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rowanc1
128 lines
3.1 KiB
Python
128 lines
3.1 KiB
Python
from SimPEG import Problem
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import numpy as np
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from scipy.constants import mu_0
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from SimPEG.Utils import sdiag, mkvc
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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, mesh, model, **kwargs):
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Problem.BaseProblem.__init__(self, mesh, model, **kwargs)
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solType = 'b'
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#TODO:
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# j_s
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# getOmega
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# getFieldsObject
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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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self._Me = self.mesh.getEdgeInnerProduct()
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self._MeSigma = self.mesh.getEdgeInnerProduct(m)
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# TODO: this will not work if tensor conductivity
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self._MeSigmaI = 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, omegaInd):
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"""
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:param int tInd: Time index
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:rtype: scipy.sparse.csr_matrix
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:return: A
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"""
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omega = self.getOmega(omegaInd)
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return self.mesh.edgeCurl.T*self.MfMui*self.mesh.edgeCurl + 1j*omega*self.MeSigma
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def getRHS(self, omegaInd):
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omega = self.getOmega(omegaInd)
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return -1j*omega*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 = self.getFieldsObject()
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return
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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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raise NotImplementedError('Jvec todo!')
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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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if __name__ == '__main__':
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from SimPEG import *
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import simpegEM as EM
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from simpegEM.Utils.Ana import hzAnalyticDipoleT
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from scipy.constants import mu_0
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import matplotlib.pyplot as plt
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cs = 5.
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ncx = 20
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ncy = 6
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npad = 20
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hx = Utils.meshTensors(((0,cs), (ncx,cs), (npad,cs)))
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hy = Utils.meshTensors(((npad,cs), (ncy,cs), (npad,cs)))
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mesh = Mesh.Cyl1DMesh([hx,hy], -hy.sum()/2)
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model = Model.Vertical1DModel(mesh)
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opts = {'txLoc':0.,
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'txType':'VMD_MVP',
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'rxLoc':np.r_[150., 0.],
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'rxType':'bz',
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'timeCh':np.logspace(-4,-2,20),
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}
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dat = EM.TDEM.DataTDEM1D(**opts)
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prb = EM.TDEM.ProblemTDEM_b(mesh, model)
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# prb.setTimes([1e-5, 5e-5, 2.5e-4], [150, 150, 150])
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# prb.setTimes([1e-5, 5e-5, 2.5e-4], [10, 10, 10])
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prb.setTimes([1e-5], [1])
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prb.pair(dat)
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sigma = np.random.rand(mesh.nCz)
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