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GudniRos
242 lines
8.0 KiB
Python
242 lines
8.0 KiB
Python
from simpegEM.Utils.EMUtils import omega
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from SimPEG import mkvc
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from scipy.constants import mu_0
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from simpegMT.BaseMT import BaseMTProblem
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from simpegMT.SurveyMT import SurveyMT
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from simpegMT.FieldsMT import FieldsMT
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from simpegMT.DataMT import DataMT
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from simpegMT.Utils.MT1Danalytic import getEHfields
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import numpy as np
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import multiprocessing, sys, time
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class eForm_psField(BaseMTProblem):
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"""
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A MT problem soving a e formulation and primary/secondary fields decomposion.
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Solves the equation
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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 = 'EF'
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def __init__(self, mesh, **kwargs):
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BaseMTProblem.__init__(self, mesh, **kwargs)
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def getA(self, freq,):
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"""
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Function to get the A matrix.
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:param float freq: Frequency
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:param logic full: Return full A or the inner part
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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.mesh.getEdgeInnerProduct(1.0/mu_0)
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Msig = self.mesh.getFaceInnerProduct(self.curModel.sigma)
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# Note: need to use the code above since in the 1D problem I want
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# e to live on Faces(nodes) and h on edges(cells). Might need to rethink this
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# Possible that _fieldType and _eqLocs can fix this
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# Mmui = self.MfMui
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# Msig = self.MeSigma
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C = self.mesh.nodalGrad
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# Make A
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A = C.T*Mmui*C + 1j*omega(freq)*Msig
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# Either return full or only the inner part of A
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return A
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def getADeriv_m(self, freq, u, v, adjoint=False):
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"""
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The derivative of A wrt sigma
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"""
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dsig_dm = self.curModel.sigmaDeriv
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dMf_dsig = self.mesh.getFaceInnerProductDeriv(self.curModel.sigma)(u) * self.curModel.sigmaDeriv
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if adjoint:
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return 1j * omega(freq) * ( dsig_dm.T * ( dMf_dsig.T * v ) )
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return 1j * omega(freq) * ( dMf_dsig * ( dsig_dm * v ) )
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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 (nF, 1), numpy.ndarray (nF, 1)
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:return: RHS for 1 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, u, v, adjoint=False):
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"""
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The derivative of the RHS wrt sigma
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"""
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Src = self.survey.getSrcByFreq(freq)[0]
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S_eDeriv = Src.S_eDeriv(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 = FieldsMT(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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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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# Calculate total e
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e = Src.ePrimary(self) + e_s
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# Store the fields
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# NOTE: only store
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F[Src, 'e_1d'] = e[:,1] # Only storing the yx polarization as 1d
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# F[Src, 'e_py'] = 0*e[:,0]
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# Note curl e = -iwb so b = -curl e /iw
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b = -( self.mesh.nodalGrad * e )/( 1j*omega(freq) )
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# F[Src, 'b_px'] = 0*b[:,0]
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F[Src, 'b_1d'] = b[:,1]
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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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return F
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class eForm_TotalField(BaseMTProblem):
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"""
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A MT problem solving a e formulation and a Total bondary domain decompostion.
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Solves the equation:
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Math:
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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 = 'EF'
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def __init__(self, mesh, **kwargs):
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BaseMTProblem.__init__(self, mesh, **kwargs)
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def getA(self, freq, full=False):
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"""
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Function to get the A matrix.
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:param float freq: Frequency
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:param logic full: Return full A or the inner part
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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.mesh.getEdgeInnerProduct(1.0/mu_0)
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Msig = self.mesh.getFaceInnerProduct(self.curModel.sigma)
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# Note: need to use the code above since in the 1D problem I want
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# e to live on Faces(nodes) and h on edges(cells). Might need to rethink this
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# Possible that _fieldType and _eqLocs can fix this
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# Mmui = self.MfMui
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# Msig = self.MeSigma
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C = self.mesh.nodalGrad
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# Make A
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A = C.T*Mmui*C + 1j*omega(freq)*Msig
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# Either return full or only the inner part of A
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if full:
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return A
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else:
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return A[1:-1,1:-1]
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def getADeriv(self, freq, u, v, adjoint=False):
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sig = self.curTModel
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dsig_dm = self.curTModelDeriv
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dMe_dsig = self.mesh.getEdgeInnerProductDeriv(sig, v=u)
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if adjoint:
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return 1j * omega(freq) * ( dsig_dm.T * ( dMe_dsig.T * v ) )
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return 1j * omega(freq) * ( dMe_dsig * ( dsig_dm * v ) )
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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 frequency
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# NOTE: Need to use the source information, doesn't really apply in 1D
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src = self.survey.getSrcByFreq(freq)
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# Get the full A
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A = self.getA(freq,full=True)
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# Define the outer part of the solution matrix
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Aio = A[1:-1,[0,-1]]
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Ed, Eu, Hd, Hu = getEHfields(self.mesh,self.curModel.sigma,freq,self.mesh.vectorNx)
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Etot = (Ed + Eu)
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sourceAmp = 1.0
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Etot = ((Etot/Etot[-1])*sourceAmp) # Scale the fields to be equal to sourceAmp at the top
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## Note: The analytic solution is derived with e^iwt
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eBC = np.r_[Etot[0],Etot[-1]]
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# The right hand side
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return Aio*eBC, eBC
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def getRHSderiv(self, freq, backSigma, u, v, adjoint=False):
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raise NotImplementedError('getRHSDeriv not implemented yet')
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return None
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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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:param np.ndarray (nC,) m_back: Background conductivity model
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'''
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self.curModel = m
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# RHS, CalcFields = self.getRHS(freq,m_back), self.calcFields
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F = FieldsMT(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, e_o = self.getRHS(freq)
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Ainv = self.Solver(A, **self.solverOpts)
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e_i = Ainv * rhs
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e = mkvc(np.r_[e_o[0], e_i, e_o[1]],2)
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# Store the fields
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Src = self.survey.getSrcByFreq(freq)
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# Store the fields
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# NOTE: only store
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F[Src, 'e_1d'] = e
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# F[Src, 'e_py'] = 0*e[:,0]
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# Note curl e = -iwb so b = -curl e /iw
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b = -( self.mesh.nodalGrad * e )/( 1j*omega(freq) )
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# F[Src, 'b_px'] = 0*b[:,0]
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F[Src, 'b_1d'] = b
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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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return F
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