r2.dot(n) / r2A * pg.besselK1(r2A * k)) /\
(pg.besselK0(r1A * k) + pg.besselK0(r2A * k))
else:
return 0.
else:
return 0.
def uAnalytical(p, sourcePos, k):
r1A = (p - sourcePos).abs()
# Mirror on surface at depth=0
r2A = (p - pg.RVector3(1.0, -1.0, 1.0) * sourcePos).abs()
# need rho here!!!!!!!!!!!!!!!!!!!!!!!!!!!1
if r1A > 1e-12 and r2A > 1e-12:
return (pg.besselK0(r1A * k) + pg.besselK0(r2A *k)) / (2.0 * np.pi)
else:
return 0.
def uAnalytical(p, sourcePos, k):
r1A = (p - sourcePos).abs()
# Mirror on surface at depth=0
r2A = (p - pg.RVector3(1.0, -1.0, 1.0) * sourcePos).abs()
# need rho here!!!!!!!!!!!!!!!!!!!!!!!!!!!1
if r1A > 1e-12 and r2A > 1e-12:
return (pg.besselK0(r1A * k) + pg.besselK0(r2A * k)) / (2.0 * np.pi)
else:
return 0.
def uAnalytical(self, p, sourcePos, k):
"""Calculate analytical potential for homogeneous halfspace
using a standard sigma = 1 [S/m] that can be scaled.
"""
r1A = (p - sourcePos).abs()
# Mirror on surface at depth=0
r2A = (p - pg.RVector3(1.0, -1.0, 1.0) * sourcePos).abs()
if r1A > 1e-12 and r2A > 1e-12:
return (pg.besselK0(r1A * k) + pg.besselK0(r2A * k)) / \
(2.0 * np.pi)
else:
return 0.
def mixedBC(boundary, userData):
sourcePos = userData['sourcePos']
k = userData['k']
r1 = boundary.center() - sourcePos
# Mirror on surface at depth=0
r2 = boundary.center() - pg.RVector3(1.0, -1.0, 1.0) * sourcePos
r1A = r1.abs()
r2A = r2.abs()
n = boundary.norm()
# need rho here !!!!!!!!!!!!!!!!!!!!!!!!!!!1
if r1A > 1e-12 and r2A > 1e-12:
return k * ((r1.dot(n)) / r1A * pg.besselK1(r1A * k) +
(r2.dot(n)) / r2A * pg.besselK1(r2A * k)) / \
(pg.besselK0(r1A * k) + pg.besselK0(r2A * k))
else:
return 0.
def mixedBC(boundary, userData):
sourcePos = userData['sourcePos']
k = userData['k']
r1 = boundary.center() - sourcePos
# Mirror on surface at depth=0
r2 = boundary.center() - pg.RVector3(1.0, -1.0, 1.0) * sourcePos
r1A = r1.abs()
r2A = r2.abs()
n = boundary.norm()
# need rho here !!!!!!!!!!!!!!!!!!!!!!!!!!!1
if r1A > 1e-12 and r2A > 1e-12:
return k * ((r1.dot(n)) / r1A * pg.besselK1(r1A * k) +
(r2.dot(n)) / r2A * pg.besselK1(r2A * k)) / \
(pg.besselK0(r1A * k) + pg.besselK0(r2A * k))
else:
return 0.
def mixedBC(boundary, userData):
"""Mixed boundary conditions.
Define the derivative of the analytical solution regarding the outer normal
direction :math:`\vec{n}`. So we can define the value for the Neumann type
Boundary conditions for the boundaries in the subsurface.
"""
sourcePos = userData['sourcePos']
k = userData['k']
r1 = boundary.center() - sourcePos
# Mirror on surface at depth=0
r2 = boundary.center() - pg.RVector3(1.0, -1.0, 1.0) * sourcePos
r1A = r1.abs()
r2A = r2.abs()
n = boundary.norm()
if r1A > 1e-12 and r2A > 1e-12:
return k * ((r1.dot(n)) / r1A * pg.besselK1(r1A * k) +
(r2.dot(n)) / r2A * pg.besselK1(r2A * k)) / \
(pg.besselK0(r1A * k) + pg.besselK0(r2A * k))
else:
return 0.
def mixedBC(boundary, userData):
"""Mixed boundary conditions.
Define the derivative of the analytical solution regarding the outer normal
direction :math:`\vec{n}`. So we can define the value for the Neumann type
Boundary conditions for the boundaries in the subsurface.
"""
sourcePos = userData['sourcePos']
k = userData['k']
r1 = boundary.center() - sourcePos
# Mirror on surface at depth=0
r2 = boundary.center() - pg.RVector3(1.0, -1.0, 1.0) * sourcePos
r1A = r1.abs()
r2A = r2.abs()
n = boundary.norm()
if r1A > 1e-12 and r2A > 1e-12:
return k * ((r1.dot(n)) / r1A * pg.besselK1(r1A * k) +
(r2.dot(n)) / r2A * pg.besselK1(r2A * k)) / \
(pg.besselK0(r1A * k) + pg.besselK0(r2A * k))
else:
return 0.
