discretize.CylMesh

class discretize.CylMesh(h=None, x0=None, **kwargs)[source]

Bases: discretize.base.base_tensor_mesh.BaseTensorMesh, discretize.base.base_mesh.BaseRectangularMesh, discretize.InnerProducts.InnerProducts, discretize.View.CylView, discretize.DiffOperators.DiffOperators

CylMesh is a mesh class for cylindrical problems. It supports both cylindrically symmetric and 3D cylindrical meshes that include an azimuthal discretization.

For a cylindrically symmetric mesh use h = [hx, 1, hz]. For example:

import discretize
from discretize import utils

cs, nc, npad = 20., 30, 8
hx = utils.meshTensor([(cs, npad+10, -0.7), (cs, nc), (cs, npad, 1.3)])
hz = utils.meshTensor([(cs, npad ,-1.3), (cs, nc), (cs, npad, 1.3)])
mesh = discretize.CylMesh([hx, 1, hz], x0=[0, 0, -hz.sum()/2])
mesh.plotGrid()

(Source code, png, hires.png, pdf)

../../_images/discretize-CylMesh-1.png

To create a 3D cylindrical mesh, we also include an azimuthal discretization

import discretize
from discretize import utils

cs, nc, npad = 20., 30, 8
nc_theta = 8
hx = utils.meshTensor([(cs, npad+10, -0.7), (cs, nc), (cs, npad, 1.3)])
hy = 2 * np.pi/nc_theta * np.ones(nc_theta)
hz = utils.meshTensor([(cs,npad, -1.3), (cs,nc), (cs, npad, 1.3)])
mesh = discretize.CylMesh([hx, hy, hz], x0=[0, 0, -hz.sum()/2])
mesh.plotGrid()

(Source code, png, hires.png, pdf)

../../_images/discretize-CylMesh-2.png

Required Properties:

  • axis_u (Vector3): Vector orientation of u-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: X
  • axis_v (Vector3): Vector orientation of v-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Y
  • axis_w (Vector3): Vector orientation of w-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Z
  • cartesianOrigin (Array): Cartesian origin of the mesh, a list or numpy array of <class ‘float’> with shape (*)
  • h (a list of Array): h is a list containing the cell widths of the tensor mesh in each dimension., a list (each item is a list or numpy array of <class ‘float’> with shape (*)) with length between 0 and 3
  • reference_system (String): The type of coordinate reference frame. Can take on the values cartesian, cylindrical, or spherical. Abbreviations of these are allowed., a unicode string, Default: cartesian
  • x0 (Array): origin of the mesh (dim, ), a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*)
Attributes:
area

Face areas

areaFx

Area of the x-faces (radial faces).

areaFy

Area of y-faces (Azimuthal faces).

areaFz

Area of z-faces.

aveCC2F

Construct the averaging operator on cell centers to faces.

aveCCV2F

Construct the averaging operator on cell centers to faces as a vector.

aveE2CC

averaging operator of edges to cell centers

aveE2CCV

averaging operator of edges to a cell centered vector

aveEx2CC

averaging operator of x-edges (radial) to cell centers

aveEy2CC

averaging operator of y-edges (azimuthal) to cell centers

aveEz2CC

averaging operator of z-edges to cell centers

aveF2CC

averaging operator of faces to cell centers

aveF2CCV

averaging operator of x-faces (radial) to cell centered vectors

aveFx2CC

averaging operator of x-faces (radial) to cell centers

aveFy2CC

averaging operator of y-faces (azimuthal) to cell centers

aveFz2CC

averaging operator of z-faces (vertical) to cell centers

aveN2CC

Construct the averaging operator on cell nodes to cell centers.

aveN2E

Construct the averaging operator on cell nodes to cell edges, keeping each dimension separate.

aveN2F

Construct the averaging operator on cell nodes to cell faces, keeping each dimension separate.

axis_u

axis_u (Vector3): Vector orientation of u-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: X

axis_v

axis_v (Vector3): Vector orientation of v-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Y

axis_w

axis_w (Vector3): Vector orientation of w-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Z

cartesianOrigin

cartesianOrigin (Array): Cartesian origin of the mesh, a list or numpy array of <class ‘float’> with shape (*)

cellGrad

The cell centered Gradient, takes you to cell faces.

cellGradBC

The cell centered Gradient boundary condition matrix

cellGradx

Cell centered Gradient in the x dimension.

cellGrady
cellGradz

Cell centered Gradient in the x dimension.

dim

The dimension of the mesh (1, 2, or 3).

edge

Edge lengths

edgeCurl

The edgeCurl (edges to faces)

edgeEx

x-edge lengths - these are the radial edges. Radial edges only exist

edgeEy

y-edge lengths - these are the azimuthal edges. Azimuthal edges exist

edgeEz

z-edge lengths - these are the vertical edges. Vertical edges only

faceDiv

Construct divergence operator (faces to cell-centres).

faceDivx

Construct divergence operator in the x component (faces to cell-centres).

faceDivy

Construct divergence operator in the y component (faces to cell-centres).

faceDivz

Construct divergence operator in the z component (faces to cell-centres).

gridCC

Cell-centered grid.

gridEx

Edge staggered grid in the x direction.

gridEy

Grid of y-edges (azimuthal-faces) in cylindrical coordinates \((r, \theta, z)\).

gridEz

Grid of z-faces (vertical-faces) in cylindrical coordinates \((r, \theta, z)\).

gridFx

Grid of x-faces (radial-faces) in cylindrical coordinates \((r, \theta, z)\).

gridFy

Face staggered grid in the y direction.

gridFz

Face staggered grid in the z direction.

gridN

Nodal grid in cylindrical coordinates \((r, \theta, z)\).

h

h (a list of Array): h is a list containing the cell widths of the tensor mesh in each dimension., a list (each item is a list or numpy array of <class ‘float’> with shape (*)) with length between 0 and 3

h_gridded

Returns an (nC, dim) numpy array with the widths of all cells in order

hx

Width of cells in the x direction

hy

Width of cells in the y direction

hz

Width of cells in the z direction

isSymmetric

Is the mesh cylindrically symmetric?

nC

Total number of cells

nCx

Number of cells in the x direction

nCy

Number of cells in the y direction

nCz

Number of cells in the z direction

nE

Total number of edges.

nEx

Number of x-edges

nEy

Number of y-edges

nEz

Returns

nF

Total number of faces.

nFx

Number of x-faces

nFy

Number of y-faces

nFz

Number of z-faces

nN

Returns

nNx

Returns

nNy

Returns

nNz

Number of nodes in the z-direction

nodalGrad

Construct gradient operator (nodes to edges).

nodalLaplacian

Construct laplacian operator (nodes to edges).

normals

Face Normals

reference_is_rotated

True if the axes are rotated from the traditional <X,Y,Z> system

reference_system

reference_system (String): The type of coordinate reference frame. Can take on the values cartesian, cylindrical, or spherical. Abbreviations of these are allowed., a unicode string, Default: cartesian

rotation_matrix

Builds a rotation matrix to transform coordinates from their coordinate system into a conventional cartesian system.

tangents

Edge Tangents

vectorCCx

Cell-centered grid vector (1D) in the x direction.

vectorCCy

Cell-centered grid vector (1D) in the y direction.

vectorCCz

Cell-centered grid vector (1D) in the z direction.

vectorNx

Nodal grid vector (1D) in the x direction.

vectorNy

Nodal grid vector (1D) in the y direction.

vectorNz

Nodal grid vector (1D) in the z direction.

vnC

Total number of cells in each direction

vnE

Total number of edges in each direction

vnEx

Number of x-edges in each direction

vnEy

Number of y-edges in each direction

vnEz

Returns

vnF

Total number of faces in each direction

vnFx

Returns

vnFy

Number of y-faces in each direction

vnFz

Number of z-faces in each direction

vnN

Total number of nodes in each direction

vol

Volume of each cell

x0

x0 (Array): origin of the mesh (dim, ), a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*)

Methods

cartesianGrid
copy Generic (shallow and deep) copying operations.
deserialize
equal
from_omf
getBCProjWF
getBCProjWF_simple
getEdgeInnerProduct
getEdgeInnerProductDeriv
getFaceInnerProduct
getFaceInnerProductDeriv
getInterpolationMat
getInterpolationMatCartMesh
getTensor
isInside
projectEdgeVector
projectFaceVector
r
save
serialize
setCellGradBC
toVTK
to_omf
to_vtk
validate
writeVTK
write_vtk
check_cartesian_origin_shape  
plotGrid  
plotImage  

Attributes

CylMesh.area

Face areas

For a 3D cyl mesh: [radial, azimuthal, vertical], while a cylindrically symmetric mesh doesn’t have y-Faces, so it returns [radial, vertical]

Returns:face areas
Return type:numpy.ndarray
CylMesh.areaFx

Area of the x-faces (radial faces). Radial faces exist on all cylindrical meshes

\[A_x = r \theta h_z\]
Returns:area of x-faces
Return type:numpy.ndarray
CylMesh.areaFy

Area of y-faces (Azimuthal faces). Azimuthal faces exist only on 3D cylindrical meshes.

\[A_y = h_x h_z\]
Returns:area of y-faces
Return type:numpy.ndarray
CylMesh.areaFz

Area of z-faces.

\[A_z = \frac{\theta}{2} (r_2^2 - r_1^2)z\]
Returns:area of the z-faces
Return type:numpy.ndarray
CylMesh.aveCC2F

Construct the averaging operator on cell centers to faces.

CylMesh.aveCCV2F

Construct the averaging operator on cell centers to faces as a vector.

CylMesh.aveE2CC

averaging operator of edges to cell centers

Returns:matrix that averages from edges to cell centers
Return type:scipy.sparse.csr_matrix
CylMesh.aveE2CCV

averaging operator of edges to a cell centered vector

Returns:matrix that averages from edges to cell centered vectors
Return type:scipy.sparse.csr_matrix
CylMesh.aveEx2CC

averaging operator of x-edges (radial) to cell centers

Returns:matrix that averages from x-edges to cell centers
Return type:scipy.sparse.csr_matrix
CylMesh.aveEy2CC

averaging operator of y-edges (azimuthal) to cell centers

Returns:matrix that averages from y-edges to cell centers
Return type:scipy.sparse.csr_matrix
CylMesh.aveEz2CC

averaging operator of z-edges to cell centers

Returns:matrix that averages from z-edges to cell centers
Return type:scipy.sparse.csr_matrix
CylMesh.aveF2CC

averaging operator of faces to cell centers

Returns:matrix that averages from faces to cell centers
Return type:scipy.sparse.csr_matrix
CylMesh.aveF2CCV

averaging operator of x-faces (radial) to cell centered vectors

Returns:matrix that averages from faces to cell centered vectors
Return type:scipy.sparse.csr_matrix
CylMesh.aveFx2CC

averaging operator of x-faces (radial) to cell centers

Returns:matrix that averages from x-faces to cell centers
Return type:scipy.sparse.csr_matrix
CylMesh.aveFy2CC

averaging operator of y-faces (azimuthal) to cell centers

Returns:matrix that averages from y-faces to cell centers
Return type:scipy.sparse.csr_matrix
CylMesh.aveFz2CC

averaging operator of z-faces (vertical) to cell centers

Returns:matrix that averages from z-faces to cell centers
Return type:scipy.sparse.csr_matrix
CylMesh.aveN2CC

Construct the averaging operator on cell nodes to cell centers.

CylMesh.aveN2E

Construct the averaging operator on cell nodes to cell edges, keeping each dimension separate.

CylMesh.aveN2F

Construct the averaging operator on cell nodes to cell faces, keeping each dimension separate.

CylMesh.axis_u

X

Type:axis_u (Vector3)
Type:Vector orientation of u-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default
CylMesh.axis_v

Y

Type:axis_v (Vector3)
Type:Vector orientation of v-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default
CylMesh.axis_w

Z

Type:axis_w (Vector3)
Type:Vector orientation of w-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default
CylMesh.cartesianOrigin

Cartesian origin of the mesh, a list or numpy array of <class ‘float’> with shape (*)

Type:cartesianOrigin (Array)
CylMesh.cellGrad

The cell centered Gradient, takes you to cell faces.

CylMesh.cellGradBC

The cell centered Gradient boundary condition matrix

CylMesh.cellGradx

Cell centered Gradient in the x dimension. Has neumann boundary conditions.

CylMesh.cellGrady
CylMesh.cellGradz

Cell centered Gradient in the x dimension. Has neumann boundary conditions.

CylMesh.dim

The dimension of the mesh (1, 2, or 3).

Returns:dimension of the mesh
Return type:int
CylMesh.edge

Edge lengths

Returns:vector of edge lengths \((r, \theta, z)\)
Return type:numpy.ndarray
CylMesh.edgeCurl

The edgeCurl (edges to faces)

Returns:edge curl operator
Return type:scipy.sparse.csr_matrix
CylMesh.edgeEx

x-edge lengths - these are the radial edges. Radial edges only exist for a 3D cyl mesh.

Returns:vector of radial edge lengths
Return type:numpy.ndarray
CylMesh.edgeEy

y-edge lengths - these are the azimuthal edges. Azimuthal edges exist for all cylindrical meshes. These are arc-lengths (\(\theta r\))

Returns:vector of the azimuthal edges
Return type:numpy.ndarray
CylMesh.edgeEz

z-edge lengths - these are the vertical edges. Vertical edges only exist for a 3D cyl mesh.

Returns:vector of the vertical edges
Return type:numpy.ndarray
CylMesh.faceDiv

Construct divergence operator (faces to cell-centres).

CylMesh.faceDivx

Construct divergence operator in the x component (faces to cell-centres).

CylMesh.faceDivy

Construct divergence operator in the y component (faces to cell-centres).

CylMesh.faceDivz

Construct divergence operator in the z component (faces to cell-centres).

CylMesh.gridCC

Cell-centered grid.

CylMesh.gridEx

Edge staggered grid in the x direction.

CylMesh.gridEy

Grid of y-edges (azimuthal-faces) in cylindrical coordinates \((r, \theta, z)\).

Returns:grid locations of azimuthal faces
Return type:numpy.ndarray
CylMesh.gridEz

Grid of z-faces (vertical-faces) in cylindrical coordinates \((r, \theta, z)\).

Returns:grid locations of radial faces
Return type:numpy.ndarray
CylMesh.gridFx

Grid of x-faces (radial-faces) in cylindrical coordinates \((r, \theta, z)\).

Returns:grid locations of radial faces
Return type:numpy.ndarray
CylMesh.gridFy

Face staggered grid in the y direction.

CylMesh.gridFz

Face staggered grid in the z direction.

CylMesh.gridN

Nodal grid in cylindrical coordinates \((r, \theta, z)\). Nodes do not exist in a cylindrically symmetric mesh.

Returns:grid locations of nodes
Return type:numpy.ndarray
CylMesh.h

h is a list containing the cell widths of the tensor mesh in each dimension., a list (each item is a list or numpy array of <class ‘float’> with shape (*)) with length between 0 and 3

Type:h (a list of Array)
CylMesh.h_gridded

Returns an (nC, dim) numpy array with the widths of all cells in order

CylMesh.hx

Width of cells in the x direction

CylMesh.hy

Width of cells in the y direction

CylMesh.hz

Width of cells in the z direction

CylMesh.isSymmetric

Is the mesh cylindrically symmetric?

Returns:True if the mesh is cylindrically symmetric, False otherwise
Return type:bool
CylMesh.nC

Total number of cells

Return type:int
Returns:nC
CylMesh.nCx

Number of cells in the x direction

Return type:int
Returns:nCx
CylMesh.nCy

Number of cells in the y direction

Return type:int
Returns:nCy or None if dim < 2
CylMesh.nCz

Number of cells in the z direction

Return type:int
Returns:nCz or None if dim < 3
CylMesh.nE

Total number of edges.

Returns:nE
Return type:int = sum([nEx, nEy, nEz])
CylMesh.nEx

Number of x-edges

Return type:int
Returns:nEx
CylMesh.nEy

Number of y-edges

Return type:int
Returns:nEy
CylMesh.nEz

returns: Number of z-edges :rtype: int

CylMesh.nF

Total number of faces.

Return type:int
Returns:sum([nFx, nFy, nFz])
CylMesh.nFx

Number of x-faces

Return type:int
Returns:nFx
CylMesh.nFy

Number of y-faces

Return type:int
Returns:nFy
CylMesh.nFz

Number of z-faces

Return type:int
Returns:nFz
CylMesh.nN

returns: Total number of nodes :rtype: int

CylMesh.nNx

returns: Number of nodes in the x-direction :rtype: int

CylMesh.nNy

returns: Number of nodes in the y-direction :rtype: int

CylMesh.nNz

Number of nodes in the z-direction

Return type:int
Returns:nNz or None if dim < 3
CylMesh.nodalGrad

Construct gradient operator (nodes to edges).

CylMesh.nodalLaplacian

Construct laplacian operator (nodes to edges).

CylMesh.normals

Face Normals

Return type:numpy.ndarray
Returns:normals, (sum(nF), dim)
CylMesh.reference_is_rotated

True if the axes are rotated from the traditional <X,Y,Z> system with vectors of \((1,0,0)\), \((0,1,0)\), and \((0,0,1)\)

CylMesh.reference_system

cartesian

Type:reference_system (String)
Type:The type of coordinate reference frame. Can take on the values cartesian, cylindrical, or spherical. Abbreviations of these are allowed., a unicode string, Default
CylMesh.rotation_matrix

Builds a rotation matrix to transform coordinates from their coordinate system into a conventional cartesian system. This is built off of the three axis_u, axis_v, and axis_w properties; these mapping coordinates use the letters U, V, and W (the three letters preceding X, Y, and Z in the alphabet) to define the projection of the X, Y, and Z durections. These UVW vectors describe the placement and transformation of the mesh’s coordinate sytem assuming at most 3 directions.

Why would you want to use these UVW mapping vectors the this rotation_matrix property? They allow us to define the realationship between local and global coordinate systems and provide a tool for switching between the two while still maintaing the connectivity of the mesh’s cells. For a visual example of this, please see the figure in the docs for the InterfaceVTK.

CylMesh.tangents

Edge Tangents

Return type:numpy.ndarray
Returns:normals, (sum(nE), dim)
CylMesh.vectorCCx

Cell-centered grid vector (1D) in the x direction.

CylMesh.vectorCCy

Cell-centered grid vector (1D) in the y direction.

CylMesh.vectorCCz

Cell-centered grid vector (1D) in the z direction.

CylMesh.vectorNx

Nodal grid vector (1D) in the x direction.

CylMesh.vectorNy

Nodal grid vector (1D) in the y direction.

CylMesh.vectorNz

Nodal grid vector (1D) in the z direction.

CylMesh.vnC

Total number of cells in each direction

Return type:numpy.ndarray
Returns:[nCx, nCy, nCz]
CylMesh.vnE

Total number of edges in each direction

Returns:
  • vnE (numpy.ndarray = [nEx, nEy, nEz], (dim, ))
  • .. plot:: – :include-source:

    import discretize import numpy as np M = discretize.TensorMesh([np.ones(n) for n in [2,3]]) M.plotGrid(edges=True, showIt=True)

CylMesh.vnEx

Number of x-edges in each direction

Return type:numpy.ndarray
Returns:vnEx
CylMesh.vnEy

Number of y-edges in each direction

Returns:vnEy or None if dim < 2, (dim, )
Return type:numpy.ndarray
CylMesh.vnEz

returns: Number of z-edges in each direction or None if nCy > 1, (dim, ) :rtype: numpy.ndarray

CylMesh.vnF

Total number of faces in each direction

Return type:numpy.ndarray
Returns:[nFx, nFy, nFz], (dim, )
import discretize
import numpy as np
M = discretize.TensorMesh([np.ones(n) for n in [2,3]])
M.plotGrid(faces=True, showIt=True)

(Source code, png, hires.png, pdf)

../../_images/discretize-CylMesh-3.png
CylMesh.vnFx

returns: Number of x-faces in each direction, (dim, ) :rtype: numpy.ndarray

CylMesh.vnFy

Number of y-faces in each direction

Return type:numpy.ndarray
Returns:vnFy or None if dim < 2
CylMesh.vnFz

Number of z-faces in each direction

Return type:numpy.ndarray
Returns:vnFz or None if dim < 3
CylMesh.vnN

Total number of nodes in each direction

Return type:numpy.ndarray
Returns:[nNx, nNy, nNz]
CylMesh.vol

Volume of each cell

Returns:cell volumes
Return type:numpy.ndarray
CylMesh.x0

origin of the mesh (dim, ), a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*)

Type:x0 (Array)

Methods

CylMesh.cartesianGrid(self, locType='CC', theta_shift=None)[source]

Takes a grid location (‘CC’, ‘N’, ‘Ex’, ‘Ey’, ‘Ez’, ‘Fx’, ‘Fy’, ‘Fz’) and returns that grid in cartesian coordinates

Parameters:locType (str) – grid location
Returns:cartesian coordinates for the cylindrical grid
Return type:numpy.ndarray
CylMesh.check_cartesian_origin_shape(self, change)[source]
CylMesh.copy(self)

Make a copy of the current mesh

classmethod CylMesh.deserialize(value, trusted=False, strict=False, assert_valid=False, **kwargs)

Creates HasProperties instance from serialized dictionary

This uses the Property deserializers to deserialize all JSON-compatible dictionary values into their corresponding Property values on a new instance of a HasProperties class. Extra keys in the dictionary that do not correspond to Properties will be ignored.

Parameters:

  • value - Dictionary to deserialize new instance from.
  • trusted - If True (and if the input dictionary has '__class__' keyword and this class is in the registry), the new HasProperties class will come from the dictionary. If False (the default), only the HasProperties class this method is called on will be constructed.
  • strict - Requires '__class__', if present on the input dictionary, to match the deserialized instance’s class. Also disallows unused properties in the input dictionary. Default is False.
  • assert_valid - Require deserialized instance to be valid. Default is False.
  • Any other keyword arguments will be passed through to the Property deserializers.
CylMesh.equal(self, other)

Determine if two HasProperties instances are equivalent

Equivalence is determined by checking if all Property values on two instances are equal, using Property.equal.

static CylMesh.from_omf(element)

Convert an OMF element to it’s proper discretize type. Automatically determines the output type. Returns both the mesh and a dictionary of model arrays.

CylMesh.getBCProjWF(self, BC, discretization='CC')

The weak form boundary condition projection matrices.

Example

# Neumann in all directions
BC = 'neumann'

# 3D, Dirichlet in y Neumann else
BC = ['neumann', 'dirichlet', 'neumann']

# 3D, Neumann in x on bottom of domain, Dirichlet else
BC = [['neumann', 'dirichlet'], 'dirichlet', 'dirichlet']
CylMesh.getBCProjWF_simple(self, discretization='CC')

The weak form boundary condition projection matrices when mixed boundary condition is used

CylMesh.getEdgeInnerProduct(self, prop=None, invProp=False, invMat=False, doFast=True)

Generate the edge inner product matrix

Parameters:
  • prop (numpy.ndarray) – material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
  • invProp (bool) – inverts the material property
  • invMat (bool) – inverts the matrix
  • doFast (bool) – do a faster implementation if available.
Returns:

M, the inner product matrix (nE, nE)

Return type:

scipy.sparse.csr_matrix

CylMesh.getEdgeInnerProductDeriv(self, prop, doFast=True, invProp=False, invMat=False)
Parameters:
  • prop (numpy.ndarray) – material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
  • doFast (bool) – do a faster implementation if available.
  • invProp (bool) – inverts the material property
  • invMat (bool) – inverts the matrix
Returns:

dMdm, the derivative of the inner product matrix (nE, nC*nA)

Return type:

scipy.sparse.csr_matrix

CylMesh.getFaceInnerProduct(self, prop=None, invProp=False, invMat=False, doFast=True)

Generate the face inner product matrix

Parameters:
  • prop (numpy.ndarray) – material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
  • invProp (bool) – inverts the material property
  • invMat (bool) – inverts the matrix
  • doFast (bool) – do a faster implementation if available.
Returns:

M, the inner product matrix (nF, nF)

Return type:

scipy.sparse.csr_matrix

CylMesh.getFaceInnerProductDeriv(self, prop, doFast=True, invProp=False, invMat=False)
Parameters:
  • prop (numpy.ndarray) – material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
  • doFast – bool do a faster implementation if available.
  • invProp (bool) – inverts the material property
  • invMat (bool) – inverts the matrix
Returns:

dMdmu(u), the derivative of the inner product matrix for a certain u

Return type:

scipy.sparse.csr_matrix

CylMesh.getInterpolationMat(self, loc, locType='CC', zerosOutside=False)[source]

Produces interpolation matrix

Parameters:
  • loc (numpy.ndarray) – Location of points to interpolate to
  • locType (str) –

    What to interpolate locType can be:

    'Ex'    -> x-component of field defined on edges
    'Ey'    -> y-component of field defined on edges
    'Ez'    -> z-component of field defined on edges
    'Fx'    -> x-component of field defined on faces
    'Fy'    -> y-component of field defined on faces
    'Fz'    -> z-component of field defined on faces
    'N'     -> scalar field defined on nodes
    'CC'    -> scalar field defined on cell centers
    'CCVx'  -> x-component of vector field defined on cell centers
    'CCVy'  -> y-component of vector field defined on cell centers
    'CCVz'  -> z-component of vector field defined on cell centers
    
Returns:

M, the interpolation matrix

Return type:

scipy.sparse.csr_matrix

CylMesh.getInterpolationMatCartMesh(self, Mrect, locType='CC', locTypeTo=None)[source]

Takes a cartesian mesh and returns a projection to translate onto the cartesian grid.

Parameters:
  • Mrect (discretize.base.BaseMesh) – the mesh to interpolate on to
  • locType (str) – grid location (‘CC’, ‘N’, ‘Ex’, ‘Ey’, ‘Ez’, ‘Fx’, ‘Fy’, ‘Fz’)
  • locTypeTo (str) – grid location to interpolate to. If None, the same grid type as locType will be assumed
Returns:

M, the interpolation matrix

Return type:

scipy.sparse.csr_matrix

CylMesh.getTensor(self, key)

Returns a tensor list.

Parameters:key (str) –

Which tensor (see below)

key can be:

'CC'    -> scalar field defined on cell centers
'N'     -> scalar field defined on nodes
'Fx'    -> x-component of field defined on faces
'Fy'    -> y-component of field defined on faces
'Fz'    -> z-component of field defined on faces
'Ex'    -> x-component of field defined on edges
'Ey'    -> y-component of field defined on edges
'Ez'    -> z-component of field defined on edges
Returns:list of the tensors that make up the mesh.
Return type:list
CylMesh.isInside(self, pts, locType='N')

Determines if a set of points are inside a mesh.

Parameters:pts (numpy.ndarray) – Location of points to test
Return type:numpy.ndarray
Returns:inside, numpy array of booleans
CylMesh.plotGrid(self, *args, **kwargs)
CylMesh.plotImage(self, *args, **kwargs)
CylMesh.projectEdgeVector(self, eV)

Given a vector, eV, in cartesian coordinates, this will project it onto the mesh using the tangents

Parameters:eV (numpy.ndarray) – edge vector with shape (nE, dim)
Return type:numpy.ndarray
Returns:projected edge vector, (nE, )
CylMesh.projectFaceVector(self, fV)

Given a vector, fV, in cartesian coordinates, this will project it onto the mesh using the normals

Parameters:fV (numpy.ndarray) – face vector with shape (nF, dim)
Return type:numpy.ndarray
Returns:projected face vector, (nF, )
CylMesh.r(self, x, xType='CC', outType='CC', format='V')

r is a quick reshape command that will do the best it can at giving you what you want.

For example, you have a face variable, and you want the x component of it reshaped to a 3D matrix.

r can fulfil your dreams:

mesh.r(V, 'F', 'Fx', 'M')
       |   |     |    |
       |   |     |    {
       |   |     |      How: 'M' or ['V'] for a matrix
       |   |     |      (ndgrid style) or a vector (n x dim)
       |   |     |    }
       |   |     {
       |   |       What you want: ['CC'], 'N',
       |   |                       'F', 'Fx', 'Fy', 'Fz',
       |   |                       'E', 'Ex', 'Ey', or 'Ez'
       |   |     }
       |   {
       |     What is it: ['CC'], 'N',
       |                  'F', 'Fx', 'Fy', 'Fz',
       |                  'E', 'Ex', 'Ey', or 'Ez'
       |   }
       {
         The input: as a list or ndarray
       }

For example:

# Separates each component of the Ex grid into 3 matrices
Xex, Yex, Zex = r(mesh.gridEx, 'Ex', 'Ex', 'M')

# Given an edge vector, return just the x edges as a vector
XedgeVector = r(edgeVector, 'E', 'Ex', 'V')

# Separates each component of the edgeVector into 3 vectors
eX, eY, eZ = r(edgeVector, 'E', 'E', 'V')
CylMesh.save(self, filename='mesh.json', verbose=False)

Save the mesh to json :param str file: filename for saving the casing properties :param str directory: working directory for saving the file

CylMesh.serialize(self, include_class=True, save_dynamic=False, **kwargs)

Serializes a HasProperties instance to dictionary

This uses the Property serializers to serialize all Property values to a JSON-compatible dictionary. Properties that are undefined are not included. If the HasProperties instance contains a reference to itself, a properties.SelfReferenceError will be raised.

Parameters:

  • include_class - If True (the default), the name of the class will also be saved to the serialized dictionary under key '__class__'
  • save_dynamic - If True, dynamic properties are written to the serialized dict (default: False).
  • Any other keyword arguments will be passed through to the Property serializers.
CylMesh.setCellGradBC(self, BC)

Function that sets the boundary conditions for cell-centred derivative operators.

Example

..code:: python

# Neumann in all directions BC = ‘neumann’

# 3D, Dirichlet in y Neumann else BC = [‘neumann’, ‘dirichlet’, ‘neumann’]

# 3D, Neumann in x on bottom of domain, Dirichlet else BC = [[‘neumann’, ‘dirichlet’], ‘dirichlet’, ‘dirichlet’]

CylMesh.toVTK(mesh, models=None)

Convert this mesh object to it’s proper VTK or pyvista data object with the given model dictionary as the cell data of that dataset.

Parameters:models (dict(numpy.ndarray)) – Name(‘s) and array(‘s). Match number of cells
CylMesh.to_omf(mesh, models=None)

Convert this mesh object to it’s proper omf data object with the given model dictionary as the cell data of that dataset.

Parameters:models (dict(numpy.ndarray)) – Name(‘s) and array(‘s). Match number of cells
CylMesh.to_vtk(mesh, models=None)

Convert this mesh object to it’s proper VTK or pyvista data object with the given model dictionary as the cell data of that dataset.

Parameters:models (dict(numpy.ndarray)) – Name(‘s) and array(‘s). Match number of cells
CylMesh.validate(self)

Call all registered class validator methods

These are all methods decorated with @properties.validator. Validator methods are expected to raise a ValidationError if they fail.

CylMesh.writeVTK(mesh, filename, models=None, directory='')

Makes and saves a VTK object from this mesh and given models

Parameters:
  • filename (str) – path to the output vtk file or just its name if directory is specified
  • models (dict) – dictionary of numpy.array - Name(‘s) and array(‘s). Match number of cells
  • directory (str) – directory where the UBC GIF file lives
CylMesh.write_vtk(mesh, filename, models=None, directory='')

Makes and saves a VTK object from this mesh and given models

Parameters:
  • filename (str) – path to the output vtk file or just its name if directory is specified
  • models (dict) – dictionary of numpy.array - Name(‘s) and array(‘s). Match number of cells
  • directory (str) – directory where the UBC GIF file lives