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https://github.com/wassname/simpeg.git
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GudniRos
139 lines
4.4 KiB
Python
139 lines
4.4 KiB
Python
from SimPEG import Survey, Problem, Utils, Models, np, sp, mkvc, SolverLU as SimpegSolver
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from SimPEG.EM.Utils import omega
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from scipy.constants import mu_0
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from SimPEG.MT.BaseMT import BaseMTProblem
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from SimPEG.MT.SurveyMT import Survey, Data
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from SimPEG.MT.FieldsMT import Fields3D_e
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import multiprocessing, sys, time
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class eForm_ps(BaseMTProblem):
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"""
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A MT problem solving a e formulation and a primary/secondary fields decompostion.
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By eliminating the magnetic flux density using
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.. math ::
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\mathbf{b} = \\frac{1}{i \omega}\\left(-\mathbf{C} \mathbf{e} \\right)
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we can write Maxwell's equations as a second order system in \\\(\\\mathbf{e}\\\) only:
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.. math ::
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\\left(\mathbf{C}^T \mathbf{M^f_{\mu^{-1}}} \mathbf{C} + i \omega \mathbf{M^e_\sigma}] \mathbf{e}_{s} =& i \omega \mathbf{M^e_{\delta \sigma}} \mathbf{e}_{p}
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which we solve for \\\(\\\mathbf{e_s}\\\). The total field \\\mathbf{e}\\ = \\\mathbf{e_p}\\ + \\\mathbf{e_s}\\.
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The primary field is estimated from a background model (commonly as a 1D model).
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"""
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# From FDEMproblem: Used to project the fields. Currently not used for MTproblem.
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_fieldType = 'e'
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_eqLocs = 'FE'
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fieldsPair = Fields3D_e
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_sigmaPrimary = None
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def __init__(self, mesh, **kwargs):
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BaseMTProblem.__init__(self, mesh, **kwargs)
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@property
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def sigmaPrimary(self):
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"""
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A background model, use for the calculation of the primary fields.
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"""
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return self._sigmaPrimary
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@sigmaPrimary.setter
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def sigmaPrimary(self, val):
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# Note: TODO add logic for val, make sure it is the correct size.
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self._sigmaPrimary = val
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def getA(self, freq):
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"""
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Function to get the A system.
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:param float freq: Frequency
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:rtype: scipy.sparse.csr_matrix
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:return: A
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"""
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Mmui = self.MfMui
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Msig = self.MeSigma
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C = self.mesh.edgeCurl
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return C.T*Mmui*C + 1j*omega(freq)*Msig
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def getADeriv_m(self, freq, u, v, adjoint=False):
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"""
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Calculate the derivative of A wrt m.
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"""
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# This considers both polarizations and returns a nE,2 matrix for each polarization
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if adjoint:
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dMe_dsigV = sp.hstack(( self.MeSigmaDeriv( u['e_pxSolution'] ).T, self.MeSigmaDeriv(u['e_pySolution'] ).T ))*v
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else:
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# Need a nE,2 matrix to be returned
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dMe_dsigV = np.hstack(( mkvc(self.MeSigmaDeriv( u['e_pxSolution'] )*v,2), mkvc( self.MeSigmaDeriv(u['e_pySolution'] )*v,2) ))
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return 1j * omega(freq) * dMe_dsigV
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def getRHS(self, freq):
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"""
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Function to return the right hand side for the system.
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:param float freq: Frequency
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:rtype: numpy.ndarray (nE, 2), numpy.ndarray (nE, 2)
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:return: RHS for both polarizations, primary fields
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"""
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# Get sources for the frequncy(polarizations)
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Src = self.survey.getSrcByFreq(freq)[0]
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S_e = Src.S_e(self)
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return -1j * omega(freq) * S_e
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def getRHSDeriv_m(self, freq, v, adjoint=False):
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"""
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The derivative of the RHS with respect to sigma
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"""
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Src = self.survey.getSrcByFreq(freq)[0]
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S_eDeriv = Src.S_eDeriv_m(self, v, adjoint)
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return -1j * omega(freq) * S_eDeriv
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def fields(self, m):
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'''
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Function to calculate all the fields for the model m.
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:param np.ndarray (nC,) m: Conductivity model
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'''
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# Set the current model
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self.curModel = m
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F = Fields3D_e(self.mesh, self.survey)
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for freq in self.survey.freqs:
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if self.verbose:
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startTime = time.time()
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print 'Starting work for {:.3e}'.format(freq)
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sys.stdout.flush()
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A = self.getA(freq)
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rhs = self.getRHS(freq)
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# Solve the system
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Ainv = self.Solver(A, **self.solverOpts)
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e_s = Ainv * rhs
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# Store the fields
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Src = self.survey.getSrcByFreq(freq)[0]
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# Store the fieldss
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F[Src, 'e_pxSolution'] = e_s[:,0]
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F[Src, 'e_pySolution'] = e_s[:,1]
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# Note curl e = -iwb so b = -curl/iw
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if self.verbose:
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print 'Ran for {:f} seconds'.format(time.time()-startTime)
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sys.stdout.flush()
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Ainv.clean()
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return F
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