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rowanc1
137 lines
4.1 KiB
Python
137 lines
4.1 KiB
Python
from BaseTDEM import ProblemBaseTDEM
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from FieldsTDEM import FieldsTDEM
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import numpy as np
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class ProblemTDEM_b(ProblemBaseTDEM):
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"""
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Time-Domain EM problem - B-formulation
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.. math::
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\dcurl \e^{(t+1)} + \\frac{\\b^{(t+1)} - \\b^{(t)}}{\delta t} = 0 \\\\
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\dcurl^\\top \MfMui \\b^{(t+1)} - \MeSig \e^{(t+1)} = \Me \j_s^{(t+1)}
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"""
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def __init__(self, mesh, model, **kwargs):
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ProblemBaseTDEM.__init__(self, mesh, model, **kwargs)
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solType = 'b'
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####################################################
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# Internal Methods
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####################################################
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def getA(self, tInd):
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"""
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:param int tInd: Time index
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:rtype: scipy.sparse.csr_matrix
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:return: A
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"""
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dt = self.getDt(tInd)
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return self.MfMui*self.mesh.edgeCurl*self.MeSigmaI*self.mesh.edgeCurl.T*self.MfMui + (1/dt)*self.MfMui
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def getRHS(self, tInd, F):
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dt = self.getDt(tInd)
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return (1/dt)*self.MfMui*F.get_b(tInd-1)
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####################################################
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# Derivatives
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####################################################
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def J(self, m, v, u=None):
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if u is None:
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u = self.fields(m)
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p = self.G(m, v, u)
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y = self.solveAh(m, p)
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return self.data.projectFields(y)
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def G(self, m, v, u=None):
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if u is None:
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u = self.fields(m)
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p = FieldsTDEM(self.mesh, 1, self.times.size, 'b')
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c = self.mesh.getEdgeMassDeriv()*self.model.transformDeriv(m)*v
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for i in range(self.times.size):
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ei = u.get_e(i)
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pVal = np.empty_like(ei)
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for j in range(ei.shape[1]):
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pVal[:,j] = -ei[:,j]*c
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p.set_e(pVal,i)
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p.set_b(np.zeros((self.mesh.nF,1)), i)
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return p
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def solveAh(self, m, p):
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def AhRHS(tInd, u):
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rhs = self.MfMui*self.mesh.edgeCurl*self.MeSigmaI*p.get_e(tInd) + self.MfMui*p.get_b(tInd)
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if tInd == 0:
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return rhs
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dt = self.getDt(tInd)
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return rhs + 1./dt*self.MfMui*u.get_b(tInd-1)
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def AhCalcFields(sol, solType, tInd):
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b = sol
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e = self.MeSigmaI*self.mesh.edgeCurl.T*self.MfMui*b - self.MeSigmaI*p.get_e(tInd)
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return {'b':b, 'e':e}
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Y = self.fields(m, useThisRhs=AhRHS, useThisCalcFields=AhCalcFields)
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return Y
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####################################################
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# Functions for tests
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####################################################
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def AhVec(self, m, u=None):
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if u is None:
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u = self.fields(m)
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self.makeMassMatrices(m)
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dt = self.getDt(0)
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b = 1/dt*u.get_b(0) + self.mesh.edgeCurl*u.get_e(0)
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e = self.mesh.edgeCurl.T*self.MfMui*u.get_b(0) - self.MeSigma*u.get_e(0)
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f = FieldsTDEM(self.mesh, 1, self.times.size, 'b')
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f.set_b(b, 0)
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f.set_e(e, 0)
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for i in range(1,self.times.size):
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dt = self.getDt(i)
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b = 1/dt*u.get_b(i) + self.mesh.edgeCurl*u.get_e(i) - 1/dt*u.get_b(i-1)
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e = self.mesh.edgeCurl.T*self.MfMui*u.get_b(i) - self.MeSigma*u.get_e(i)
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f.set_b(b, i)
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f.set_e(e, i)
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return f
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if __name__ == '__main__':
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from SimPEG import *
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import simpegEM as EM
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from simpegEM.Utils.Ana import hzAnalyticDipoleT
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from scipy.constants import mu_0
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import matplotlib.pyplot as plt
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cs = 5.
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ncx = 20
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ncy = 6
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npad = 20
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hx = Utils.meshTensors(((0,cs), (ncx,cs), (npad,cs)))
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hy = Utils.meshTensors(((npad,cs), (ncy,cs), (npad,cs)))
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mesh = Mesh.Cyl1DMesh([hx,hy], -hy.sum()/2)
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model = Model.Vertical1DModel(mesh)
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opts = {'txLoc':0.,
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'txType':'VMD_MVP',
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'rxLoc':np.r_[150., 0.],
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'rxType':'bz',
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'timeCh':np.logspace(-4,-2,20),
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}
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dat = EM.TDEM.DataTDEM1D(**opts)
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prb = EM.TDEM.ProblemTDEM_b(mesh, model)
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# prb.setTimes([1e-5, 5e-5, 2.5e-4], [150, 150, 150])
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# prb.setTimes([1e-5, 5e-5, 2.5e-4], [10, 10, 10])
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prb.setTimes([1e-5], [1])
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prb.pair(dat)
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sigma = np.random.rand(mesh.nCz)
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