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start of the FDEM
This commit is contained in:
Lindsey Heagy
@@ -0,0 +1,50 @@
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from SimPEG import Utils, np
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from SimPEG.Data import BaseData
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from FieldsFDEM import FieldsFDEM
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class DataFDEM(BaseData):
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"""
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docstring for DataFDEM
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"""
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txLoc = None #: txLoc
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txType = None #: txType
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nTx = 1 #: Number of transmitters
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rxLoc = None #: rxLoc
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rxType = None #: rxType
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freq = None #: freq
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@property
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def omega(self):
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return 2*np.pi*self.freq
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@property
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def nFreq(self):
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"""Number of frequencies"""
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return self.freq.size
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def __init__(self, **kwargs):
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BaseData.__init__(self, **kwargs)
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Utils.setKwargs(self, **kwargs)
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def projectFields(self, u):
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#TODO: this is hardcoded to 1Tx
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return self.Qrx.dot(u.b[:,:,0].T).T
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def projectFieldsAdjoint(self, d):
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# TODO: fix this
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pass
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####################################################
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# Interpolation Matrices
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####################################################
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@property
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def Qrx(self):
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if self._Qrx is None:
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if self.rxType == 'bz':
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locType = 'Fz'
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self._Qrx = self.prob.mesh.getInterpolationMat(self.rxLoc, locType=locType)
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return self._Qrx
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_Qrx = None
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+59
-24
@@ -1,7 +1,9 @@
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from SimPEG import Problem
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from SimPEG import Problem, Solver
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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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from FieldsFDEM import FieldsFDEM
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from DataFDEM import DataFDEM
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class ProblemFDEM_e(Problem.BaseProblem):
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@@ -18,11 +20,18 @@ class ProblemFDEM_e(Problem.BaseProblem):
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Problem.BaseProblem.__init__(self, mesh, model, **kwargs)
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solType = 'b'
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storeTheseFields = 'e'
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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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dataPair = DataFDEM
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solveOpts = {'factorize':False, 'backend':'scipy'}
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j_s = None
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def getFieldsObject(self):
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F = FieldsFDEM(self.mesh, self.data.nTx, self.data.nFreq, store=self.storeTheseFields)
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return F
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####################################################
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# Mass Matrices
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@@ -41,8 +50,10 @@ class ProblemFDEM_e(Problem.BaseProblem):
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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(m)
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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 = sdiag(1/self.MeSigma.diagonal())
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#TODO: assuming constant mu
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@@ -52,17 +63,17 @@ class ProblemFDEM_e(Problem.BaseProblem):
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# Internal Methods
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####################################################
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def getA(self, omegaInd):
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def getA(self, freqInd):
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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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omega = self.data.omega[freqInd]
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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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def getRHS(self, freqInd):
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omega = self.data.omega[freqInd]
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return -1j*omega*self.Me*self.j_s
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@@ -73,8 +84,18 @@ class ProblemFDEM_e(Problem.BaseProblem):
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F = self.getFieldsObject()
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for freqInd in range(self.data.nFreq):
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A = self.getA(freqInd)
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b = self.getRHS(freqInd)
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e = Solver(A, options=self.solveOpts).solve(b)
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return
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F.set_e(e, freqInd)
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omega = self.data.omega[freqInd]
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#TODO: check if mass matrices needed:
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b = -1./(1j*omega)*self.mesh.edgeCurl*e
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F.set_b(b, freqInd)
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return F
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def Jvec(self, m, v, u=None):
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@@ -99,28 +120,42 @@ if __name__ == '__main__':
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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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ncx = 6
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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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ncz = 6
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npad = 3
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hx = Utils.meshTensors(((npad,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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hz = Utils.meshTensors(((npad,cs), (ncz,cs), (npad,cs)))
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mesh = Mesh.TensorMesh([hx,hy,hz])
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XY = Utils.ndgrid(np.linspace(20,50,3), np.linspace(20,50,3))
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rxLoc = np.c_[XY, np.ones(XY.shape[0])*40]
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model = Model.LogModel(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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'rxLoc': rxLoc,
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'rxType':'bz',
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'timeCh':np.logspace(-4,-2,20),
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'freq': np.logspace(0,3,4),
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}
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dat = EM.TDEM.DataTDEM1D(**opts)
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dat = EM.FDEM.DataFDEM(**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 = EM.FDEM.ProblemFDEM_e(mesh, model)
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prb.pair(dat)
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sigma = np.random.rand(mesh.nCz)
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sigma = np.log(np.ones(mesh.nC)*1e-3)
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j_sx = np.zeros(mesh.vnEx)
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j_sx[6,6,6] = 1
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j_s = np.r_[Utils.mkvc(j_sx),np.zeros(mesh.nEy+mesh.nEz)]
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prb.j_s = j_s
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f = prb.fields(sigma)
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colorbar(mesh.plotSlice((f.get_e(3)), 'E', ind=11, normal='Z', view='real')[0])
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plt.show()
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@@ -0,0 +1,52 @@
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import numpy as np
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class FieldsFDEM(object):
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"""docstring for FieldsFDEM"""
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phi = None #: Electric potential
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A = None #: Magnetic vector potential
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e = None #: Electric field
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b = None #: Magnetic flux density
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j = None #: Current density
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h = None #: Magnetic field
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def __init__(self, mesh, nTx, nFreq, store='e'):
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self.nFreq = nFreq #: Number of times
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self.nTx = nTx #: Number of transmitters
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self.mesh = mesh
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def update(self, newFields, fInd):
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self.set_b(newFields['b'], fInd)
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self.set_e(newFields['e'], fInd)
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####################################################
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# Get Methods
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####################################################
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def get_b(self, ind):
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return self.b[ind,:,:]
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def get_e(self, ind):
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return self.e[ind,:,:]
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####################################################
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# Set Methods
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####################################################
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def set_b(self, b, ind):
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if self.b is None:
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self.b = np.zeros((self.nFreq, np.sum(self.mesh.nF), self.nTx), dtype=complex)
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self.b[:] = np.nan
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if len(b.shape) == 1:
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b = b[:, np.newaxis]
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self.b[ind,:,:] = b
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def set_e(self, e, ind):
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if self.e is None:
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self.e = np.zeros((self.nFreq, np.sum(self.mesh.nE), self.nTx), dtype=complex)
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self.e[:] = np.nan
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if len(e.shape) == 1:
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e = e[:, np.newaxis]
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self.e[ind,:,:] = e
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@@ -0,0 +1,3 @@
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from FieldsFDEM import FieldsFDEM
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from DataFDEM import DataFDEM
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from FDEM import ProblemFDEM_e
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@@ -2,13 +2,14 @@ from BaseTDEM import ProblemBaseTDEM
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from FieldsTDEM import FieldsTDEM
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from SimPEG.Utils import mkvc
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import numpy as np
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from DataTDEM import DataTDEM1D
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class ProblemTDEM_b(ProblemBaseTDEM):
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"""
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Time-Domain EM problem - B-formulation
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TDEM_b treats the following discretization of Maxwell's equations
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.. math::
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\dcurl \e^{(t+1)} + \\frac{\\b^{(t+1)} - \\b^{(t)}}{\delta t} = 0 \\\\
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\dcurl^\\top \MfMui \\b^{(t+1)} - \MeSig \e^{(t+1)} = \Me \j_s^{(t+1)}
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@@ -20,6 +21,8 @@ class ProblemTDEM_b(ProblemBaseTDEM):
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solType = 'b'
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dataPair = DataTDEM1D
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####################################################
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# Internal Methods
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####################################################
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@@ -66,7 +69,7 @@ class ProblemTDEM_b(ProblemBaseTDEM):
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:rtype: simpegEM.TDEM.FieldsTDEM
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:return: f
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Multiply G by a vector where
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Multiply G by a vector where
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"""
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if u is None:
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u = self.fields(sigma)
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@@ -108,14 +111,14 @@ class ProblemTDEM_b(ProblemBaseTDEM):
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return self.forward(m, AhRHS, AhCalcFields)
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def solveAht(self, m, p):
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def AhtRHS(tInd, u):
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rhs = self.MfMui*self.mesh.edgeCurl*self.MeSigmaI*p.get_e(tInd) + p.get_b(tInd)
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if tInd == self.nTimes-1:
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return rhs
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dt = self.getDt(tInd+1)
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return rhs + 1./dt*self.MfMui*u.get_b(tInd+1)
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def AhtCalcFields(sol, solType, tInd):
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b = sol
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e = self.MeSigmaI*self.mesh.edgeCurl.T*self.MfMui*b - self.MeSigmaI*p.get_e(tInd)
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@@ -159,7 +162,7 @@ class ProblemTDEM_b(ProblemBaseTDEM):
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-\\frac{1}{\delta t} \MfMui & 0 \\\\
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0 & 0
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\end{array}
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\\right] \\\\
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\\right] \\\\
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"""
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self.makeMassMatrices(sigma)
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@@ -208,7 +211,7 @@ class ProblemTDEM_b(ProblemBaseTDEM):
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-\\frac{1}{\delta t} \MfMui & 0 \\\\
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0 & 0
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\end{array}
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\\right] \\\\
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\\right] \\\\
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"""
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self.makeMassMatrices(sigma)
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f = FieldsTDEM(self.mesh, 1, self.times.size, 'b')
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@@ -1,3 +1,4 @@
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# from EM import *
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import Utils
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import TDEM
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import TDEM
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import FDEM
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