discretize.CurvilinearMesh¶

class discretize.CurvilinearMesh(nodes=None, **kwargs)[source]¶

Bases: discretize.base.base_mesh.BaseRectangularMesh, discretize.DiffOperators.DiffOperators, discretize.InnerProducts.InnerProducts, discretize.View.CurviView

CurvilinearMesh is a mesh class that deals with curvilinear meshes.

Example of a curvilinear mesh:

import discretize
X, Y = discretize.utils.exampleLrmGrid([3,3],'rotate')
mesh = discretize.CurvilinearMesh([X, Y])
mesh.plotGrid(showIt=True)

(Source code)

../../_images/discretize-CurvilinearMesh-1.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
nodes (a list of Array): List of arrays describing the node locations, a list (each item is a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*, *, *) or (*, *)) with length between 2 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.CurvilinearMesh`¶

Mesh Types

Basic Forward 2D DC Resistivity

Overview of mesh types

Attributes¶

CurvilinearMesh.area¶: Area of the faces

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

CurvilinearMesh.aveCCV2F¶: Construct the averaging operator on cell centers to faces as a vector.

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

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

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

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

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

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

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

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

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

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

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

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

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

CurvilinearMesh.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

CurvilinearMesh.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

CurvilinearMesh.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

CurvilinearMesh.cellGrad¶: The cell centered Gradient, takes you to cell faces.

CurvilinearMesh.cellGradBC¶: The cell centered Gradient boundary condition matrix

CurvilinearMesh.cellGradx¶: Cell centered Gradient in the x dimension. Has neumann boundary conditions.

CurvilinearMesh.cellGrady¶

CurvilinearMesh.cellGradz¶: Cell centered Gradient in the x dimension. Has neumann boundary conditions.

CurvilinearMesh.dim¶

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

Returns:	dimension of the mesh
Return type:	int

CurvilinearMesh.edge¶: Edge lengths

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

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

CurvilinearMesh.faceDivx¶: Construct divergence operator in the x component (face-stg to cell-centres).

CurvilinearMesh.faceDivy¶

CurvilinearMesh.faceDivz¶: Construct divergence operator in the z component (face-stg to cell-centers).

CurvilinearMesh.gridCC¶: Cell-centered grid

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

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

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

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

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

CurvilinearMesh.gridFz¶: Face staggered grid in the y direction.

CurvilinearMesh.gridN¶: Nodal grid.

CurvilinearMesh.nC¶

Total number of cells

Return type:	int
Returns:	nC

CurvilinearMesh.nCx¶

Number of cells in the x direction

Return type:	int
Returns:	nCx

CurvilinearMesh.nCy¶

Number of cells in the y direction

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

CurvilinearMesh.nCz¶

Number of cells in the z direction

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

CurvilinearMesh.nE¶

Total number of edges.

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

CurvilinearMesh.nEx¶

Number of x-edges

Return type:	int
Returns:	nEx

CurvilinearMesh.nEy¶

Number of y-edges

Return type:	int
Returns:	nEy

CurvilinearMesh.nEz¶

Number of z-edges

Return type:	int
Returns:	nEz

CurvilinearMesh.nF¶

Total number of faces.

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

CurvilinearMesh.nFx¶

Number of x-faces

Return type:	int
Returns:	nFx

CurvilinearMesh.nFy¶

Number of y-faces

Return type:	int
Returns:	nFy

CurvilinearMesh.nFz¶

Number of z-faces

Return type:	int
Returns:	nFz

CurvilinearMesh.nN¶

Total number of nodes

Return type:	int
Returns:	nN

CurvilinearMesh.nNx¶

Number of nodes in the x-direction

Return type:	int
Returns:	nNx

CurvilinearMesh.nNy¶

Number of nodes in the y-direction

Return type:	int
Returns:	nNy or None if dim < 2

CurvilinearMesh.nNz¶

Number of nodes in the z-direction

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

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

CurvilinearMesh.nodalLaplacian¶: Construct laplacian operator (nodes to edges).

CurvilinearMesh.nodes¶

List of arrays describing the node locations, a list (each item is a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*, *, *) or (*, *)) with length between 2 and 3

Type:	nodes (a list of `Array`)

CurvilinearMesh.normals¶

calling this will average the computed normals so that there is one per face. This is especially relevant in 3D, as there are up to 4 different normals for each face that will be different.

To reshape the normals into a matrix and get the y component:

NyX, NyY, NyZ = M.r(M.normals, 'F', 'Fy', 'M')

Type:	Face normals

CurvilinearMesh.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 \((0,0,1)\)

CurvilinearMesh.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

CurvilinearMesh.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.

CurvilinearMesh.tangents¶: Edge tangents

CurvilinearMesh.vnC¶

Total number of cells in each direction

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

CurvilinearMesh.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)

CurvilinearMesh.vnEx¶

Number of x-edges in each direction

Return type:	numpy.ndarray
Returns:	vnEx

CurvilinearMesh.vnEy¶

Number of y-edges in each direction

Return type:	numpy.ndarray
Returns:	vnEy or None if dim < 2

CurvilinearMesh.vnEz¶

Number of z-edges in each direction

Return type:	numpy.ndarray
Returns:	vnEz or None if dim < 3

CurvilinearMesh.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)

../../_images/discretize-CurvilinearMesh-2.png

CurvilinearMesh.vnFx¶

Number of x-faces in each direction

Return type:	numpy.ndarray
Returns:	vnFx

CurvilinearMesh.vnFy¶

Number of y-faces in each direction

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

CurvilinearMesh.vnFz¶

Number of z-faces in each direction

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

CurvilinearMesh.vnN¶

Total number of nodes in each direction

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

CurvilinearMesh.vol¶: Construct cell volumes of the 3D model as 1d array

CurvilinearMesh.x0¶

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

Type:	x0 (`Array`)

Methods¶

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

classmethod CurvilinearMesh.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.

CurvilinearMesh.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.

CurvilinearMesh.getBCProjWF(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']

CurvilinearMesh.getBCProjWF_simple(discretization='CC')¶: The weak form boundary condition projection matrices when mixed boundary condition is used

CurvilinearMesh.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

CurvilinearMesh.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

CurvilinearMesh.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

CurvilinearMesh.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

CurvilinearMesh.plotGrid(ax=None, nodes=False, faces=False, centers=False, edges=False, lines=True, showIt=False, **kwargs)¶

Plot the nodal, cell-centered and staggered grids for 1, 2 and 3 dimensions.

import discretize
X, Y = discretize.utils.exampleLrmGrid([3, 3], 'rotate')
M = discretize.CurvilinearMesh([X, Y])
M.plotGrid(showIt=True)

(Source code)

../../_images/discretize-CurvilinearMesh-3.png

CurvilinearMesh.plotImage(I, ax=None, showIt=False, grid=False, clim=None)¶

CurvilinearMesh.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, )

CurvilinearMesh.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, )

CurvilinearMesh.r(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')

CurvilinearMesh.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

CurvilinearMesh.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.

CurvilinearMesh.setCellGradBC(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’]

CurvilinearMesh.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

CurvilinearMesh.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.

CurvilinearMesh.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

discretize.CurvilinearMesh¶

Examples using discretize.CurvilinearMesh¶

Attributes¶

Methods¶

Examples using `discretize.CurvilinearMesh`¶