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simpegEM --> SimPEG.EM

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This commit is contained in:
Rowan Cockett
2015-11-04 10:13:24 -08:00
parent e622dfb5cc
commit 4db756b060
6 changed files with 96 additions and 96 deletions
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SimPEG/EM/FDEM/FDEM.py
+44 -44
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@@ -2,33 +2,33 @@ from SimPEG import Survey, Problem, Utils, np, sp, Solver as SimpegSolver
from scipy.constants import mu_0
from SurveyFDEM import SurveyFDEM
from FieldsFDEM import FieldsFDEM, FieldsFDEM_e, FieldsFDEM_b, FieldsFDEM_h, FieldsFDEM_j
from simpegEM.Base import BaseEMProblem
from simpegEM.Utils.EMUtils import omega
from SimPEG.EM.Base import BaseEMProblem
from SimPEG.EM.Utils.EMUtils import omega
class BaseFDEMProblem(BaseEMProblem):
"""
We start by looking at Maxwell's equations in the electric
field \\\(\\\mathbf{e}\\\) and the magnetic flux
We start by looking at Maxwell's equations in the electric
field \\\(\\\mathbf{e}\\\) and the magnetic flux
density \\\(\\\mathbf{b}\\\)
.. math ::
\mathbf{C} \mathbf{e} + i \omega \mathbf{b} = \mathbf{s_m} \\\\
{\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{b} - \mathbf{M_{\sigma}^e} \mathbf{e} = \mathbf{M^e} \mathbf{s_e}}
if using the E-B formulation (:code:`ProblemFDEM_e`
or :code:`ProblemFDEM_b`) or the magnetic field
if using the E-B formulation (:code:`ProblemFDEM_e`
or :code:`ProblemFDEM_b`) or the magnetic field
\\\(\\\mathbf{h}\\\) and current density \\\(\\\mathbf{j}\\\)
.. math ::
.. math ::
\mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{j} + i \omega \mathbf{M_{\mu}^e} \mathbf{h} = \mathbf{M^e} \mathbf{s_m} \\\\
\mathbf{C} \mathbf{h} - \mathbf{j} = \mathbf{s_e}
if using the H-J formulation (:code:`ProblemFDEM_j` or :code:`ProblemFDEM_h`).
The problem performs the elimination so that we are solving the system for \\\(\\\mathbf{e},\\\mathbf{b},\\\mathbf{j} \\\) or \\\(\\\mathbf{h}\\\)
The problem performs the elimination so that we are solving the system for \\\(\\\mathbf{e},\\\mathbf{b},\\\mathbf{j} \\\) or \\\(\\\mathbf{h}\\\)
"""
surveyPair = SurveyFDEM
@@ -36,7 +36,7 @@ class BaseFDEMProblem(BaseEMProblem):
def fields(self, m=None):
"""
Solve the forward problem for the fields.
Solve the forward problem for the fields.
"""
self.curModel = m
@@ -59,7 +59,7 @@ class BaseFDEMProblem(BaseEMProblem):
"""
if f is None:
f = self.fields(m)
f = self.fields(m)
self.curModel = m
@@ -67,7 +67,7 @@ class BaseFDEMProblem(BaseEMProblem):
for freq in self.survey.freqs:
dA_du = self.getA(freq) #
dA_duI = self.Solver(dA_du, **self.solverOpts)
dA_duI = self.Solver(dA_du, **self.solverOpts)
for src in self.survey.getSrcByFreq(freq):
ftype = self._fieldType + 'Solution'
@@ -97,7 +97,7 @@ class BaseFDEMProblem(BaseEMProblem):
return Utils.mkvc(Jv)
def Jtvec(self, m, v, f=None):
def Jtvec(self, m, v, f=None):
"""
Sensitivity transpose times a vector
"""
@@ -157,7 +157,7 @@ class BaseFDEMProblem(BaseEMProblem):
def getSourceTerm(self, freq):
"""
Evaluates the sources for a given frequency and puts them in matrix form
Evaluates the sources for a given frequency and puts them in matrix form
:param float freq: Frequency
:rtype: numpy.ndarray (nE or nF, nSrc)
@@ -165,11 +165,11 @@ class BaseFDEMProblem(BaseEMProblem):
"""
Srcs = self.survey.getSrcByFreq(freq)
if self._eqLocs is 'FE':
S_m = np.zeros((self.mesh.nF,len(Srcs)), dtype=complex)
S_m = np.zeros((self.mesh.nF,len(Srcs)), dtype=complex)
S_e = np.zeros((self.mesh.nE,len(Srcs)), dtype=complex)
elif self._eqLocs is 'EF':
S_m = np.zeros((self.mesh.nE,len(Srcs)), dtype=complex)
S_e = np.zeros((self.mesh.nF,len(Srcs)), dtype=complex)
S_e = np.zeros((self.mesh.nF,len(Srcs)), dtype=complex)
for i, src in enumerate(Srcs):
smi, sei = src.eval(self)
@@ -198,9 +198,9 @@ class ProblemFDEM_e(BaseFDEMProblem):
.. math ::
\\left(\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{C}+ i \omega \mathbf{M^e_{\sigma}} \\right)\mathbf{e} = \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f}\mathbf{s_m} -i\omega\mathbf{M^e}\mathbf{s_e}
\\left(\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{C}+ i \omega \mathbf{M^e_{\sigma}} \\right)\mathbf{e} = \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f}\mathbf{s_m} -i\omega\mathbf{M^e}\mathbf{s_e}
which we solve for \\\(\\\mathbf{e}\\\).
which we solve for \\\(\\\mathbf{e}\\\).
"""
_fieldType = 'e'
@@ -271,10 +271,10 @@ class ProblemFDEM_e(BaseFDEMProblem):
return - 1j * omega(freq) * S_eDerivv
else:
return None
else:
else:
S_mDerivv, S_eDerivv = S_mDeriv(v), S_eDeriv(v)
if S_mDerivv is not None and S_eDerivv is not None:
if S_mDerivv is not None and S_eDerivv is not None:
return C.T * (MfMui * S_mDerivv) -1j * omega(freq) * S_eDerivv
elif S_mDerivv is not None:
return C.T * (MfMui * S_mDerivv)
@@ -289,17 +289,17 @@ class ProblemFDEM_b(BaseFDEMProblem):
We eliminate \\\(\\\mathbf{e}\\\) using
.. math ::
\mathbf{e} = \mathbf{M^e_{\sigma}}^{-1} \\left(\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{b} - \mathbf{s_e}\\right)
and solve for \\\(\\\mathbf{b}\\\) using:
.. math ::
\\left(\mathbf{C} \mathbf{M^e_{\sigma}}^{-1} \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} + i \omega \\right)\mathbf{b} = \mathbf{s_m} + \mathbf{M^e_{\sigma}}^{-1}\mathbf{M^e}\mathbf{s_e}
\\left(\mathbf{C} \mathbf{M^e_{\sigma}}^{-1} \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} + i \omega \\right)\mathbf{b} = \mathbf{s_m} + \mathbf{M^e_{\sigma}}^{-1}\mathbf{M^e}\mathbf{s_e}
.. note ::
The inverse problem will not work with full anisotropy
The inverse problem will not work with full anisotropy
"""
_fieldType = 'b'
@@ -345,14 +345,14 @@ class ProblemFDEM_b(BaseFDEMProblem):
return MeSigmaIDeriv.T * (C.T * v)
if self._makeASymmetric is True:
return MfMui.T * ( C * ( MeSigmaIDeriv * v ) )
return C * ( MeSigmaIDeriv * v )
return MfMui.T * ( C * ( MeSigmaIDeriv * v ) )
return C * ( MeSigmaIDeriv * v )
def getRHS(self, freq):
"""
.. math ::
\mathbf{RHS} = \mathbf{s_m} + \mathbf{M^e_{\sigma}}^{-1}\mathbf{s_e}
\mathbf{RHS} = \mathbf{s_m} + \mathbf{M^e_{\sigma}}^{-1}\mathbf{s_e}
:param float freq: Frequency
:rtype: numpy.ndarray (nE, nSrc)
@@ -404,7 +404,7 @@ class ProblemFDEM_b(BaseFDEMProblem):
SrcDeriv = C * (self.MeSigmaI * S_eDeriv)
elif adjoint:
SrcDeriv = self.MeSigmaI.T * ( C.T * S_eDeriv)
else:
else:
SrcDeriv = None
if RHSderiv is not None and SrcDeriv is not None:
@@ -412,7 +412,7 @@ class ProblemFDEM_b(BaseFDEMProblem):
elif SrcDeriv is not None:
RHSderiv = SrcDeriv
if RHSderiv is not None:
if RHSderiv is not None:
if self._makeASymmetric is True and not adjoint:
return MfMui.T * RHSderiv
@@ -427,13 +427,13 @@ class ProblemFDEM_b(BaseFDEMProblem):
class ProblemFDEM_j(BaseFDEMProblem):
"""
We eliminate \\\(\\\mathbf{h}\\\) using
We eliminate \\\(\\\mathbf{h}\\\) using
.. math ::
.. math ::
\mathbf{h} = \\frac{1}{i \omega} \mathbf{M_{\mu}^e}^{-1} \\left(-\mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{j} + \mathbf{M^e} \mathbf{s_m} \\right)
and solve for \\\(\\\mathbf{j}\\\) using
and solve for \\\(\\\mathbf{j}\\\) using
.. math ::
@@ -510,7 +510,7 @@ class ProblemFDEM_j(BaseFDEMProblem):
S_m, S_e = self.getSourceTerm(freq)
C = self.mesh.edgeCurl
MeMuI = self.MeMuI
MeMuI = self.MeMuI
RHS = C * (MeMuI * S_m) - 1j * omega(freq) * S_e
if self._makeASymmetric is True:
@@ -521,7 +521,7 @@ class ProblemFDEM_j(BaseFDEMProblem):
def getRHSDeriv_m(self, src, v, adjoint=False):
C = self.mesh.edgeCurl
MeMuI = self.MeMuI
MeMuI = self.MeMuI
S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint)
if adjoint:
@@ -538,10 +538,10 @@ class ProblemFDEM_j(BaseFDEMProblem):
return - 1j * omega(freq) * S_eDerivv
else:
return None
else:
else:
S_mDerivv, S_eDerivv = S_mDeriv(v), S_eDeriv(v)
if S_mDerivv is not None and S_eDerivv is not None:
if S_mDerivv is not None and S_eDerivv is not None:
RHSDeriv = C * (MeMuI * S_mDerivv) - 1j * omega(freq) * S_eDerivv
elif S_mDerivv is not None:
RHSDeriv = C * (MeMuI * S_mDerivv)
@@ -560,17 +560,17 @@ class ProblemFDEM_j(BaseFDEMProblem):
class ProblemFDEM_h(BaseFDEMProblem):
"""
We eliminate \\\(\\\mathbf{j}\\\) using
We eliminate \\\(\\\mathbf{j}\\\) using
.. math ::
\mathbf{j} = \mathbf{C} \mathbf{h} - \mathbf{s_e}
and solve for \\\(\\\mathbf{h}\\\) using
and solve for \\\(\\\mathbf{h}\\\) using
.. math ::
\\left(\mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{C} + i \omega \mathbf{M_{\mu}^e}\\right) \mathbf{h} = \mathbf{M^e} \mathbf{s_m} + \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{s_e}
\\left(\mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{C} + i \omega \mathbf{M_{\mu}^e}\\right) \mathbf{h} = \mathbf{M^e} \mathbf{s_m} + \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{s_e}
"""
@@ -612,7 +612,7 @@ class ProblemFDEM_h(BaseFDEMProblem):
"""
.. math ::
\mathbf{RHS} = \mathbf{M^e} \mathbf{s_m} + \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{s_e}
\mathbf{RHS} = \mathbf{M^e} \mathbf{s_m} + \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{s_e}
:param float freq: Frequency
:rtype: numpy.ndarray (nE, nSrc)
@@ -647,12 +647,12 @@ class ProblemFDEM_h(BaseFDEMProblem):
S_eDeriv = S_eDeriv(v)
if S_mDeriv is not None:
if RHSDeriv is not None:
if RHSDeriv is not None:
RHSDeriv += S_mDeriv(v)
else:
else:
RHSDeriv = S_mDeriv(v)
if S_eDeriv is not None:
if RHSDeriv is not None:
if RHSDeriv is not None:
RHSDeriv += C.T * (MfRho * S_e)
else:
RHSDeriv = C.T * (MfRho * S_e)