2D Sub Meshes

class pybamm.ScikitSubMesh2D(edges, coord_sys, tabs)

2D submesh class. Contains information about the 2D finite element mesh. Note: This class only allows for the use of piecewise-linear triangular finite elements.

Parameters:

• edges (array_like) – An array containing the points corresponding to the edges of the submesh

• coord_sys (string) – The coordinate system of the submesh

• tabs (dict, optional) – A dictionary that contains information about the size and location of the tabs

Extends: pybamm.meshes.meshes.SubMesh

on_boundary(y, z, tab)

A method to get the degrees of freedom corresponding to the subdomains for the tabs.

class pybamm.ScikitUniform2DSubMesh(lims, npts)

Contains information about the 2D finite element mesh with uniform grid spacing (can be different spacing in y and z). Note: This class only allows for the use of piecewise-linear triangular finite elements.

Parameters:

• lims (dict) – A dictionary that contains the limits of each spatial variable

• npts (dict) – A dictionary that contains the number of points to be used on each spatial variable

Extends: pybamm.meshes.scikit_fem_submeshes.ScikitSubMesh2D

class pybamm.ScikitExponential2DSubMesh(lims, npts, side='top', stretch=2.3)

Contains information about the 2D finite element mesh generated by taking the tensor product of a uniformly spaced grid in the y direction, and a unequally spaced grid in the z direction in which the points are clustered close to the top boundary using an exponential formula on the interval [a,b]. The gridpoints in the z direction are given by

\[z_{k} = (b-a) + \frac{\exp{-\alpha k / N} - 1}{\exp{-\alpha} - 1} + a,\]

for k = 1, …, N, where N is the number of nodes. Here alpha is a stretching factor. As the number of gridpoints tends to infinity, the ratio of the largest and smallest grid cells tends to exp(alpha).

Note: in the future this will be extended to allow points to be clustered near any of the boundaries.

Parameters:

• lims (dict) – A dictionary that contains the limits of each spatial variable

• npts (dict) – A dictionary that contains the number of points to be used on each spatial variable

• side (str, optional) – Whether the points are clustered near to a particular boundary. At present, can only be “top”. Default is “top”.

• stretch (float, optional) – The factor (alpha) which appears in the exponential. Default is 2.3.

Extends: pybamm.meshes.scikit_fem_submeshes.ScikitSubMesh2D

class pybamm.ScikitChebyshev2DSubMesh(lims, npts)

Contains information about the 2D finite element mesh generated by taking the tensor product of two 1D meshes which use Chebyshev nodes on the interval (a, b), given by

\[x_{k} = \frac{1}{2}(a+b) + \frac{1}{2}(b-a) \cos(\frac{2k-1}{2N}\pi),\]

for k = 1, …, N, where N is the number of nodes. Note: this mesh then appends the boundary edgess, so that the 1D mesh edges are given by

\[a < x_{1} < ... < x_{N} < b.\]

Note: This class only allows for the use of piecewise-linear triangular finite elements.

Parameters:

• lims (dict) – A dictionary that contains the limits of each spatial variable

• npts (dict) – A dictionary that contains the number of points to be used on each spatial variable

Extends: pybamm.meshes.scikit_fem_submeshes.ScikitSubMesh2D

class pybamm.UserSupplied2DSubMesh(lims, npts, y_edges=None, z_edges=None)

A class to generate a tensor product submesh on a 2D domain by using two user supplied vectors of edges: one for the y-direction and one for the z-direction. Note: this mesh should be created using UserSupplied2DSubMeshGenerator.

Parameters:

• lims (dict) – A dictionary that contains the limits of the spatial variables

• npts (dict) – A dictionary that contains the number of points to be used on each spatial variable. Note: the number of nodes (located at the cell centres) is npts, and the number of edges is npts+1.

• y_edges (array_like) – The array of points which correspond to the edges in the y direction of the mesh.

• z_edges (array_like) – The array of points which correspond to the edges in the z direction of the mesh.

Extends: pybamm.meshes.scikit_fem_submeshes.ScikitSubMesh2D