diff --git a/docs/api_FDEM.rst b/docs/api_FDEM.rst index 4c173568..28317098 100644 --- a/docs/api_FDEM.rst +++ b/docs/api_FDEM.rst @@ -124,13 +124,13 @@ E-B Formulation: .. math :: \mathbf{C} \mathbf{e} + i \omega \mathbf{b} = \mathbf{s_m} \\ - \mathbf{C^T} \mathbf{M^f_{\mu^{-1}}} \mathbf{b} - \mathbf{M^e_\sigma} \mathbf{e} = \mathbf{s_e} + \mathbf{C^T} \mathbf{M^f_{\mu^{-1}}} \mathbf{b} - \mathbf{M^e_\sigma} \mathbf{e} = \mathbf{M^e} \mathbf{s_e} H-J Formulation: **************** .. math :: - \mathbf{C^T} \mathbf{M^f_\rho} \mathbf{j} + i \omega \mathbf{M^e_\mu} \mathbf{h} = \mathbf{s_m} \\ + \mathbf{C^T} \mathbf{M^f_\rho} \mathbf{j} + i \omega \mathbf{M^e_\mu} \mathbf{h} = \mathbf{M^e} \mathbf{s_m} \\ \mathbf{C} \mathbf{h} - \mathbf{j} = \mathbf{s_e} diff --git a/simpegEM/FDEM/FDEM.py b/simpegEM/FDEM/FDEM.py index 546c2ac2..38de9a66 100644 --- a/simpegEM/FDEM/FDEM.py +++ b/simpegEM/FDEM/FDEM.py @@ -15,7 +15,7 @@ class BaseFDEMProblem(BaseEMProblem): .. math :: \mathbf{C} \mathbf{e} + i \omega \mathbf{b} = \mathbf{s_m} \\\\ - {\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{b} - \mathbf{M_{\sigma}^e} \mathbf{e} = \mathbf{s_e}} + {\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{b} - \mathbf{M_{\sigma}^e} \mathbf{e} = \mathbf{M^e} \mathbf{s_e}} if using the E-B formulation (:code:`ProblemFDEM_e` or :code:`ProblemFDEM_b`) or the magnetic field @@ -23,7 +23,7 @@ class BaseFDEMProblem(BaseEMProblem): .. math :: - \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{j} + i \omega \mathbf{M_{\mu}^e} \mathbf{h} = \mathbf{s_m} \\\\ + \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{j} + i \omega \mathbf{M_{\mu}^e} \mathbf{h} = \mathbf{M^e} \mathbf{s_m} \\\\ \mathbf{C} \mathbf{h} - \mathbf{j} = \mathbf{s_e} if using the H-J formulation (:code:`ProblemFDEM_j` or :code:`ProblemFDEM_h`). @@ -198,7 +198,7 @@ class ProblemFDEM_e(BaseFDEMProblem): .. math :: - \\left(\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{C}+ i \omega \mathbf{M^e_{\sigma}} \\right)\mathbf{e} = \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f}\mathbf{s_m} -i\omega\mathbf{s_e} + \\left(\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{C}+ i \omega \mathbf{M^e_{\sigma}} \\right)\mathbf{e} = \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f}\mathbf{s_m} -i\omega\mathbf{M^e}\mathbf{s_e} which we solve for \\\(\\\mathbf{e}\\\). """ @@ -238,7 +238,7 @@ class ProblemFDEM_e(BaseFDEMProblem): def getRHS(self, freq): """ .. math :: - \mathbf{RHS} = \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f}\mathbf{s_m} -i\omega\mathbf{s_e} + \mathbf{RHS} = \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f}\mathbf{s_m} -i\omega\mathbf{M_e}\mathbf{s_e} :param float freq: Frequency :rtype: numpy.ndarray (nE, nSrc) @@ -246,16 +246,18 @@ class ProblemFDEM_e(BaseFDEMProblem): """ S_m, S_e = self.getSourceTerm(freq) + Me = self.Me C = self.mesh.edgeCurl MfMui = self.MfMui - RHS = C.T * (MfMui * S_m) -1j*omega(freq)*S_e + RHS = C.T * (MfMui * S_m) -1j * omega(freq) * Me * S_e return RHS def getRHSDeriv_m(self, src, v, adjoint=False): C = self.mesh.edgeCurl MfMui = self.MfMui + Me = self.Me S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint) if adjoint: @@ -263,22 +265,22 @@ class ProblemFDEM_e(BaseFDEMProblem): S_mDerivv = S_mDeriv(dRHS) S_eDerivv = S_eDeriv(v) if S_mDerivv is not None and S_eDerivv is not None: - return S_mDerivv - 1j*omega(freq)*S_eDerivv + return S_mDerivv - 1j * omega(freq) * Me.T * S_eDerivv elif S_mDerivv is not None: return S_mDerivv elif S_eDerivv is not None: - return - 1j*omega(freq)*S_eDerivv + return - 1j * omega(freq) * Me.T * S_eDerivv else: return None else: S_mDerivv, S_eDerivv = S_mDeriv(v), S_eDeriv(v) if S_mDerivv is not None and S_eDerivv is not None: - return C.T * (MfMui * S_mDerivv) -1j*omega(freq)*S_eDerivv + return C.T * (MfMui * S_mDerivv) -1j * omega(freq) * Me * S_eDerivv elif S_mDerivv is not None: return C.T * (MfMui * S_mDerivv) elif S_eDerivv is not None: - return -1j*omega(freq)*S_eDerivv + return -1j * omega(freq) * Me * S_eDerivv else: return None @@ -295,7 +297,7 @@ class ProblemFDEM_b(BaseFDEMProblem): .. math :: - \\left(\mathbf{C} \mathbf{M^e_{\sigma}}^{-1} \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} + i \omega \\right)\mathbf{b} = \mathbf{s_m} + \mathbf{M^e_{\sigma}}^{-1}\mathbf{s_e} + \\left(\mathbf{C} \mathbf{M^e_{\sigma}}^{-1} \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} + i \omega \\right)\mathbf{b} = \mathbf{s_m} + \mathbf{M^e_{\sigma}}^{-1}\mathbf{M^e}\mathbf{s_e} .. note :: The inverse problem will not work with full anisotropy @@ -323,7 +325,7 @@ class ProblemFDEM_b(BaseFDEMProblem): C = self.mesh.edgeCurl iomega = 1j * omega(freq) * sp.eye(self.mesh.nF) - A = C*MeSigmaI*C.T*MfMui + iomega + A = C * (MeSigmaI * (C.T * MfMui)) + iomega if self._makeASymmetric is True: return MfMui.T*A @@ -334,7 +336,7 @@ class ProblemFDEM_b(BaseFDEMProblem): MfMui = self.MfMui C = self.mesh.edgeCurl MeSigmaIDeriv = self.MeSigmaIDeriv - vec = C.T*(MfMui*u) + vec = C.T * (MfMui * u) MeSigmaIDeriv = MeSigmaIDeriv(vec) @@ -361,12 +363,13 @@ class ProblemFDEM_b(BaseFDEMProblem): S_m, S_e = self.getSourceTerm(freq) C = self.mesh.edgeCurl MeSigmaI = self.MeSigmaI + Me = self.Me - RHS = S_m + C * ( MeSigmaI * S_e ) + RHS = S_m + C * ( MeSigmaI * Me * S_e ) if self._makeASymmetric is True: MfMui = self.MfMui - return MfMui.T*RHS + return MfMui.T * RHS return RHS @@ -374,12 +377,13 @@ class ProblemFDEM_b(BaseFDEMProblem): C = self.mesh.edgeCurl S_m, S_e = src.eval(self) MfMui = self.MfMui + Me = self.Me if self._makeASymmetric and adjoint: v = self.MfMui * v if S_e is not None: - MeSigmaIDeriv = self.MeSigmaIDeriv(Utils.mkvc(S_e)) + MeSigmaIDeriv = self.MeSigmaIDeriv(Utils.mkvc( Me * S_e)) if not adjoint: RHSderiv = C * (MeSigmaIDeriv * v) elif adjoint: @@ -391,16 +395,16 @@ class ProblemFDEM_b(BaseFDEMProblem): S_mDeriv, S_eDeriv = S_mDeriv(v), S_eDeriv(v) if S_mDeriv is not None and S_eDeriv is not None: if not adjoint: - SrcDeriv = S_mDeriv + C * (self.MeSigmaI * S_eDeriv) + SrcDeriv = S_mDeriv + C * (self.MeSigmaI * (Me * S_eDeriv)) elif adjoint: - SrcDeriv = S_mDeriv + Self.MeSigmaI.T * ( C.T * S_eDeriv) + SrcDeriv = S_mDeriv + Me.T * (Self.MeSigmaI.T * ( C.T * S_eDeriv)) elif S_mDeriv is not None: SrcDeriv = S_mDeriv elif S_eDeriv is not None: if not adjoint: - SrcDeriv = C * (self.MeSigmaI * S_eDeriv) + SrcDeriv = C * (self.MeSigmaI * (Me * S_eDeriv)) elif adjoint: - SrcDeriv = self.MeSigmaI.T * ( C.T * S_eDeriv) + SrcDeriv = Me.T * (self.MeSigmaI.T * ( C.T * S_eDeriv)) else: SrcDeriv = None @@ -428,13 +432,13 @@ class ProblemFDEM_j(BaseFDEMProblem): .. math :: - \mathbf{h} = \\frac{1}{i \omega} \mathbf{M_{\mu}^e}^{-1} \\left(-\mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{j} + \mathbf{s_m} \\right) + \mathbf{h} = \\frac{1}{i \omega} \mathbf{M_{\mu}^e}^{-1} \\left(-\mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{j} + \mathbf{M^e} \mathbf{s_m} \\right) and solve for \\\(\\\mathbf{j}\\\) using .. math :: - \\left(\mathbf{C} \mathbf{M_{\mu}^e}^{-1} \mathbf{C}^T \mathbf{M_{\\rho}^f} + i \omega\\right)\mathbf{j} = \mathbf{C} \mathbf{M_{\mu}^e}^{-1}\mathbf{s_m} -i\omega\mathbf{s_e} + \\left(\mathbf{C} \mathbf{M_{\mu}^e}^{-1} \mathbf{C}^T \mathbf{M_{\\rho}^f} + i \omega\\right)\mathbf{j} = \mathbf{C} \mathbf{M_{\mu}^e}^{-1} \mathbf{M^e} \mathbf{s_m} -i\omega\mathbf{s_e} .. note:: This implementation does not yet work with full anisotropy!! @@ -507,10 +511,11 @@ class ProblemFDEM_j(BaseFDEMProblem): S_m, S_e = self.getSourceTerm(freq) C = self.mesh.edgeCurl - MeMuI = self.MeMuI + MeMuI = self.MeMuI + Me = self.Me - RHS = C * (MeMuI * S_m) - 1j * omega(freq) * S_e + RHS = C * (MeMuI * (Me * S_m)) - 1j * omega(freq) * S_e if self._makeASymmetric is True: MfRho = self.MfRho return MfRho.T*RHS @@ -520,6 +525,7 @@ class ProblemFDEM_j(BaseFDEMProblem): def getRHSDeriv_m(self, src, v, adjoint=False): C = self.mesh.edgeCurl MeMuI = self.MeMuI + Me = self.Me S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint) if adjoint: @@ -529,20 +535,20 @@ class ProblemFDEM_j(BaseFDEMProblem): S_mDerivv = S_mDeriv(MeMuI.T * (C.T * v)) S_eDerivv = S_eDeriv(v) if S_mDerivv is not None and S_eDerivv is not None: - return S_mDerivv - 1j*omega(freq)*S_eDerivv + return Me.T * S_mDerivv - 1j * omega(freq) * S_eDerivv elif S_mDerivv is not None: - return S_mDerivv + return Me.T * S_mDerivv elif S_eDerivv is not None: - return - 1j*omega(freq)*S_eDerivv + return - 1j * omega(freq) * S_eDerivv else: return None else: S_mDerivv, S_eDerivv = S_mDeriv(v), S_eDeriv(v) if S_mDerivv is not None and S_eDerivv is not None: - RHSDeriv = C * (MeMuI * S_mDerivv) - 1j * omega(freq) * S_eDerivv + RHSDeriv = C * (MeMuI * (Me * S_mDerivv)) - 1j * omega(freq) * S_eDerivv elif S_mDerivv is not None: - RHSDeriv = C * (MeMuI * S_mDerivv) + RHSDeriv = C * (MeMuI * (Me * S_mDerivv)) elif S_eDerivv is not None: RHSDeriv = - 1j * omega(freq) * S_eDerivv else: @@ -568,7 +574,7 @@ class ProblemFDEM_h(BaseFDEMProblem): .. math :: - \\left(\mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{C} + i \omega \mathbf{M_{\mu}^e}\\right) \mathbf{h} = \mathbf{s_m} + \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{s_e} + \\left(\mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{C} + i \omega \mathbf{M_{\mu}^e}\\right) \mathbf{h} = \mathbf{M^e} \mathbf{s_m} + \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{s_e} """ @@ -594,7 +600,7 @@ class ProblemFDEM_h(BaseFDEMProblem): MfRho = self.MfRho C = self.mesh.edgeCurl - return C.T * MfRho * C + 1j*omega(freq)*MeMu + return C.T * (MfRho * C) + 1j*omega(freq)*MeMu def getADeriv_m(self, freq, u, v, adjoint=False): @@ -610,7 +616,7 @@ class ProblemFDEM_h(BaseFDEMProblem): """ .. math :: - \mathbf{RHS} = \mathbf{s_m} + \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{s_e} + \mathbf{RHS} = \mathbf{M^e} \mathbf{s_m} + \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{s_e} :param float freq: Frequency :rtype: numpy.ndarray (nE, nSrc) @@ -620,8 +626,9 @@ class ProblemFDEM_h(BaseFDEMProblem): S_m, S_e = self.getSourceTerm(freq) C = self.mesh.edgeCurl MfRho = self.MfRho + Me = self.Me - RHS = S_m + C.T * ( MfRho * S_e ) + RHS = Me * S_m + C.T * ( MfRho * S_e ) return RHS @@ -629,6 +636,7 @@ class ProblemFDEM_h(BaseFDEMProblem): _, S_e = src.eval(self) C = self.mesh.edgeCurl MfRho = self.MfRho + Me = self.Me RHSDeriv = None @@ -643,11 +651,15 @@ class ProblemFDEM_h(BaseFDEMProblem): S_mDeriv = S_mDeriv(v) S_eDeriv = S_eDeriv(v) + + if adjoint: + Me = Me.T + if S_mDeriv is not None: if RHSDeriv is not None: - RHSDeriv += S_mDeriv(v) + RHSDeriv += Me * S_mDeriv(v) else: - RHSDeriv = S_mDeriv(v) + RHSDeriv = Me * S_mDeriv(v) if S_eDeriv is not None: if RHSDeriv is not None: RHSDeriv += C.T * (MfRho * S_e) diff --git a/simpegEM/FDEM/FieldsFDEM.py b/simpegEM/FDEM/FieldsFDEM.py index 99866bc3..1c57c1ca 100644 --- a/simpegEM/FDEM/FieldsFDEM.py +++ b/simpegEM/FDEM/FieldsFDEM.py @@ -109,6 +109,7 @@ class FieldsFDEM_b(FieldsFDEM): self._MeSigmaI = self.survey.prob.MeSigmaI self._MfMui = self.survey.prob.MfMui self._MeSigmaIDeriv = self.survey.prob.MeSigmaIDeriv + self._Me = self.survey.prob.Me def _bPrimary(self, bSolution, srcList): bPrimary = np.zeros_like(bSolution) @@ -144,7 +145,7 @@ class FieldsFDEM_b(FieldsFDEM): for i,src in enumerate(srcList): _,S_e = src.eval(self.prob) if S_e is not None: - e[:,i] += -self._MeSigmaI*S_e + e[:,i] += -self._MeSigmaI * (self._Me * S_e) return e def _eSecondaryDeriv_u(self, src, v, adjoint=False): @@ -156,10 +157,14 @@ class FieldsFDEM_b(FieldsFDEM): def _eSecondaryDeriv_m(self, src, v, adjoint=False): bSolution = self[[src],'bSolution'] _,S_e = src.eval(self.prob) + Me = self._Me + + if adjoint: + Me = Me.T w = self._edgeCurl.T * (self._MfMui * bSolution) if S_e is not None: - w += -Utils.mkvc(S_e,2) + w += -Utils.mkvc(Me * S_e,2) if not adjoint: de_dm = self._MeSigmaIDeriv(w) * v @@ -170,7 +175,7 @@ class FieldsFDEM_b(FieldsFDEM): Se_Deriv = S_eDeriv(v) if Se_Deriv is not None: - de_dm += -self._MeSigmaI * Se_Deriv + de_dm += -self._MeSigmaI * (self._Me * Se_Deriv) return de_dm @@ -205,6 +210,7 @@ class FieldsFDEM_j(FieldsFDEM): self._MeMuI = self.survey.prob.MeMuI self._MfRho = self.survey.prob.MfRho self._MfRhoDeriv = self.survey.prob.MfRhoDeriv + self._Me = self.survey.prob.Me def _jPrimary(self, jSolution, srcList): jPrimary = np.zeros_like(jSolution,dtype = complex) @@ -236,25 +242,19 @@ class FieldsFDEM_j(FieldsFDEM): return hPrimary def _hSecondary(self, jSolution, srcList): - MeMuI = self._MeMuI - C = self._edgeCurl - MfRho = self._MfRho - h = MeMuI * (C.T * (MfRho * jSolution) ) + h = self._MeMuI * (self._edgeCurl.T * (self._MfRho * jSolution) ) for i, src in enumerate(srcList): h[:,i] *= -1./(1j*omega(src.freq)) S_m,_ = src.eval(self.prob) if S_m is not None: - h[:,i] += 1./(1j*omega(src.freq)) * MeMuI * S_m + h[:,i] += 1./(1j*omega(src.freq)) * self._MeMuI * (self._Me * S_m) return h def _hSecondaryDeriv_u(self, src, v, adjoint=False): - MeMuI = self._MeMuI - C = self._edgeCurl - MfRho = self._MfRho if not adjoint: - return -1./(1j*omega(src.freq)) * MeMuI * (C.T * (MfRho * v) ) + return -1./(1j*omega(src.freq)) * self._MeMuI * (self._edgeCurl.T * (self._MfRho * v) ) elif adjoint: - return -1./(1j*omega(src.freq)) * MfRho.T * (C * ( MeMuI.T * v)) + return -1./(1j*omega(src.freq)) * self._MfRho.T * (self._edgeCurl * ( self._MeMuI.T * v)) def _hSecondaryDeriv_m(self, src, v, adjoint=False): jSolution = self[[src],'jSolution'] @@ -262,6 +262,7 @@ class FieldsFDEM_j(FieldsFDEM): C = self._edgeCurl MfRho = self._MfRho MfRhoDeriv = self._MfRhoDeriv + Me = self._Me if not adjoint: hDeriv_m = -1./(1j*omega(src.freq)) * MeMuI * (C.T * (MfRhoDeriv(jSolution)*v ) ) @@ -273,9 +274,9 @@ class FieldsFDEM_j(FieldsFDEM): if not adjoint: S_mDeriv = S_mDeriv(v) if S_mDeriv is not None: - hDeriv_m += 1./(1j*omega(src.freq)) * MeMuI * S_mDeriv + hDeriv_m += 1./(1j*omega(src.freq)) * MeMuI * (Me * S_mDeriv) elif adjoint: - S_mDeriv = S_mDeriv(MeMuI.T * v) + S_mDeriv = S_mDeriv(Me.T * (MeMuI.T * v)) if S_mDeriv is not None: hDeriv_m += 1./(1j*omega(src.freq)) * S_mDeriv return hDeriv_m diff --git a/simpegEM/TDEM/SurveyTDEM.py b/simpegEM/TDEM/SurveyTDEM.py index 63cc008a..bcd83962 100644 --- a/simpegEM/TDEM/SurveyTDEM.py +++ b/simpegEM/TDEM/SurveyTDEM.py @@ -102,7 +102,7 @@ class SrcTDEM_CircularLoop_MVP(SrcTDEM): def __init__(self,rxList,loc,radius): self.loc = loc - self.radius =radius + self.radius = radius SrcTDEM.__init__(self,rxList) def getInitialFields(self, mesh): diff --git a/simpegEM/Tests/test_FDEM.py b/simpegEM/Tests/test_FDEM.py index 24c9205f..7f91236b 100644 --- a/simpegEM/Tests/test_FDEM.py +++ b/simpegEM/Tests/test_FDEM.py @@ -12,14 +12,14 @@ testHJ = True verbose = False -TOL = 1e-4 +TOL = 1e-6 FLR = 1e-20 # "zero", so if residual below this --> pass regardless of order CONDUCTIVITY = 1e1 MU = mu_0 freq = 1e-1 addrandoms = True -SrcType = 'MagDipole' #or 'MAgDipole_Bfield', 'CircularLoop', 'RawVec' +SrcType = 'RawVec' #or 'MAgDipole_Bfield', 'CircularLoop', 'RawVec' def getProblem(fdemType, comp):