working on DC problem CC and N

SimPEG/EM/Analytics/DC.py

@@ -0,0 +1,34 @@
+import numpy as np
+from scipy.constants import mu_0, pi
+
+def DCAnalytic(txloc, rxlocs, sigma, flag="wholespace"):
+    """
+        Analytic solution for electric potential from a postive pole
+
+        Input variables:
+
+            txloc =  a xyz location of A (+) electrode (np.r_[xa, ya, za])
+
+            rxlocs = [M, N]
+                M: xyz locations of M (+) electrode (np.c_[xmlocs, ymlocs, zmlocs])
+                N: xyz locations of N (-) electrode (np.c_[xnlocs, ynlocs, znlocs])
+
+            sigma = conductivity (either float or complex)
+            flag = "wholsespace" or "halfspace"
+
+    """
+    M = rxlocs[0]
+    N = rxlocs[1]
+
+    rM = np.sqrt( (M[:,0]-txloc[0])**2 + (M[:,1]-txloc[1])**2 + (M[:,2]-txloc[1])**2 )
+    rN = np.sqrt( (N[:,0]-txloc[0])**2 + (N[:,1]-txloc[1])**2 + (N[:,2]-txloc[1])**2 )
+
+    phiM = 1./(4*np.pi*rM*sigma)
+    phiN = 1./(4*np.pi*rN*sigma)
+    phi = phiM - phiN
+
+    if flag == "halfspace":
+        phi *= 2
+
+    return phi
+

SimPEG/EM/Analytics/__init__.py

@@ -1,3 +1,4 @@
 from TDEM import hzAnalyticDipoleT
 from FDEM import hzAnalyticDipoleF
 from FDEMcasing import *
+from DC import DCAnalytic

SimPEG/EM/Static/DC/FieldsDC.py

@@ -69,4 +69,41 @@ class Fields_CC(Fields):
     def _e(self, phiSolution, srcList):
         raise NotImplementedError
 
+class Fields_N(Fields):
+    knownFields = {'phiSolution':'N'}
+    aliasFields = {
+                    'phi': ['phiSolution','N','_phi'],
+                    'j' : ['phiSolution','E','_j'],
+                    'e' : ['phiSolution','E','_e'],
+                  }
+                  # primary - secondary
+                  # N variables
 
+    def __init__(self, mesh, survey, **kwargs):
+        Fields.__init__(self, mesh, survey, **kwargs)
+
+    def startup(self):
+        self.prob = self.survey.prob
+
+    def _GLoc(self, fieldType):
+        if fieldType == 'phi':
+            return 'N'
+        elif fieldType == 'e' or fieldType == 'j':
+            return 'E'
+        else:
+            raise Exception('Field type must be phi, e, j')
+
+    def _phi(self, phiSolution, srcList):
+        return phiSolution
+
+    def _phiDeriv_u():
+        return Identity()
+
+    def _phiDeriv_m():
+        return Zero()
+
+    def _j(self, phiSolution, srcList):
+        raise NotImplementedError
+
+    def _e(self, phiSolution, srcList):
+        raise NotImplementedError

SimPEG/EM/Static/DC/ProblemDC.py

@@ -1,7 +1,8 @@
 from SimPEG import Problem
 from SimPEG.EM.Base import BaseEMProblem
 from SurveyDC import Survey
-from FieldsDC import Fields, Fields_CC
+from FieldsDC import Fields, Fields_CC, Fields_N
+from SimPEG.Utils import sdiag
 import numpy as np
 
 class BaseDCProblem(BaseEMProblem):
@@ -53,16 +54,15 @@ class BaseDCProblem(BaseEMProblem):
             q[:,i] = src.eval(self)
         return q
 
-class Problem3D_CC(BaseDCProblem):
+class Problem3D_N(BaseDCProblem):
 
     _solutionType = 'phiSolution'
-    _formulation  = 'HJ' # CC potentials means J is on faces
+    _formulation  = 'EB' # N potentials means B is on faces
-    fieldsPair    = Fields_CC
+    fieldsPair    = Fields_N
 
     def __init__(self, mesh, **kwargs):
         BaseDCProblem.__init__(self, mesh, **kwargs)
 
-
     def getA(self):
         """
 
@@ -73,18 +73,21 @@ class Problem3D_CC(BaseDCProblem):
         """
 
         # TODO: this won't work for full anisotropy
-
+        MeSigma = self.MeSigma
-        D = self.mesh.faceDiv
+        Grad = self.mesh.nodalGrad
-        MfRhoI = self.MfRhoI
+        A = Grad.T * MeSigma * Grad
-        V = self.Vol
+        # if self._makeASymmetric is True:
-        A = D * ( MfRhoI * ( D.T * V ) )
+        #     return V.T * A
-
-        if self._makeASymmetric is True:
-            return V.T * A
         return A
 
-    def getADeriv():
+    def getADeriv(self, u, v, adoint=False):
-        raise NotImplementedError
+        """
+
+        Product of the derivative of our system matrix with respect to the model and a vector
+
+        """
+        return Div*self.MfRhoIDeriv(Div.T*u)
+
 
     def getRHS(self):
         """
@@ -94,12 +97,71 @@ class Problem3D_CC(BaseDCProblem):
         """
 
         RHS = self.getSourceTerm()
-        if self._makeASymmetric is True:
+        # if self._makeASymmetric is True:
-            return self.Vol.T * RHS
+        #     return self.Vol.T * RHS
         return RHS
 
-    def getRHSDeriv():
+    def getRHSDeriv(self, src, v, adjoint=False):
-        raise NotImplementedError
+        """
+        Derivative of the right hand side with respect to the model
+        """
+        qDeriv = src.evalDeriv(self, adjoint=adjoint)
+        return qDeriv
+
+class Problem3D_CC(BaseDCProblem):
+
+    _solutionType = 'phiSolution'
+    _formulation  = 'HJ' # CC potentials means J is on faces
+    fieldsPair    = Fields_CC
+
+    def __init__(self, mesh, **kwargs):
+        BaseDCProblem.__init__(self, mesh, **kwargs)
+
+    def getA(self):
+        """
+
+        Make the A matrix for the cell centered DC resistivity problem
+
+        A = D MfRhoI D^\\top V
+
+        """
+
+        # TODO: this won't work for full anisotropy
+        # V = self.Vol
+        # Div = V*self.mesh.faceDiv
+        MfRhoI = self.MfRhoI
+        A = self.Div * MfRhoI * self.Div.T
+        # if self._makeASymmetric is True:
+        #     return V.T * A
+        return A
+
+    def getADeriv(self, u, v, adoint=False):
+        """
+
+        Product of the derivative of our system matrix with respect to the model and a vector
+
+        """
+        return Div*self.MfRhoIDeriv(Div.T*u)
+
+
+    def getRHS(self):
+        """
+        RHS for the DC problem
+
+        q
+        """
+
+        RHS = self.getSourceTerm()
+        # if self._makeASymmetric is True:
+        #     return self.Vol.T * RHS
+        return RHS
+
+    def getRHSDeriv(self, src, v, adjoint=False):
+        """
+        Derivative of the right hand side with respect to the model
+        """
+        qDeriv = src.evalDeriv(self, adjoint=adjoint)
+        return qDeriv
 
 
 

SimPEG/Mesh/MeshIO.py

@@ -21,7 +21,7 @@ class TensorMeshIO(object):
                 if '*' in seg:
                     st = seg
                     sp = seg.split('*')
-                    re = np.array(sp[0],dtype=int)*(' ' + sp[1])
+                    re = int(sp[0])*(' ' + sp[1])
                     line = line.replace(st,re.strip())
             return np.array(line.split(),dtype=float)