discretize.TreeMesh

class discretize.TreeMesh(h, x0=None, **kwargs)

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’> with shape (*)

Examples using discretize.TreeMesh

QuadTree: Creation

QuadTree: Hanging Nodes

Mesh Types

Basic: PlotImage

QuadTree: FaceDiv

Overview of mesh types

Attributes

TreeMesh.area

TreeMesh.aveCC2F

TreeMesh.aveCC2Fx

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

TreeMesh.aveE2CC

TreeMesh.aveE2CCV

TreeMesh.aveEx2CC

TreeMesh.aveEy2CC

TreeMesh.aveEz2CC

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

TreeMesh.aveFy2CC

TreeMesh.aveFz2CC

TreeMesh.aveN2CC

TreeMesh.aveN2E

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

TreeMesh.aveN2Ex

TreeMesh.aveN2Ey

TreeMesh.aveN2Ez

TreeMesh.aveN2F

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

TreeMesh.aveN2Fx

TreeMesh.aveN2Fy

TreeMesh.aveN2Fz

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

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 (Gradx) 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

TreeMesh.edgeCurl

TreeMesh.faceBoundaryInd

TreeMesh.faceDiv

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 an M by N numpy array with the center locations of all cells in order. M is the number of cells and N=2,3 is the dimension of the mesh.

TreeMesh.gridEx

TreeMesh.gridEy

TreeMesh.gridEz

TreeMesh.gridFx

TreeMesh.gridFy

TreeMesh.gridFz

TreeMesh.gridN

Returns an M by N numpy array with the widths of all cells in order. M is the number of nodes and N=2,3 is the dimension of the mesh.

TreeMesh.gridhEx

TreeMesh.gridhEy

TreeMesh.gridhEz

TreeMesh.gridhFx

TreeMesh.gridhFy

TreeMesh.gridhFz

TreeMesh.gridhN

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.

TreeMesh.max_level

TreeMesh.nC

TreeMesh.nE

TreeMesh.nEx

TreeMesh.nEy

TreeMesh.nEz

TreeMesh.nF

TreeMesh.nFx

TreeMesh.nFy

TreeMesh.nFz

TreeMesh.nN

TreeMesh.nhE

TreeMesh.nhEx

TreeMesh.nhEy

TreeMesh.nhEz

TreeMesh.nhF

TreeMesh.nhFx

TreeMesh.nhFy

TreeMesh.nhFz

TreeMesh.nhN

TreeMesh.nodalGrad

TreeMesh.normals

Face Normals

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

TreeMesh.ntE

TreeMesh.ntEx

TreeMesh.ntEy

TreeMesh.ntEz

TreeMesh.ntF

TreeMesh.ntFx

TreeMesh.ntFy

TreeMesh.ntFz

TreeMesh.ntN

TreeMesh.permuteCC

TreeMesh.permuteE

TreeMesh.permuteF

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 vtkInterface.

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, showIt=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, showIt=True)

(Source code)

TreeMesh.vntE

TreeMesh.vntF

TreeMesh.vol

TreeMesh.x0

Methods

TreeMesh.copy(*args, **kwargs)

Make a copy of the current mesh

classmethod TreeMesh.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.

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()

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()

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.insert_cells()

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.load(*args, **kwargs)

TreeMesh.number()

TreeMesh.plotGrid()

TreeMesh.plotImage()

TreeMesh.plotSlice(v, vType='CC', normal='Z', ind=None, grid=True, view='real', ax=None, clim=None, showIt=False, pcolorOpts=None, streamOpts=None, gridOpts=None)

TreeMesh.point2index(locs)

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()

TreeMesh.save(*args, **kwargs)

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

TreeMesh.serialize(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.

TreeMesh.toVTK(models=None)

Convert this mesh object to it’s proper vtki 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

TreeMesh.validate()

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.

TreeMesh.writeUBC(fileName, models=None)

Write UBC ocTree mesh and model files from a octree mesh and model. :param string fileName: File to write to :param dict models: Models in a dict, where each key is the filename

TreeMesh.writeVTK(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