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rowanc1
129 lines
3.4 KiB
Python
129 lines
3.4 KiB
Python
from SimPEG import Problem, Solver, Utils, np, sp
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from scipy.constants import mu_0
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from SurveyFDEM import SurveyFDEM, DataFDEM, FieldsFDEM
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def omega(freq):
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"""Change frequency to angular frequency, omega"""
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return 2.*np.pi*freq
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class ProblemFDEM_e(Problem.BaseProblem):
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"""
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Frequency-Domain EM problem - E-formulation
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.. math::
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\dcurl E + i \omega B = 0 \\\\
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\dcurl^\\top \MfMui B - \MeSig E = \Me \j_s
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"""
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def __init__(self, model, **kwargs):
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Problem.BaseProblem.__init__(self, model, **kwargs)
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solType = 'b'
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storeTheseFields = 'e'
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surveyPair = SurveyFDEM
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dataPair = DataFDEM
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solveOpts = {'factorize':False, 'backend':'scipy'}
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####################################################
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# Mass Matrices
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####################################################
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@property
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def MfMui(self): return self._MfMui
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@property
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def Me(self): return self._Me
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@property
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def MeSigma(self): return self._MeSigma
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@property
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def MeSigmaI(self): return self._MeSigmaI
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def makeMassMatrices(self, m):
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#TODO: hardcoded to sigma as the model
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sigma = self.model.transform(m)
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self._Me = self.mesh.getEdgeInnerProduct()
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self._MeSigma = self.mesh.getEdgeInnerProduct(sigma)
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# TODO: this will not work if tensor conductivity
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self._MeSigmaI = Utils.sdiag(1/self.MeSigma.diagonal())
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#TODO: assuming constant mu
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self._MfMui = self.mesh.getFaceInnerProduct(1/mu_0)
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####################################################
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# Internal Methods
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####################################################
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def getA(self, freq):
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"""
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:param int fInd: Frequency index
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:rtype: scipy.sparse.csr_matrix
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:return: A
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"""
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return self.mesh.edgeCurl.T*self.MfMui*self.mesh.edgeCurl + 1j*omega(freq)*self.MeSigma
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def getRHS(self, freq):
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#TODO: this needs to also depend on your transmitter!
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return -1j*omega(freq)*self.Me*self.j_s
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def fields(self, m, useThisRhs=None):
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RHS = useThisRhs or self.getRHS
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self.makeMassMatrices(m)
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F = FieldsFDEM(self.mesh, self.survey)
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for freq in self.survey.freqs:
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A = self.getA(freq)
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b = self.getRHS(freq)
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e = Solver(A, options=self.solveOpts).solve(b)
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F[freq, 'e'] = e
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#TODO: check if mass matrices needed:
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b = -1./(1j*omega(freq))*self.mesh.edgeCurl*e
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F[freq, 'b'] = b
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return F
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def Jvec(self, m, v, u=None):
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if u is None:
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u = self.fields(m)
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Jv = self.dataPair(self.survey)
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for i, freq in enumerate(self.survey.freqs):
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e = u[freq, 'e']
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A = self.getA(freq)
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solver = Solver(A, options=self.solveOpts)
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for tx in self.survey.getTransmitters(freq):
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dMe_dsig = self.mesh.getEdgeInnerProductDeriv(m, v=e)
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dsig_dm = self.model.transformDeriv(m)
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b = 1j*omega(freq) * ( dMe_dsig * ( dsig_dm * v ) )
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Ab = solver.solve(b)
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P = tx.projectFieldsDeriv(self.mesh, u)
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Jv[tx] = -P*Ab
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return Utils.mkvc(Jv)
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def Jtvec(self, m, v, u=None):
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if u is None:
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u = self.fields(m)
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raise NotImplementedError('Jtvec todo!')
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