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rowanc1
135 lines
3.6 KiB
Python
135 lines
3.6 KiB
Python
from SimPEG import Mesh, Problem, Utils, np, sp
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import BaseMag
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from scipy.constants import mu_0
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from MagAnalytics import spheremodel, CongruousMagBC
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class MagneticsDiffSecondary(Problem.BaseProblem):
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"""Secondary field approach using differential equations!"""
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dataPair = BaseMag.BaseMagData
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modelPair = BaseMag.BaseMagModel
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def __init__(self, mesh, model, **kwargs):
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Problem.BaseProblem.__init__(self, mesh, model, **kwargs)
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Pbc, Pin, self._Pout = \
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self.mesh.getBCProjWF('neumann', discretization='CC')
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Dface = self.mesh.faceDiv
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Mc = Utils.sdiag(self.mesh.vol)
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self._Div = Mc*Dface*Pin.T*Pin
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@property
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def MfMuI(self): return self._MfMuI
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@property
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def MfMu0(self): return self._MfMu0
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def makeMassMatrices(self, m):
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mu = self.model.transform(m)
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MfMui = self.mesh.getFaceInnerProduct(1./mu)
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#TODO: this will break if tensor mu
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self._MfMuI = Utils.sdiag(1./MfMui.diagonal())
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self._MfMu0 = self.mesh.getFaceInnerProduct(1/mu_0)
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def getRHS(self, m):
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b0 = self.data.B0
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B0 = np.r_[b0[0]*np.ones(self.mesh.nFx),
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b0[1]*np.ones(self.mesh.nFy),
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b0[2]*np.ones(self.mesh.nFz)]
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Dface = self.mesh.faceDiv
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Mc = Utils.sdiag(self.mesh.vol)
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chi = self.model.transform(m, asMu=False)
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Bbc = CongruousMagBC(self.mesh, self.data.B0, chi)
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return -self._Div*self.MfMuI*self.MfMu0*B0 + self._Div*B0 - Mc*Dface*self._Pout.T*Bbc
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def getA(self, m):
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"""
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GetA creates and returns the A matrix for the Magnetics problem
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The A matrix has the form:
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.. math::
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\mathbf{A} = \mathbf{D}\mu\mathbf{G}u
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"""
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return -self._Div*self.MfMuI*self._Div.T
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def fields(self, m):
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self.makeMassMatrices(m)
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#TODO: change to pos def A
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A = self.getA(m)
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rhs = self.getRHS(m)
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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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#TODO: make onPair function call
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b0 = self.data.B0
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B0 = np.r_[b0[0]*np.ones(self.mesh.nFx),
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b0[1]*np.ones(self.mesh.nFy),
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b0[2]*np.ones(self.mesh.nFz)]
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B = self.MfMuI*self.MfMu0*B0-B0-self.MfMuI*self._Div.T*phi
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return B
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# F = self.getInitialFields()
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# return self.forward(m, self.getRHS, self.calcFields, F=F)
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if __name__ == '__main__':
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import matplotlib.pyplot as plt
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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),(1,25,1.3))
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hx, hy, hz = Utils.meshTensors(hxind, hyind, hzind)
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mesh = Mesh.TensorMesh([hx, hy, hz], [-hx.sum()/2,-hy.sum()/2,-hz.sum()/2])
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chibkg = 0.
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chiblk = 0.01
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chi = np.ones(mesh.nC)*chibkg
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sph_ind = spheremodel(mesh, 0., 0., 0., 100)
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chi[sph_ind] = chiblk
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model = BaseMag.BaseMagModel(mesh)
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# mu = (1.+chi)*mu_0
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data = BaseMag.BaseMagData()
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data.setBackgroundField(x=1., y=1., z=0.)
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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((xr.size, yr.size))*150
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rxLoc = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
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data.rxLoc = rxLoc
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prob = MagneticsDiffSecondary(mesh, model)
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prob.pair(data)
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B = prob.fields(chi)
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mesh.plotSlice(B, 'F', view='vec', showIt=True)
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dpred = data.dpred(chi, u=B)
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plt.pcolor(X, Y, dpred.reshape(X.shape, order='F'))
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plt.show()
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