Added 1D Cylindrical mesh.

SimPEG/mesh/Cyl1DMesh.py

@@ -0,0 +1,330 @@
+import numpy as np
+import scipy.sparse as sp
+from scipy.constants import pi
+from SimPEG.utils import mkvc, ndgrid, sdiag
+
+class Cyl1DMesh(object):
+    """
+    Cyl1DMesh is a mesh class for cylindrically symmetric 1D problems  
+    """ 
+
+    _meshType = 'CYL1D'
+
+    def __init__(self, h, z0=None):
+        assert len(h) == 2, "len(h) must equal 2"
+        if z0 is not None:
+            assert z0.size == 1, "z0.size must equal 1"
+
+        for i, h_i in enumerate(h):
+            assert type(h_i) == np.ndarray, ("h[%i] is not a numpy array." % i)
+            assert len(h_i.shape) == 1, ("h[%i] must be a 1D numpy array." % i)
+
+        # Ensure h contains 1D vectors
+        self._h = [mkvc(x) for x in h]
+
+        if z0 is None:
+            z0 = 0
+        self._z0 = z0
+
+    ####################################################
+    # Mesh properties
+    ####################################################
+
+    def h():
+        doc = "list containing the width of each cell"
+        def fget(self):
+            return self._h
+        return locals()
+    h = property(**h())
+
+    def z0():
+        doc = "The z-origin"
+        def fget(self):
+            return self._z0
+        return locals()
+    z0 = property(**z0())
+
+    def hr():
+        doc = "Width of the cells in the r direction"
+        def fget(self):
+            return self._h[0]
+        return locals()
+    hr = property(**hr())
+
+    def hz():
+        doc = "Width of the cells in the z direction"
+        def fget(self):
+            return self._h[1]
+        return locals()
+    hz = property(**hz())
+
+    ####################################################
+    # Counting
+    ####################################################
+
+    def nCr():
+        doc = "Number of cells in the radial direction"
+        fget = lambda self: self.hr.size
+        return locals()
+    nCr = property(**nCr())
+
+    def nCz():
+        doc = "Number of cells in the z direction"
+        fget = lambda self: self.hz.size
+        return locals()
+    nCz = property(**nCz())
+
+    def nC():
+        doc = "Total number of cells"
+        fget = lambda self: self.nCr * self.nCz
+        return locals()
+    nC = property(**nC())
+
+    def nNr():
+        doc = "Number of nodes in the radial direction"
+        fget = lambda self: self.hr.size
+        return locals()
+    nNr = property(**nNr())
+
+    def nNz():
+        doc = "Number of nodes in the radial direction"
+        fget = lambda self: self.hz.size + 1
+        return locals()
+    nNz = property(**nNz())
+
+    def nN():
+        doc = "Total number of nodes"
+        fget = lambda self: self.nNr * self.nNz
+        return locals()
+    nN = property(**nN())
+
+    def nFr():
+        doc = "Number of r faces"
+        fget = lambda self: self.nNr * self.nCz
+        return locals()
+    nFr = property(**nFr())
+
+    def nFz():
+        doc = "Number of z faces"
+        fget = lambda self: self.nNz * self.nCr
+        return locals()
+    nFz = property(**nFz())
+
+    def nF():
+        doc = "Total number of faces"
+        fget = lambda self: self.nFr + self.nFz
+        return locals()
+    nF = property(**nF())
+
+    def nE():
+        doc = "Number of edges"
+        fget = lambda self: self.nN
+        return locals()
+    nE = property(**nE())
+
+    ####################################################
+    # Vectors & Grids
+    ####################################################
+
+    def vectorNr():
+        doc = "Nodal grid vector (1D) in the r direction"
+        fget = lambda self: self.hr.cumsum()
+        return locals()
+    vectorNr = property(**vectorNr())
+
+    def vectorNz():
+        doc = "Nodal grid vector (1D) in the z direction"
+        fget = lambda self: np.r_[0, self.hz.cumsum()] + self._z0
+        return locals()
+    vectorNz = property(**vectorNz())
+
+    def vectorCCr():
+        doc = "Cell centered grid vector (1D) in the r direction"
+        fget = lambda self: np.r_[0, self.hr.cumsum()[1:] - self.hr[1:]/2]
+        return locals()
+    vectorCCr = property(**vectorCCr())
+
+    def vectorCCz():
+        doc = "Cell centered grid vector (1D) in the z direction"
+        fget = lambda self: self.hz.cumsum() - self.hz/2 + self._z0 
+        return locals()
+    vectorCCz = property(**vectorCCz())
+
+    def gridCC():
+        doc = "Cell-centered grid"
+        def fget(self):
+            if self._gridCC is None:
+                self._gridCC = ndgrid([self.vectorCCr, self.vectorCCz])
+            return self._gridCC
+        return locals()
+    _gridCC = None
+    gridCC = property(**gridCC())
+
+    def gridN():
+        doc = "Nodal grid"
+        def fget(self):
+            if self._gridN is None:
+                self._gridN = ndgrid([self.vectorNr, self.vectorNz])
+            return self._gridN
+        return locals()
+    _gridN = None
+    gridN = property(**gridN())
+
+    def gridFr():
+        doc = "r face grid"
+        def fget(self):
+            if self._gridFr is None:
+                self._gridFr = ndgrid([self.vectorNr, self.vectorCCz])
+            return self._gridFr
+        return locals()
+    _gridFr = None    
+    gridFr = property(**gridFr())
+
+    def gridFz():
+        doc = "z face grid"
+        def fget(self):
+            if self._gridFz is None:
+                self._gridFz = ndgrid([self.vectorCCr, self.vectorNz])
+            return self._gridFz
+        return locals()
+    _gridFz = None    
+    gridFz = property(**gridFz())
+
+    ####################################################
+    # Geometries
+    ####################################################
+
+    def edge():
+        doc = "Edge lengths"
+        def fget(self):
+            if self._edge is None:
+                self._edge = 2*pi*self.gridN[:,0]
+            return self._edge
+        return locals()
+    _edge = None
+    edge = property(**edge())
+
+    def area():
+        doc = "Face areas"
+        def fget(self):
+            if self._area is None:
+                areaR = np.kron(self.hz, 2*pi*self.vectorNr)
+                areaZ = np.kron(np.ones_like(self.vectorNz),pi*(self.vectorNr**2 - np.r_[0, self.vectorNr[:-1]]**2))
+                self._area = np.r_[areaR, areaZ]
+            return self._area
+        return locals()
+    _area = None
+    area = property(**area())
+
+    def vol():
+        doc = "Volume of each cell"
+        def fget(self):
+            if self._vol is None:
+                az = pi*(self.vectorNr**2 - np.r_[0, self.vectorNr[:-1]]**2)
+                self._vol = np.kron(self.hz,az)
+            return self._vol
+        return locals()
+    _vol = None
+    vol = property(**vol())
+
+    ####################################################
+    # Operators
+    ####################################################
+
+    def edgeCurl():
+        doc = "The edgeCurl property."
+        def fget(self):
+            if self._edgeCurl is None:
+                #1D Difference matricies
+                dr = sp.spdiags((np.ones((self.nCr+1, 1))*[-1, 1]).T, [-1,0], self.nCr, self.nCr, format="csr")
+                dz = sp.spdiags((np.ones((self.nCz+1, 1))*[-1, 1]).T, [0,1], self.nCz, self.nCz+1, format="csr")
+
+                #2D Difference matricies
+                Dr = sp.kron(sp.eye(self.nNz), dr)
+                Dz = -sp.kron(dz, sp.eye(self.nCr))  #Not sure about this negative
+
+                #Edge curl operator
+                self._edgeCurl = sp.diags(1/self.area,0)*sp.vstack((Dz, Dr))*sp.diags(self.edge,0)
+            return self._edgeCurl
+        return locals()
+    _edgeCurl = None
+    edgeCurl = property(**edgeCurl())
+
+    def aveE2CC():
+        doc = "Averaging operator from cell edges to cell centres"
+        def fget(self):
+            if self._aveE2CC is None:
+                az = sp.spdiags(0.5*np.ones((2, self.nNz)), [-1,0], self.nNz, self.nCz, format='csr')
+                ar = sp.spdiags(0.5*np.ones((2, self.nCr)), [0, 1], self.nCr, self.nCr, format='csr')
+                ar[0,0] = 1
+                self._aveE2CC = sp.kron(az, ar).T
+            return self._aveE2CC
+        return locals()
+    _aveE2CC = None
+    aveE2CC = property(**aveE2CC())
+
+    def aveF2CC():
+        doc = "Averaging operator from cell faces to cell centres"
+        def fget(self):
+            if self._aveF2CC is None:
+                az = sp.spdiags(0.5*np.ones((2, self.nNz)), [-1,0], self.nNz, self.nCz, format='csr')
+                ar = sp.spdiags(0.5*np.ones((2, self.nCr)), [0, 1], self.nCr, self.nCr, format='csr')
+                ar[0,0] = 1
+                Afr = sp.kron(sp.eye(self.nCz),ar)
+                Afz = sp.kron(az,sp.eye(self.nCr))
+                self._aveF2CC = sp.vstack((Afr,Afz)).T
+            return self._aveF2CC
+        return locals()
+    _aveF2CC = None
+    aveF2CC = property(**aveF2CC())
+
+    ####################################################
+    # Methods
+    ####################################################
+
+
+    def getMass(self, materialProp=None, loc='e'):
+        """ Produces mass matricies.
+
+        :param str loc: Average to location: 'e'-edges, 'f'-faces
+        :param None,float,numpy.ndarray materialProp: property to be averaged (see below)
+        :rtype: scipy.sparse.csr.csr_matrix
+        :return: M, the mass matrix
+
+        materialProp can be::
+
+            None            -> takes materialProp = 1 (default)
+            float           -> a constant value for entire domain
+            numpy.ndarray   -> if materialProp.size == self.nC
+                                    3D property model
+                               if materialProp.size = self.nCz
+                                    1D (layered eath) property model
+        """
+        if materialProp is None:
+            materialProp = np.ones(self.nC)
+        elif type(materialProp) is float:
+            materialProp = np.ones(self.nC)*materialProp
+        elif materialProp.shape == (self.nCz,):
+            materialProp = materialProp.repeat(self.nCr)
+        materialProp = mkvc(materialProp)
+        assert materialProp.shape == (self.nC,), "materialProp incorrect shape"
+
+        if loc=='e':
+            Av = self.aveE2CC
+        elif loc=='f':
+            Av = self.aveF2CC
+        else:
+            raise ValueError('Invalid loc')
+
+        diag = Av.T * (self.vol * mkvc(materialProp))
+
+        return sdiag(diag)
+
+    def getEdgeMass(self, materialProp=None):
+        """mass matrix for products of edge functions w'*M(materialProp)*e"""
+        return self.getMass(loc='e', materialProp=materialProp)
+
+    def getFaceMass(self, materialProp=None):
+        """mass matrix for products of face functions w'*M(materialProp)*f"""
+        return self.getMass(loc='f', materialProp=materialProp)
+

SimPEG/mesh/__init__.py

@@ -1,3 +1,4 @@
+from Cyl1DMesh import Cyl1DMesh
 from TensorMesh import TensorMesh
 from LogicallyOrthogonalMesh import LogicallyOrthogonalMesh
 from BaseMesh import BaseMesh
@@ -5,4 +6,3 @@ from TensorView import TensorView
 from LomView import LomView
 from InnerProducts import InnerProducts
 from DiffOperators import DiffOperators
-

docs/api_Cyl1DMesh.rst

@@ -0,0 +1,8 @@
+.. _api_Cyl1DMesh:
+
+Cylindrical 1D Mesh
+*******************
+
+.. automodule:: SimPEG.mesh.Cyl1DMesh
+    :members:
+    :undoc-members:

docs/index.rst

@@ -26,6 +26,7 @@ Meshing & Operators
    api_TensorMesh
    api_TensorView
    api_LogicallyOrthogonalMesh
+   api_Cyl1DMesh
    api_LOMView
    api_DiffOperators
    api_InnerProducts