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Start of JH implementation, solving for h. Derivatives for ProblemFDEM_h NOT working yet
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Lindsey
@@ -338,6 +338,7 @@ class ProblemFDEM_b(BaseFDEMProblem):
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raise NotImplementedError('fieldType "%s" is not implemented.' % fieldType)
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##########################################################################################
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################################ H-J Formulation #########################################
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##########################################################################################
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@@ -424,6 +425,7 @@ class ProblemFDEM_j(BaseFDEMProblem):
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rhs[i] = np.concatenate((SRCx, SRCy, SRCz))
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a = np.concatenate(rhs).reshape((self.mesh.nF, len(Txs)), order='F')
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a = Utils.mkvc(a)
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MeMui = self.MeMui
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C = self.mesh.edgeCurl
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@@ -463,3 +465,153 @@ class ProblemFDEM_j(BaseFDEMProblem):
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else:
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return -(1./(1j*omega(freq))) * dsig_dm.T * ( dsigi_dsig.T * ( dMf_dsigi.T * ( C * ( MeMui.T * v ) ) ) )
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raise NotImplementedError('fieldType "%s" is not implemented.' % fieldType)
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# Solving for h! - NOTE: WE ARE GOING TO NEED dRHS / dm !
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class ProblemFDEM_h(BaseFDEMProblem):
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"""
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Using the H-J formulation of Maxwell's equations
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.. math::
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\\nabla \\times \\sigma^{-1} \\vec{J} + i\\omega\\mu\\vec{H} = 0
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\\nabla \\times \\vec{H} - \\vec{J} = \\vec{J_s}
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Since \(\\vec{J}\) is a flux and \(\\vec{H}\) is a field, we discretize \(\\vec{J}\) on faces and \(\\vec{H}\) on edges.
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For this implementation, we solve for J using \( \\vec{J} = \\nabla \\times \\vec{H} - \\vec{J_s} \)
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.. math::
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\\nabla \\times \\sigma^{-1} \\nabla \\times \\vec{H} + i\\omega\\mu\\vec{H} = \\nabla \\times \\sigma^{-1} \\vec{J_s}
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.. note::
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This implementation does not yet work with full anisotropy!!
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"""
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solType = 'h'
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storeTheseFields = ['j','h']
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def __init__(self, model, **kwargs):
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BaseFDEMProblem.__init__(self, model, **kwargs)
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def getA(self, freq):
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"""
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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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MeMu = self.MeMu
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MfSigi = self.MfSigmai
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C = self.mesh.edgeCurl
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return C.T * MfSigi * C + 1j*omega(freq)*MeMu
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def getADeriv(self, freq, u, v, adjoint=False):
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MeMu = self.MeMu
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C = self.mesh.edgeCurl
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sig = self.curModel.transform
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sigi = 1/sig
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dsig_dm = self.curModel.transformDeriv
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dsigi_dsig = -Utils.sdiag(sigi)**2
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dMf_dsigi = self.mesh.getFaceInnerProductDeriv(sigi)(C*u)
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if adjoint:
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return (dsig_dm.T * (dsigi_dsig.T * (dMf_dsigi.T * (C * v))))
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return (C.T * (dMf_dsigi * (dsigi_dsig * (dsig_dm * v))))
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def getjs(self,freq):
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"""
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:param float freq: Frequency
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:rtype: numpy.ndarray (nE, nTx)
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:return: j_s
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"""
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Txs = self.survey.getTransmitters(freq)
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rhs = range(len(Txs))
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for i, tx in enumerate(Txs):
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if tx.txType == 'VMD':
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src = Sources.MagneticDipoleVectorPotential
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SRCx = src(tx.loc, self.mesh.gridFx, 'x')
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SRCy = src(tx.loc, self.mesh.gridFy, 'y')
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SRCz = src(tx.loc, self.mesh.gridFz, 'z')
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elif tx.txType == 'CircularLoop':
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src = Sources.MagneticLoopVectorPotential
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SRCx = src(tx.loc, self.mesh.gridFx, 'x', tx.radius)
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SRCy = src(tx.loc, self.mesh.gridFy, 'y', tx.radius)
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SRCz = src(tx.loc, self.mesh.gridFz, 'z', tx.radius)
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else:
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raise NotImplemented('%s txType is not implemented' % tx.txType)
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rhs[i] = np.concatenate((SRCx, SRCy, SRCz))
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a = np.concatenate(rhs).reshape((self.mesh.nF, len(Txs)), order='F')
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a = Utils.mkvc(a)
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MeMui = self.MeMui
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C = self.mesh.edgeCurl
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return C*MeMui*C.T*a
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def getRHS(self, freq):
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"""
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:param float freq: Frequency
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:rtype: numpy.ndarray (nE, nTx)
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:return: RHS
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"""
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MfSigi = self.MfSigmai
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C = self.mesh.edgeCurl
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j_s = self.getjs(freq)
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return C.T*MfSigi*j_s
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def getRHSDeriv(self, freq, v, adjoint=False):
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"""
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:param float freq: Frequency
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:rtype: numpy.ndarray (nE, nTx)
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:return: RHSDeriv
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"""
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C = self.mesh.edgeCurl
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sig = self.curModel.transform
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sigi = 1/sig
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j_s = self.getjs(freq)
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dMf_dsigi = self.mesh.getFaceInnerProductDeriv(sigi)(j_s)
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dsig_dm = self.curModel.transformDeriv
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dsigi_dsig = -Utils.sdiag(sigi)**2 # only works for diagonal matrices
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if adjoint:
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return dsig_dm.T * dsigi_dsig.T * dMf_dsigi.T * C * v
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return C.T * dMf_dsigi * dsigi_dsig * dsig_dm * v
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def calcFields(self, sol, freq, fieldType, adjoint=False):
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h = sol
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if fieldType == 'j':
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NotImplementedError('fieldType "%s" is not implemented.' % fieldType)
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C = self.mesh.edgeCurl
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j_s = self.getjs(freq)
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if adjoint:
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NotImplementedError('fieldType "%s" is not implemented.' % fieldType)
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# return C.T*h # TODO: THIS IS WRONG
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NotImplementedError('fieldType "%s" is not implemented.' % fieldType)
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return C*h # - j_s
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elif fieldType == 'h':
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return h
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raise NotImplementedError('fieldType "%s" is not implemented.' % fieldType)
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def calcFieldsDeriv(self, sol, freq, fieldType, v, adjoint=False):
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h = sol
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if fieldType == 'j':
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NotImplementedError('fieldType "%s" is not implemented.' % fieldType)
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C = self.mesh.edgeCurl
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drhs = self.getRHSDeriv(freq,v,adjoint)
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if adjoint:
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NotImplementedError('fieldType "%s" is not implemented.' % fieldType)
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# return -C.T * drhs
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NotImplementedError('fieldType "%s" is not implemented.' % fieldType)
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# return -C * drhs
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elif fieldType == 'h':
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return -self.getRHSDeriv(freq,v,adjoint)
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raise NotImplementedError('fieldType "%s" is not implemented.' % fieldType)
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@@ -1,2 +1,2 @@
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from SurveyFDEM import *
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from FDEM import ProblemFDEM_e, ProblemFDEM_b, ProblemFDEM_j
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from FDEM import ProblemFDEM_e, ProblemFDEM_b, ProblemFDEM_j, ProblemFDEM_h
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@@ -8,6 +8,7 @@ TOL = 1e-4
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FLR = 1e-15 # "zero", so if residual below this --> pass regardless of order
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CONDUCTIVITY = 1e1
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MU = mu_0
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freq = 1
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addrandoms = True # important to addrandoms if testing HJ formulation with VMD source! (or else jz ~ 0)
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def getProblem(fdemType, comp):
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@@ -24,7 +25,7 @@ def getProblem(fdemType, comp):
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x = np.linspace(-30,30,6)
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XYZ = Utils.ndgrid(x,x,np.r_[0])
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Rx0 = EM.FDEM.RxFDEM(XYZ, comp)
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Tx0 = EM.FDEM.TxFDEM(np.r_[0.,0.,0.], 'VMD', 1, [Rx0])
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Tx0 = EM.FDEM.TxFDEM(np.r_[0.,0.,0.], 'VMD', freq, [Rx0])
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survey = EM.FDEM.SurveyFDEM([Tx0])
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@@ -36,6 +37,8 @@ def getProblem(fdemType, comp):
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prb = EM.FDEM.ProblemFDEM_b(mesh, mapping=mapping)
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elif fdemType == 'j':
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prb = EM.FDEM.ProblemFDEM_j(mesh, mapping=mapping)
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elif fdemType == 'h':
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prb = EM.FDEM.ProblemFDEM_h(mesh, mapping=mapping)
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else:
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raise NotImplementedError()
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prb.pair(survey)
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@@ -83,7 +86,7 @@ def derivTest(fdemType, comp):
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x0 = x0 + np.random.randn(prb.mesh.nC)*CONDUCTIVITY*1e-1
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mu = mu + np.random.randn(prb.mesh.nC)*MU*1e-1
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prb.mu = mu
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prb.mu = mu
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survey = prb.survey
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def fun(x):
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return survey.dpred(x), lambda x: prb.Jvec(x0, x)
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@@ -221,6 +224,32 @@ class FDEM_DerivTests(unittest.TestCase):
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def test_Jvec_hzi_Jform(self):
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self.assertTrue(derivTest('j', 'hzi'))
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# def test_Jvec_hxr_Hform(self):
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# self.assertTrue(derivTest('h', 'hxr'))
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# def test_Jvec_hyr_Hform(self):
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# self.assertTrue(derivTest('h', 'hyr'))
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# def test_Jvec_hzr_Hform(self):
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# self.assertTrue(derivTest('h', 'hzr'))
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# def test_Jvec_hxi_Hform(self):
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# self.assertTrue(derivTest('h', 'hxi'))
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# def test_Jvec_hyi_Hform(self):
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# self.assertTrue(derivTest('h', 'hyi'))
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# def test_Jvec_hzi_Hform(self):
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# self.assertTrue(derivTest('h', 'hzi'))
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# def test_Jvec_hxr_Hform(self):
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# self.assertTrue(derivTest('h', 'jxr'))
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# def test_Jvec_hyr_Hform(self):
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# self.assertTrue(derivTest('h', 'jyr'))
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# def test_Jvec_hzr_Hform(self):
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# self.assertTrue(derivTest('h', 'jzr'))
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# def test_Jvec_hxi_Hform(self):
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# self.assertTrue(derivTest('h', 'jxi'))
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# def test_Jvec_hyi_Hform(self):
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# self.assertTrue(derivTest('h', 'jyi'))
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# def test_Jvec_hzi_Hform(self):
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# self.assertTrue(derivTest('h', 'jzi'))
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def test_Jtvec_adjointTest_jxr_Jform(self):
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self.assertTrue(adjointTest('j', 'jxr'))
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def test_Jtvec_adjointTest_jyr_Jform(self):
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@@ -247,6 +276,33 @@ class FDEM_DerivTests(unittest.TestCase):
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def test_Jtvec_adjointTest_hzi_Jform(self):
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self.assertTrue(adjointTest('j', 'hzi'))
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# def test_Jtvec_adjointTest_hxr_Hform(self):
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# self.assertTrue(adjointTest('h', 'hxr'))
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# def test_Jtvec_adjointTest_hyr_Hform(self):
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# self.assertTrue(adjointTest('h', 'hyr'))
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# def test_Jtvec_adjointTest_hzr_Hform(self):
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# self.assertTrue(adjointTest('h', 'hzr'))
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# def test_Jtvec_adjointTest_hxi_Hform(self):
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# self.assertTrue(adjointTest('h', 'hxi'))
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# def test_Jtvec_adjointTest_hyi_Hform(self):
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# self.assertTrue(adjointTest('h', 'hyi'))
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# def test_Jtvec_adjointTest_hzi_Hform(self):
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# self.assertTrue(adjointTest('h', 'hzi'))
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# def test_Jtvec_adjointTest_hxr_Hform(self):
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# self.assertTrue(adjointTest('h', 'jxr'))
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# def test_Jtvec_adjointTest_hyr_Hform(self):
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# self.assertTrue(adjointTest('h', 'jyr'))
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# def test_Jtvec_adjointTest_hzr_Hform(self):
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# self.assertTrue(adjointTest('h', 'jzr'))
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# def test_Jtvec_adjointTest_hxi_Hform(self):
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# self.assertTrue(adjointTest('h', 'jxi'))
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# def test_Jtvec_adjointTest_hyi_Hform(self):
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# self.assertTrue(adjointTest('h', 'jyi'))
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# def test_Jtvec_adjointTest_hzi_Hform(self):
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# self.assertTrue(adjointTest('h', 'jzi'))
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if __name__ == '__main__':
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unittest.main()
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