mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-28 08:08:16 +08:00
Lindsey Heagy
244 lines
7.9 KiB
Python
244 lines
7.9 KiB
Python
import unittest
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from SimPEG import *
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from SimPEG import EM
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from scipy.constants import mu_0
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plotIt = False
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tol_EBdipole = 1e-2
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if plotIt:
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import matplotlib.pylab
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class FDEM_analyticTests(unittest.TestCase):
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def setUp(self):
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cs = 10.
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ncx, ncy, ncz = 10, 10, 10
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npad = 4
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freq = 1e2
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hx = [(cs,npad,-1.3), (cs,ncx), (cs,npad,1.3)]
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hy = [(cs,npad,-1.3), (cs,ncy), (cs,npad,1.3)]
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hz = [(cs,npad,-1.3), (cs,ncz), (cs,npad,1.3)]
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mesh = Mesh.TensorMesh([hx,hy,hz], 'CCC')
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mapping = Maps.ExpMap(mesh)
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x = np.linspace(-10,10,5)
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XYZ = Utils.ndgrid(x,np.r_[0],np.r_[0])
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rxList = EM.FDEM.Rx(XYZ, 'exi')
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Src0 = EM.FDEM.Src.MagDipole([rxList],loc=np.r_[0.,0.,0.], freq=freq)
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survey = EM.FDEM.Survey([Src0])
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prb = EM.FDEM.Problem_b(mesh, mapping=mapping)
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prb.pair(survey)
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try:
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from pymatsolver import MumpsSolver
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prb.Solver = MumpsSolver
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except ImportError, e:
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prb.Solver = SolverLU
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sig = 1e-1
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sigma = np.ones(mesh.nC)*sig
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sigma[mesh.gridCC[:,2] > 0] = 1e-8
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m = np.log(sigma)
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self.prb = prb
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self.mesh = mesh
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self.m = m
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self.Src0 = Src0
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self.sig = sig
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def test_Transect(self):
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print 'Testing Transect for analytic'
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u = self.prb.fields(self.m)
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bfz = self.mesh.r(u[self.Src0, 'b'],'F','Fz','M')
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x = np.linspace(-55,55,12)
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XYZ = Utils.ndgrid(x,np.r_[0],np.r_[0])
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P = self.mesh.getInterpolationMat(XYZ, 'Fz')
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an = EM.Analytics.FDEM.hzAnalyticDipoleF(x, self.Src0.freq, self.sig)
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diff = np.log10(np.abs(P*np.imag(u[self.Src0, 'b']) - mu_0*np.imag(an)))
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if plotIt:
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import matplotlib.pyplot as plt
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plt.plot(x,np.log10(np.abs(P*np.imag(u[self.Src0, 'b']))))
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plt.plot(x,np.log10(np.abs(mu_0*np.imag(an))), 'r')
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plt.plot(x,diff,'g')
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plt.show()
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# We want the difference to be an orderMag less
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# than the analytic solution. Note that right at
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# the source, both the analytic and the numerical
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# solution will be poor. Use plotIt up top to see that...
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orderMag = 1.6
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passed = np.abs(np.mean(diff - np.log10(np.abs(mu_0*np.imag(an))))) > orderMag
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self.assertTrue(passed)
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def test_CylMeshEBDipoles(self):
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print 'Testing CylMesh Electric and Magnetic Dipoles in a wholespace- Analytic: J-formulation'
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sigmaback = 1.
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mur = 2.
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freq = 1.
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skdpth = 500./np.sqrt(sigmaback*freq)
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csx, ncx, npadx = 5, 50, 25
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csz, ncz, npadz = 5, 50, 25
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hx = Utils.meshTensor([(csx,ncx), (csx,npadx,1.3)])
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hz = Utils.meshTensor([(csz,npadz,-1.3), (csz,ncz), (csz,npadz,1.3)])
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mesh = Mesh.CylMesh([hx,1,hz], [0.,0.,-hz.sum()/2]) # define the cylindrical mesh
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if plotIt:
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mesh.plotGrid()
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# make sure mesh is big enough
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self.assertTrue(mesh.hz.sum() > skdpth*2.)
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self.assertTrue(mesh.hx.sum() > skdpth*2.)
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SigmaBack = sigmaback*np.ones((mesh.nC))
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MuBack = mur*mu_0*np.ones((mesh.nC))
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# set up source
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# test electric dipole
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src_loc = np.r_[0.,0.,0.]
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s_ind = Utils.closestPoints(mesh,src_loc,'Fz') + mesh.nFx
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de = np.zeros(mesh.nF,dtype=complex)
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de[s_ind] = 1./csz
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de_p = [EM.FDEM.Src.RawVec_e([],freq,de/mesh.area)]
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dm_p = [EM.FDEM.Src.MagDipole([],freq,src_loc)]
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# Pair the problem and survey
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surveye = EM.FDEM.Survey(de_p)
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surveym = EM.FDEM.Survey(dm_p)
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mapping = [('sigma', Maps.IdentityMap(mesh)),('mu', Maps.IdentityMap(mesh))]
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prbe = EM.FDEM.Problem_h(mesh, mapping=mapping)
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prbm = EM.FDEM.Problem_e(mesh, mapping=mapping)
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prbe.pair(surveye) # pair problem and survey
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prbm.pair(surveym)
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# solve
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fieldsBackE = prbe.fields(np.r_[SigmaBack, MuBack]) # Done
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fieldsBackM = prbm.fields(np.r_[SigmaBack, MuBack]) # Done
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rlim = [20.,500.]
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lookAtTx = de_p
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r = mesh.vectorCCx[np.argmin(np.abs(mesh.vectorCCx-rlim[0])):np.argmin(np.abs(mesh.vectorCCx-rlim[1]))]
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z = 100.
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# where we choose to measure
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XYZ = Utils.ndgrid(r, np.r_[0.], np.r_[z])
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Pf = mesh.getInterpolationMat(XYZ, 'CC')
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Zero = sp.csr_matrix(Pf.shape)
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Pfx,Pfz = sp.hstack([Pf,Zero]),sp.hstack([Zero,Pf])
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jn = fieldsBackE[de_p,'j']
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bn = fieldsBackM[dm_p,'b']
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Rho = Utils.sdiag(1./SigmaBack)
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Rho = sp.block_diag([Rho,Rho])
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en = Rho*mesh.aveF2CCV*jn
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bn = mesh.aveF2CCV*bn
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ex,ez = Pfx*en, Pfz*en
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bx,bz = Pfx*bn, Pfz*bn
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# get analytic solution
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exa, eya, eza = EM.Analytics.FDEM.ElectricDipoleWholeSpace(XYZ, src_loc, sigmaback, freq,orientation='Z',mu= mur*mu_0)
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exa, eya, eza = Utils.mkvc(exa,2), Utils.mkvc(eya,2), Utils.mkvc(eza,2)
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bxa, bya, bza = EM.Analytics.FDEM.MagneticDipoleWholeSpace(XYZ, src_loc, sigmaback, freq,orientation='Z',mu= mur*mu_0)
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bxa, bya, bza = Utils.mkvc(bxa,2), Utils.mkvc(bya,2), Utils.mkvc(bza,2)
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print ' comp, anayltic, numeric, num - ana, (num - ana)/ana'
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print ' ex:', np.linalg.norm(exa), np.linalg.norm(ex), np.linalg.norm(exa-ex), np.linalg.norm(exa-ex)/np.linalg.norm(exa)
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print ' ez:', np.linalg.norm(eza), np.linalg.norm(ez), np.linalg.norm(eza-ez), np.linalg.norm(eza-ez)/np.linalg.norm(eza)
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print ' bx:', np.linalg.norm(bxa), np.linalg.norm(bx), np.linalg.norm(bxa-bx), np.linalg.norm(bxa-bx)/np.linalg.norm(bxa)
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print ' bz:', np.linalg.norm(bza), np.linalg.norm(bz), np.linalg.norm(bza-bz), np.linalg.norm(bza-bz)/np.linalg.norm(bza)
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if plotIt:
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# Edipole
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plt.subplot(221)
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plt.plot(r,ex.real,'o',r,exa.real,linewidth=2)
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plt.grid(which='both')
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plt.title('Ex Real')
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plt.xlabel('r (m)')
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plt.subplot(222)
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plt.plot(r,ex.imag,'o',r,exa.imag,linewidth=2)
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plt.grid(which='both')
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plt.title('Ex Imag')
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plt.legend(['Num','Ana'],bbox_to_anchor=(1.5,0.5))
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plt.xlabel('r (m)')
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plt.subplot(223)
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plt.plot(r,ez.real,'o',r,eza.real,linewidth=2)
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plt.grid(which='both')
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plt.title('Ez Real')
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plt.xlabel('r (m)')
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plt.subplot(224)
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plt.plot(r,ez.imag,'o',r,eza.imag,linewidth=2)
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plt.grid(which='both')
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plt.title('Ez Imag')
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plt.xlabel('r (m)')
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plt.tight_layout()
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# Bdipole
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plt.subplot(221)
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plt.plot(r,bx.real,'o',r,bxa.real,linewidth=2)
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plt.grid(which='both')
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plt.title('Bx Real')
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plt.xlabel('r (m)')
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plt.subplot(222)
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plt.plot(r,bx.imag,'o',r,bxa.imag,linewidth=2)
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plt.grid(which='both')
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plt.title('Bx Imag')
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plt.legend(['Num','Ana'],bbox_to_anchor=(1.5,0.5))
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plt.xlabel('r (m)')
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plt.subplot(223)
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plt.plot(r,bz.real,'o',r,bza.real,linewidth=2)
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plt.grid(which='both')
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plt.title('Bz Real')
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plt.xlabel('r (m)')
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plt.subplot(224)
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plt.plot(r,bz.imag,'o',r,bza.imag,linewidth=2)
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plt.grid(which='both')
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plt.title('Bz Imag')
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plt.xlabel('r (m)')
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plt.tight_layout()
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self.assertTrue(np.linalg.norm(exa-ex)/np.linalg.norm(exa) < tol_EBdipole)
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self.assertTrue(np.linalg.norm(eza-ez)/np.linalg.norm(eza) < tol_EBdipole)
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self.assertTrue(np.linalg.norm(bxa-bx)/np.linalg.norm(bxa) < tol_EBdipole)
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self.assertTrue(np.linalg.norm(bza-bz)/np.linalg.norm(bza) < tol_EBdipole)
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if __name__ == '__main__':
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unittest.main()
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