discretize.base.BaseTensorMesh¶

class discretize.base.BaseTensorMesh(h=None, x0=None, **kwargs)[source]¶

Bases: discretize.base.base_mesh.BaseMesh

Base class for tensor-product style meshes

This class contains properites and methods that are common to cartesian and cylindrical meshes defined by tensor-produts of vectors describing cell spacings.

Do not use this class directly, instead, inherit it if you plan to develop a tensor-style mesh (e.g. a spherical mesh) or use the discretize.TensorMesh() class to create a cartesian tensor mesh.

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 (*)

Attributes¶

BaseTensorMesh.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

BaseTensorMesh.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

BaseTensorMesh.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

BaseTensorMesh.dim¶

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

Returns:	dimension of the mesh
Return type:	int

BaseTensorMesh.gridCC¶: Cell-centered grid.

BaseTensorMesh.gridEx¶: Edge staggered grid in the x direction.

BaseTensorMesh.gridEy¶: Edge staggered grid in the y direction.

BaseTensorMesh.gridEz¶: Edge staggered grid in the z direction.

BaseTensorMesh.gridFx¶: Face staggered grid in the x direction.

BaseTensorMesh.gridFy¶: Face staggered grid in the y direction.

BaseTensorMesh.gridFz¶: Face staggered grid in the z direction.

BaseTensorMesh.gridN¶: Nodal grid.

BaseTensorMesh.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`)

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

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

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

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

BaseTensorMesh.nC¶

Total number of cells in the mesh.

Returns:	number of cells in the mesh
Return type:	int

Example

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

print(mesh.nC)

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

../../_images/discretize-base-BaseTensorMesh-1.png

BaseTensorMesh.nE¶

Total number of edges.

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

BaseTensorMesh.nEx¶

Number of x-edges

Returns:	nEx
Return type:	int

BaseTensorMesh.nEy¶

Number of y-edges

Returns:	nEy
Return type:	int

BaseTensorMesh.nEz¶

Number of z-edges

Returns:	nEz
Return type:	int

BaseTensorMesh.nF¶

Total number of faces.

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

BaseTensorMesh.nFx¶

Number of x-faces

Return type:	int
Returns:	nFx

BaseTensorMesh.nFy¶

Number of y-faces

Return type:	int
Returns:	nFy

BaseTensorMesh.nFz¶

Number of z-faces

Return type:	int
Returns:	nFz

BaseTensorMesh.nN¶

Total number of nodes

Returns:	number of nodes in the mesh
Return type:	int

Example

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

print(mesh.nN)

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

../../_images/discretize-base-BaseTensorMesh-2.png

BaseTensorMesh.normals¶

Face Normals

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

BaseTensorMesh.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 \((0,0,1)\)

BaseTensorMesh.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

BaseTensorMesh.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.

BaseTensorMesh.tangents¶

Edge Tangents

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

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

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

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

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

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

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

BaseTensorMesh.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)

BaseTensorMesh.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-base-BaseTensorMesh-3.png

BaseTensorMesh.x0¶

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

Type:	x0 (`Array`)

Methods¶

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

classmethod BaseTensorMesh.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.

BaseTensorMesh.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.

BaseTensorMesh.getInterpolationMat(loc, locType='CC', zerosOutside=False)[source]¶

Produces interpolation matrix

Parameters:

loc (numpy.ndarray) – Location of points to interpolate to

locType (str) –

What to interpolate (see below)

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

BaseTensorMesh.getTensor(key)[source]¶

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

BaseTensorMesh.isInside(pts, locType='N')[source]¶

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

BaseTensorMesh.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, )

BaseTensorMesh.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, )

BaseTensorMesh.save(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

BaseTensorMesh.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.

BaseTensorMesh.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

BaseTensorMesh.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.

BaseTensorMesh.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