mirror of
https://github.com/wassname/simpeg.git
synced 2026-07-09 04:48:12 +08:00
Lindsey Heagy
82 lines
3.0 KiB
Python
82 lines
3.0 KiB
Python
from SimPEG import *
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import matplotlib.pyplot as plt
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from simpegPF.MagAnalytics import spheremodel, MagSphereAnaFun, CongruousMagBC
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import time
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# Step1: Generate 3D tensor mesh
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hxind = ((5,25,1.3),(41, 12.5),(5,25,1.3))
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hyind = ((5,25,1.3),(41, 12.5),(5,25,1.3))
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hzind = ((5,25,1.3),(40, 12.5),(5,25,1.3))
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hx, hy, hz = Utils.meshTensors(hxind, hyind, hzind)
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M3 = Mesh.TensorMesh([hx, hy, hz], [-sum(hx)/2,-sum(hy)/2,-sum(hz)/2])
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# Step2: Generate susceptibility model
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mu0 = 4*np.pi*1e-7
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chibkg = 0.
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chiblk = 1.
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chi = np.ones(M3.nC)*chibkg
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sph_ind = spheremodel(M3, 0., 0., 0., 50)
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chi[sph_ind] = chiblk
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mu = (1.+chi)*mu0
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# Step3: Generate Boundary
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BC = [['neumann', 'neumann'], ['neumann', 'neumann'], ['neumann', 'neumann']]
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Box = 1 # Primary field in x-direction (background)
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Boy = 0 # Primary field in y-direction (background)
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Boz = 0 # Primary field in z-direction (background)
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B0 = np.r_[Box*np.ones(np.prod(M3.nFx)), Boy*np.ones(np.prod(M3.nFy)), Boz*np.ones(np.prod(M3.nFz))]
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Bbc, Bbcderiv = CongruousMagBC(M3, np.array([Box, Boy, Boz]), chi)
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# Step4: Compute system matrix and right hand side
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Dface = M3.faceDiv
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Pbc, Pin, Pout = M3.getBCProjWF(BC, discretization='CC')
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Mc = Utils.sdiag(M3.vol)
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Div = Mc*Dface*Pin.T*Pin
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MfmuI = Utils.sdiag(1/M3.getFaceInnerProduct(1/mu).diagonal())
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Mfmu0 = 1/mu0*M3.getFaceInnerProduct()
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A = -Div*MfmuI*Div.T
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rhs = -Div*MfmuI*Mfmu0*B0 + Div*B0 - Mc*Dface*Pout.T*Bbc
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# Step5: Solve !!
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start = time.clock()
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m1 = sp.linalg.interface.aslinearoperator(Utils.sdiag(-1/A.diagonal()))
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phi, info = sp.linalg.bicgstab(A, rhs, tol=1e-6, maxiter = 1000, M =m1)
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elapsed = (time.clock() - start)
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print np.linalg.norm(A*phi-rhs)/np.linalg.norm(rhs)
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print ('Cpu time = %10.3e ms') % (elapsed*1000)
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# Step6: Update for B and project to receiver locations
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B = MfmuI*Mfmu0*B0-B0-MfmuI*Div.T*phi
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xr = np.linspace(-300, 300, 41)
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yr = np.linspace(-300, 300, 41)
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X, Y = np.meshgrid(xr, yr)
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Z = np.ones((np.size(xr), np.size(yr)))*80
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rxLoc = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
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Qfx = M3.getInterpolationMat(rxLoc,'Fx')
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Qfy = M3.getInterpolationMat(rxLoc,'Fy')
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Qfz = M3.getInterpolationMat(rxLoc,'Fz')
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Bxr = np.reshape(Qfx*B, (np.size(xr), np.size(yr)), order='F')
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Byr = np.reshape(Qfy*B, (np.size(xr), np.size(yr)), order='F')
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Bzr = np.reshape(Qfz*B, (np.size(xr), np.size(yr)), order='F')
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H0 = Box/mu0
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flag = 'secondary'
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Bxra, Byra, Bzra = MagSphereAnaFun(X, Y, Z, 50., 0., 0., 0., mu0, mu0*(1+chiblk), H0, flag)
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Bxra = np.reshape(Bxra, (np.size(xr), np.size(yr)), order='F')
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Byra = np.reshape(Byra, (np.size(xr), np.size(yr)), order='F')
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Bzra = np.reshape(Bzra, (np.size(xr), np.size(yr)), order='F')
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# Step6: comparison to analytics
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fig, ax = plt.subplots(3,2, figsize = (10,15))
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dat1 = ax[0,0].imshow(Bxr); fig.colorbar(dat1, ax=ax[0,0])
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dat2 = ax[0,1].imshow(Bxra); fig.colorbar(dat2, ax=ax[0,1])
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dat3 = ax[1,0].imshow(Byr); fig.colorbar(dat3, ax=ax[1,0])
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dat4 = ax[1,1].imshow(Byra); fig.colorbar(dat4, ax=ax[1,1])
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dat5 = ax[2,0].imshow(Bzr); fig.colorbar(dat5, ax=ax[2,0])
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dat6 = ax[2,1].imshow(Bzra); fig.colorbar(dat6, ax=ax[2,1])
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plt.show() |