discretize.TreeMesh¶

class discretize.TreeMesh(*args, **kwargs)[source]¶

Bases: discretize.tree_ext._TreeMesh, discretize.base.base_tensor_mesh.BaseTensorMesh, discretize.InnerProducts.InnerProducts, discretize.MeshIO.TreeMeshIO

TreeMesh is a class for adaptive QuadTree (2D) and OcTree (3D) meshes.

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
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: Returns a numpy array of length nF with the area (length in 2D) of all faces ordered by x, then y, then z.
aveCC2F: Construct the averaging operator on cell centers to cell faces.
aveCC2Fx: Construct the averaging operator on cell centers to cell x-faces.
aveCC2Fy: Construct the averaging operator on cell centers to cell y-faces.
aveCC2Fz: Construct the averaging operator on cell centers to cell z-faces.
aveCCV2F: Construct the averaging operator on cell centers to cell faces.
aveE2CC: Construct the averaging operator on cell edges to cell centers.
aveE2CCV: Construct the averaging operator on cell edges to cell centers.
aveEx2CC: Construct the averaging operator on cell edges in the x direction to cell centers.
aveEy2CC: Construct the averaging operator on cell edges in the y direction to cell centers.
aveEz2CC: Construct the averaging operator on cell edges in the z direction to cell centers.
aveF2CC: Construct the averaging operator on cell faces to cell centers.
aveF2CCV: Construct the averaging operator on cell faces to cell centers.
aveFx2CC: Construct the averaging operator on cell faces in the x direction to cell centers.
aveFy2CC: Construct the averaging operator on cell faces in the y direction to cell centers.
aveFz2CC: Construct the averaging operator on cell faces in the z direction 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.
aveN2Ex: Averaging operator on cell nodes to x-edges
aveN2Ey: Averaging operator on cell nodes to y-edges
aveN2Ez: Averaging operator on cell nodes to z-edges
aveN2F: Construct the averaging operator on cell nodes to cell edges, keeping each dimension separate.
aveN2Fx: Averaging operator on cell nodes to x-faces
aveN2Fy: Averaging operator on cell nodes to y-faces
aveN2Fz: Averaging operator on cell nodes to z-faces
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
cellBoundaryInd: Returns a tuple of arrays of indexes for boundary cells in each direction
cellGrad: Cell centered Gradient operator built off of the faceDiv operator.
cellGradStencil
cellGradx: Cell centered Gradient operator in x-direction (Gradx)
cellGrady: Cell centered Gradient operator in y-direction (Grady)
cellGradz: Cell centered Gradient operator in z-direction (Gradz)
dim: The dimension of the mesh (1, 2, or 3).
edge: Returns a numpy array of length nE with the length of all edges ordered by x, then y, then z.
edgeCurl: Construct the 3D curl operator.
faceBoundaryInd: Returns a tuple of arrays of indexes for boundary faces in each direction
faceDiv: Construct divergence operator (face-stg to cell-centres).
faceDivx
faceDivy
faceDivz
fill: How filled is the mesh compared to a TensorMesh? As a fraction: [0, 1].
gridCC: Returns a numpy arrayof shape (nC, dim) with the center locations of all cells in order.
gridEx: Returns a numpy array of shape (nEx, dim) with the centers of all non-hanging edges along the first dimension in order.
gridEy: Returns a numpy array of shape (nEy, dim) with the centers of all non-hanging edges along the second dimension in order.
gridEz: Returns a numpy array of shape (nEz, dim) with the centers of all non-hanging edges along the third dimension in order.
gridFx: Returns a numpy array of shape (nFx, dim) with the centers of all non-hanging faces along the first dimension in order.
gridFy: Returns a numpy array of shape (nFy, dim) with the centers of all non-hanging faces along the second dimension in order.
gridFz: Returns a numpy array of shape (nFz, dim) with the centers of all non-hanging faces along the third dimension in order.
gridN: Returns a numpy array of shape (nN, dim) with the locations of all non-hanging nodes in order.
gridhEx: Returns a numpy array of shape (nhEx, dim) with the centers of all hanging edges along the first dimension in order.
gridhEy: Returns a numpy array of shape (nhEy, dim) with the centers of all hanging edges along the second dimension in order.
gridhEz: Returns a numpy array of shape (nhEz, dim) with the centers of all hanging edges along the third dimension in order.
gridhFx: Returns a numpy array of shape (nhFx, dim) with the centers of all hanging faces along the first dimension in order.
gridhFy: Returns a numpy array of shape (nhFy, dim) with the centers of all hanging faces along the second dimension in order.
gridhFz: Returns a numpy array of shape (nhFz, dim) with the centers of all hanging faces along the third dimension in order.
gridhN: Returns a numpy array of shape (nN, dim) with the locations of all hanging nodes in order.
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
maxLevel: The maximum level used, which may be less than levels or max_level.
max_level: The maximum possible level for a cell on this mesh
nC: Number of cells
nE: Total number of non-hanging edges amongst all dimensions
nEx: Number of non-hanging edges oriented along the first dimension
nEy: Number of non-hanging edges oriented along the second dimension
nEz: Number of non-hanging edges oriented along the third dimension
nF: Total number of non-hanging faces amongst all dimensions
nFx: Number of non-hanging faces oriented along the first dimension
nFy: Number of non-hanging faces oriented along the second dimension
nFz: Number of non-hanging faces oriented along the third dimension
nN: Number of non-hanging nodes
nhE: Total number of hanging edges amongst all dimensions
nhEx: Number of hanging edges oriented along the first dimension
nhEy: Number of hanging edges oriented along the second dimension
nhEz: Number of hanging edges oriented along the third dimension
nhF: Total number of hanging faces amongst all dimensions
nhFx: Number of hanging faces oriented along the first dimension
nhFy: Number of hanging faces oriented along the second dimension
nhFz: Number of hanging faces oriented along the third dimension
nhN: Number of hanging nodes
nodalGrad: Construct gradient operator (nodes to edges).
nodalLaplacian
normals: Face Normals
ntE: Total number of non-hanging and hanging edges amongst all dimensions
ntEx: Number of non-hanging and hanging edges oriented along the first dimension
ntEy: Number of non-hanging and hanging edges oriented along the second dimension
ntEz: Number of non-hanging and hanging edges oriented along the third dimension
ntF: Total number of hanging and non-hanging faces amongst all dimensions
ntFx: Number of non-hanging and hanging faces oriented along the first dimension
ntFy: Number of non-hanging and hanging faces oriented along the second dimension
ntFz: Number of non-hanging and hanging faces oriented along the third dimension
ntN: Number of non-hanging and hanging nodes
permuteCC: Permutation matrix re-ordering of cells sorted by x, then y, then z
permuteE: Permutation matrix re-ordering of edges sorted by x, then y, then z
permuteF: Permutation matrix re-ordering of faces sorted by x, then y, then z
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.
vnE: Total number of edges in each direction
vnF: Total number of faces in each direction
vntE: Total number of hanging and non-hanging edges in a [nx,ny,nz] form
vntF: Total number of hanging and non-hanging faces in a [nx,ny,nz] form
vol: Returns a numpy array of length nC with the volumes (areas in 2D) of all cells in order.
x0: x0 (Array): origin of the mesh (dim, ), a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*)

Methods

copy

Generic (shallow and deep) copying operations.

plotSlice

Examples using `discretize.TreeMesh`¶

Basic: PlotImage¶

QuadTree: FaceDiv¶

QuadTree: Hanging Nodes¶

Overview of Mesh Types¶

Tree Meshes¶

Differential Operators¶

Attributes¶

TreeMesh.area¶: Returns a numpy array of length nF with the area (length in 2D) of all faces ordered by x, then y, then z.

TreeMesh.aveCC2F¶: Construct the averaging operator on cell centers to cell faces.

TreeMesh.aveCC2Fx¶: Construct the averaging operator on cell centers to cell x-faces.

TreeMesh.aveCC2Fy¶: Construct the averaging operator on cell centers to cell y-faces.

TreeMesh.aveCC2Fz¶: Construct the averaging operator on cell centers to cell z-faces.

TreeMesh.aveCCV2F¶: Construct the averaging operator on cell centers to cell faces.

TreeMesh.aveE2CC¶: Construct the averaging operator on cell edges to cell centers.

TreeMesh.aveE2CCV¶: Construct the averaging operator on cell edges to cell centers.

TreeMesh.aveEx2CC¶: Construct the averaging operator on cell edges in the x direction to cell centers.

TreeMesh.aveEy2CC¶: Construct the averaging operator on cell edges in the y direction to cell centers.

TreeMesh.aveEz2CC¶: Construct the averaging operator on cell edges in the z direction to cell centers.

TreeMesh.aveF2CC¶: Construct the averaging operator on cell faces to cell centers.

TreeMesh.aveF2CCV¶: Construct the averaging operator on cell faces to cell centers.

TreeMesh.aveFx2CC¶: Construct the averaging operator on cell faces in the x direction to cell centers.

TreeMesh.aveFy2CC¶: Construct the averaging operator on cell faces in the y direction to cell centers.

TreeMesh.aveFz2CC¶: Construct the averaging operator on cell faces in the z direction to cell centers.

TreeMesh.aveN2CC¶: Construct the averaging operator on cell nodes to cell centers.

TreeMesh.aveN2E¶: Construct the averaging operator on cell nodes to cell edges, keeping each dimension separate.

TreeMesh.aveN2Ex¶: Averaging operator on cell nodes to x-edges

TreeMesh.aveN2Ey¶: Averaging operator on cell nodes to y-edges

TreeMesh.aveN2Ez¶: Averaging operator on cell nodes to z-edges

TreeMesh.aveN2F¶: Construct the averaging operator on cell nodes to cell edges, keeping each dimension separate.

TreeMesh.aveN2Fx¶: Averaging operator on cell nodes to x-faces

TreeMesh.aveN2Fy¶: Averaging operator on cell nodes to y-faces

TreeMesh.aveN2Fz¶: Averaging operator on cell nodes to z-faces

TreeMesh.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

TreeMesh.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

TreeMesh.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

TreeMesh.cellBoundaryInd¶: Returns a tuple of arrays of indexes for boundary cells in each direction xdown, xup, ydown, yup, zdown, zup

TreeMesh.cellGrad¶: Cell centered Gradient operator built off of the faceDiv operator. Grad = - (Mf)^{-1} * Div * diag (volume)

TreeMesh.cellGradStencil¶

TreeMesh.cellGradx¶: Cell centered Gradient operator in x-direction (Gradx) Grad = sp.vstack((Gradx, Grady, Gradz))

TreeMesh.cellGrady¶: Cell centered Gradient operator in y-direction (Grady) Grad = sp.vstack((Gradx, Grady, Gradz))

TreeMesh.cellGradz¶: Cell centered Gradient operator in z-direction (Gradz) Grad = sp.vstack((Gradx, Grady, Gradz))

TreeMesh.dim¶

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

Returns: dimension of the mesh
Return type: int

TreeMesh.edge¶: Returns a numpy array of length nE with the length of all edges ordered by x, then y, then z.

TreeMesh.edgeCurl¶: Construct the 3D curl operator.

TreeMesh.faceBoundaryInd¶: Returns a tuple of arrays of indexes for boundary faces in each direction xdown, xup, ydown, yup, zdown, zup

TreeMesh.faceDiv¶: Construct divergence operator (face-stg to cell-centres).

TreeMesh.faceDivx¶

TreeMesh.faceDivy¶

TreeMesh.faceDivz¶

TreeMesh.fill¶: How filled is the mesh compared to a TensorMesh? As a fraction: [0, 1].

TreeMesh.gridCC¶: Returns a numpy arrayof shape (nC, dim) with the center locations of all cells in order.

TreeMesh.gridEx¶: Returns a numpy array of shape (nEx, dim) with the centers of all non-hanging edges along the first dimension in order.

TreeMesh.gridEy¶: Returns a numpy array of shape (nEy, dim) with the centers of all non-hanging edges along the second dimension in order.

TreeMesh.gridEz¶: Returns a numpy array of shape (nEz, dim) with the centers of all non-hanging edges along the third dimension in order.

TreeMesh.gridFx¶: Returns a numpy array of shape (nFx, dim) with the centers of all non-hanging faces along the first dimension in order.

TreeMesh.gridFy¶: Returns a numpy array of shape (nFy, dim) with the centers of all non-hanging faces along the second dimension in order.

TreeMesh.gridFz¶: Returns a numpy array of shape (nFz, dim) with the centers of all non-hanging faces along the third dimension in order.

TreeMesh.gridN¶: Returns a numpy array of shape (nN, dim) with the locations of all non-hanging nodes in order.

TreeMesh.gridhEx¶: Returns a numpy array of shape (nhEx, dim) with the centers of all hanging edges along the first dimension in order.

TreeMesh.gridhEy¶: Returns a numpy array of shape (nhEy, dim) with the centers of all hanging edges along the second dimension in order.

TreeMesh.gridhEz¶: Returns a numpy array of shape (nhEz, dim) with the centers of all hanging edges along the third dimension in order.

TreeMesh.gridhFx¶: Returns a numpy array of shape (nhFx, dim) with the centers of all hanging faces along the first dimension in order.

TreeMesh.gridhFy¶: Returns a numpy array of shape (nhFy, dim) with the centers of all hanging faces along the second dimension in order.

TreeMesh.gridhFz¶: Returns a numpy array of shape (nhFz, dim) with the centers of all hanging faces along the third dimension in order.

TreeMesh.gridhN¶: Returns a numpy array of shape (nN, dim) with the locations of all hanging nodes in order.

TreeMesh.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)

TreeMesh.h_gridded¶: Returns an (nC, dim) numpy array with the widths of all cells in order

TreeMesh.hx¶: Width of cells in the x direction

TreeMesh.hy¶: Width of cells in the y direction

TreeMesh.hz¶: Width of cells in the z direction

TreeMesh.maxLevel¶: The maximum level used, which may be less than levels or max_level.

TreeMesh.max_level¶: The maximum possible level for a cell on this mesh

TreeMesh.nC¶: Number of cells

TreeMesh.nE¶: Total number of non-hanging edges amongst all dimensions

TreeMesh.nEx¶: Number of non-hanging edges oriented along the first dimension

TreeMesh.nEy¶: Number of non-hanging edges oriented along the second dimension

TreeMesh.nEz¶: Number of non-hanging edges oriented along the third dimension

TreeMesh.nF¶: Total number of non-hanging faces amongst all dimensions

TreeMesh.nFx¶: Number of non-hanging faces oriented along the first dimension

TreeMesh.nFy¶: Number of non-hanging faces oriented along the second dimension

TreeMesh.nFz¶: Number of non-hanging faces oriented along the third dimension

TreeMesh.nN¶: Number of non-hanging nodes

TreeMesh.nhE¶: Total number of hanging edges amongst all dimensions

TreeMesh.nhEx¶: Number of hanging edges oriented along the first dimension

TreeMesh.nhEy¶: Number of hanging edges oriented along the second dimension

TreeMesh.nhEz¶: Number of hanging edges oriented along the third dimension

TreeMesh.nhF¶: Total number of hanging faces amongst all dimensions

TreeMesh.nhFx¶: Number of hanging faces oriented along the first dimension

TreeMesh.nhFy¶: Number of hanging faces oriented along the second dimension

TreeMesh.nhFz¶: Number of hanging faces oriented along the third dimension

TreeMesh.nhN¶: Number of hanging nodes

TreeMesh.nodalGrad¶: Construct gradient operator (nodes to edges).

TreeMesh.nodalLaplacian¶

TreeMesh.normals¶

Face Normals

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

TreeMesh.ntE¶: Total number of non-hanging and hanging edges amongst all dimensions

TreeMesh.ntEx¶: Number of non-hanging and hanging edges oriented along the first dimension

TreeMesh.ntEy¶: Number of non-hanging and hanging edges oriented along the second dimension

TreeMesh.ntEz¶: Number of non-hanging and hanging edges oriented along the third dimension

TreeMesh.ntF¶: Total number of hanging and non-hanging faces amongst all dimensions

TreeMesh.ntFx¶: Number of non-hanging and hanging faces oriented along the first dimension

TreeMesh.ntFy¶: Number of non-hanging and hanging faces oriented along the second dimension

TreeMesh.ntFz¶: Number of non-hanging and hanging faces oriented along the third dimension

TreeMesh.ntN¶: Number of non-hanging and hanging nodes

TreeMesh.permuteCC¶: Permutation matrix re-ordering of cells sorted by x, then y, then z

TreeMesh.permuteE¶: Permutation matrix re-ordering of edges sorted by x, then y, then z

TreeMesh.permuteF¶: Permutation matrix re-ordering of faces sorted by x, then y, then z

TreeMesh.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 \((0,0,1)\)

TreeMesh.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

TreeMesh.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.

TreeMesh.tangents¶

Edge Tangents

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

TreeMesh.vectorCCx¶: Cell-centered grid vector (1D) in the x direction.

TreeMesh.vectorCCy¶: Cell-centered grid vector (1D) in the y direction.

TreeMesh.vectorCCz¶: Cell-centered grid vector (1D) in the z direction.

TreeMesh.vectorNx¶: Nodal grid vector (1D) in the x direction.

TreeMesh.vectorNy¶: Nodal grid vector (1D) in the y direction.

TreeMesh.vectorNz¶: Nodal grid vector (1D) in the z direction.

TreeMesh.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, show_it=True)

TreeMesh.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, show_it=True)

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

TreeMesh.vntE¶: Total number of hanging and non-hanging edges in a [nx,ny,nz] form

TreeMesh.vntF¶: Total number of hanging and non-hanging faces in a [nx,ny,nz] form

TreeMesh.vol¶: Returns a numpy array of length nC with the volumes (areas in 2D) of all cells in order.

TreeMesh.x0¶

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

Type: x0 (Array)

Methods¶

TreeMesh.cell_levels_by_index(indices)[source]¶

Fast function to return a list of levels for the given cell indices

Parameters: index (array_like of length (N)) – Cell indexes to query
Returns: Levels for the cells.
Return type: numpy.array of length (N)

TreeMesh.copy()¶: Make a copy of the current mesh

classmethod TreeMesh.deserialize(serial)[source]¶

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.

TreeMesh.equal(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.

TreeMesh.finalize(self)¶: Finalize the TreeMesh Called after finished cronstruction of the mesh. Can only be called once. After finalize is called, all other attributes and functions are valid.

static TreeMesh.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.

TreeMesh.getEdgeInnerProduct(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

TreeMesh.getEdgeInnerProductDeriv(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

TreeMesh.getFaceInnerProduct(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

TreeMesh.getFaceInnerProductDeriv(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

TreeMesh.getInterpolationMat(locs, locType, 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

Returns

M, the interpolation matrix

Return type

scipy.sparse.csr_matrix

TreeMesh.getTensor(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

TreeMesh.get_boundary_cells(self, active_ind=None, direction='zu')¶

Returns the indices of boundary cells in a given direction given an active index array.

Parameters

active_ind (array_like of bool, optional) – If not None, then this must show which cells are active
direction (str, optional) – must be one of (‘zu’, ‘zd’, ‘xu’, ‘xd’, ‘yu’, ‘yd’)

Returns

Array of indices for the boundary cells in the requested direction

Return type

numpy.array

TreeMesh.get_cells_along_line(self, x0, x1)¶

Finds the cells along a line segment defined by two points

Parameters: x0,x1 (array_like of length (dim)) – Begining and ending point of the line segment.
Returns: Indexes for cells that contain the a line defined by the two input points, ordered in the direction of the line.
Return type: list of ints

TreeMesh.insert_cells(self, points, levels, finalize=True)¶

Insert cells into the TreeMesh that contain given points

Insert cell(s) into the TreeMesh that contain the given point(s) at the assigned level(s).

Parameters

points (array_like with shape (N, dim)) –
levels (array_like of integers with shape (N)) –
finalize (bool, optional) – Whether to finalize after inserting point(s)

Examples

>>> from discretize import TreeMesh
>>> mesh = TreeMesh([32,32])
>>> mesh.insert_cells([0.5, 0.5], mesh.max_level)
>>> print(mesh)
---- QuadTreeMesh ----
 x0: 0.00
 y0: 0.00
 hx: 32*0.03,
 hy: 32*0.03,
nC: 40
Fill: 3.91%

TreeMesh.isInside(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

TreeMesh.number(self)¶: Number the cells, nodes, faces, and edges of the TreeMesh

TreeMesh.plotGrid(self, ax=None, nodes=False, faces=False, centers=False, edges=False, lines=True, cell_line=False, faces_x=False, faces_y=False, faces_z=False, edges_x=False, edges_y=False, edges_z=False, show_it=False, **kwargs)¶

Plot the nodel, cell-centered, and staggered grids for 2 and 3 dimensions Plots the mesh grid in either 2D or 3D of the TreeMesh

Parameters

ax (matplotlib.axes.Axes or None, optional) – The axes handle to plot on
nodes (bool, optional) – Plot the nodal points
faces (bool, optional) – Plot the center points of the faces
centers (bool, optional) – Plot the center points of the cells
edges (bool, optional) – Plot the center points of the edges
lines (bool, optional) – Plot the lines connecting the nodes
cell_line (bool, optional) – Plot the line through the cell centers in order
faces_y, faces_z (faces_x,) – Plot the center points of the x, y, or z faces
edges_y, edges_z (edges_x,) – Plot the center points of the x, y, or z edges
show_it (bool, optional) – whether to call plt.show() within the codes
color (Color or str, optional) – if lines=True, the color of the lines, defaults to first color.
linewidth (float, optional) – if lines=True, the linewidth for the lines.

Returns

Axes handle for the plot

Return type

matplotlib.axes.Axes

TreeMesh.plotImage(self, v, v_type='CC', grid=False, view='real', ax=None, clim=None, show_it=False, pcolor_opts=None, grid_opts=None, range_x=None, range_y=None, **kwargs)¶

Plots an image of values defined on the TreeMesh If 3D, this function plots a default slice of the TreeMesh

Parameters

v (array_like) – Array containing the values to plot
v_type (str, optional) – type of value in v one of ‘CC’, ‘N’, ‘Fx’, ‘Fy’, ‘Fz’, ‘Ex’, ‘Ey’, or ‘Ez’
grid (bool, optional) – plot the grid lines
view (['real', 'imag', 'abs'], optional) – The values to plot from v
ax (matplotlib.axes.Axes or None, optional) – The axes handle
clim (array_like of length 2, or None, optional) – A pair of [min, max] for the Colorbar
pcolor_opts (dict, or None) – options to be passed on to pcolormesh
gridOpt (dict, or None) – options for the plotting the grid
range_y (range_x,) – pairs of [min, max] values for the x and y ranges

TreeMesh.plotSlice(v, v_type='CC', normal='Z', ind=None, grid=False, view='real', ax=None, clim=None, show_it=False, pcolor_opts=None, stream_opts=None, grid_opts=None, range_x=None, range_y=None, **kwargs)[source]¶

TreeMesh.point2index(locs)[source]¶

Finds cells that contain the given points. Returns an array of index values of the cells that contain the given points

Parameters: locs (array_like of shape (N, dim)) – points to search for the location of
Returns: Cell indices that contain the points
Return type: numpy.array of integers of length(N)

TreeMesh.projectEdgeVector(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, )

TreeMesh.projectFaceVector(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, )

TreeMesh.readModelUBC(fileName)¶: Read UBC OcTree model and get vector :param string fileName: path to the UBC GIF model file to read :rtype: numpy.ndarray :return: OcTree model

classmethod TreeMesh.readUBC(meshFile)¶: Read UBC 3D OcTree mesh file Input: :param str meshFile: path to the UBC GIF OcTree mesh file to read :rtype: discretize.TreeMesh :return: The octree mesh

TreeMesh.refine(self, function, finalize=True)¶

Refine a TreeMesh using a user supplied function.

Refines the TreeMesh using a function that is recursively called on each cell of the mesh. It must accept an object of type discretize.TreeMesh.Cell and return an integer like object defining the desired level. The function can also simply be an integer, which will then cause all cells to be at least that level.

Parameters

function (callable | int) – a function describing the desired level, or an integer to refine all cells to at least that level.
finalize (bool, optional) – Whether to finalize the mesh

Examples

>>> from discretize import TreeMesh
>>> mesh = TreeMesh([32,32])
>>> def func(cell):
>>>     r = np.linalg.norm(cell.center-0.5)
>>>     return mesh.max_level if r<0.2 else mesh.max_level-1
>>> mesh.refine(func)
>>> mesh
---- QuadTreeMesh ----
 x0: 0.00
 y0: 0.00
 hx: 32*0.03,
 hy: 32*0.03,
nC: 352
Fill: 34.38%

discretize.TreeMesh¶

Examples using discretize.TreeMesh¶

Attributes¶

Methods¶

Examples using `discretize.TreeMesh`¶