1D Sub Meshes

class pybamm.SubMesh1D(edges, coord_sys, tabs=None)

1D submesh class. Contains the position of the nodes, the number of mesh points, and (optionally) information about the tab locations.

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.SubMesh) –

class pybamm.Uniform1DSubMesh(lims, npts)

A class to generate a uniform submesh on a 1D domain

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.

• **Extends (“”: pybamm.SubMesh1D) –

class pybamm.Exponential1DSubMesh(lims, npts, side='symmetric', stretch=None)

A class to generate a submesh on a 1D domain in which the points are clustered close to one or both of boundaries using an exponential formula on the interval [a,b].

If side is “left”, the gridpoints are given by

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

for k = 1, …, N, where N is the number of nodes.

Is side is “right”, the gridpoints are given by

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

for k = 1, …, N.

If side is “symmetric”, the first half of the interval is meshed using the gridpoints

\[x_{k} = (b/2-a) + \frac{\exp{\alpha k / N} - 1}{\exp{\alpha} - 1}} + a,\]

for k = 1, …, N. The grid spacing is then reflected to contruct the grid on the full interval [a,b].

In the above, 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).

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.

• side (str, optional) – Whether the points are clustered near to the left or right boundary, or both boundaries. Can be “left”, “right” or “symmetric”. Default is “symmetric”

• stretch (float, optional) – The factor (alpha) which appears in the exponential. If side is “symmetric” then the default stretch is 1.15. If side is “left” or “right” then the default stretch is 2.3.

• **Extends (“”: pybamm.SubMesh1D) –

class pybamm.Chebyshev1DSubMesh(lims, npts, tabs=None)

A class to generate a submesh on a 1D domain using 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 edges, so that the mesh edges are given by

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

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.

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

• **Extends (“”: pybamm.SubMesh1D) –

class pybamm.UserSupplied1DSubMesh(lims, npts, edges=None)

A class to generate a submesh on a 1D domain from a user supplied array of edges.

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.

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

• **Extends (“”: pybamm.SubMesh1D) –