Mesh

The Mesh class assembles a collection of submeshes across all model domains. Submesh types and the number of grid points are configured via the submesh_types and var_pts dictionaries.

The mesh defines how each domain in the battery geometry is divided into discrete cells. PyBaMM provides several 1D submesh types with different node distributions, plus a 2D submesh for current-collector problems.

pybamm.Mesh

pybamm.Mesh(geometry, submesh_types, var_pts)

geometry · dict · required

Geometry dictionary produced by e.g. pybamm.battery_geometry() after calling param.process_geometry(geometry).

submesh_types · dict · required

Maps domain name → submesh class or MeshGenerator instance. Example:

{
    "negative electrode": pybamm.Uniform1DSubMesh,
    "separator": pybamm.Uniform1DSubMesh,
    "positive electrode": pybamm.Uniform1DSubMesh,
}

var_pts · dict · required

Maps spatial variable → number of cell-centre nodes. Can use variable objects or name strings as keys:

{pybamm.standard_spatial_vars.x_n: 10,
 pybamm.standard_spatial_vars.x_s: 5,
 pybamm.standard_spatial_vars.x_p: 10,
 pybamm.standard_spatial_vars.r_n: 10,
 pybamm.standard_spatial_vars.r_p: 10}

import pybamm

model = pybamm.lithium_ion.SPM()
param = pybamm.ParameterValues("Chen2020")

geometry = model.default_geometry
param.process_geometry(geometry)

var_pts = {
    pybamm.standard_spatial_vars.x_n: 10,
    pybamm.standard_spatial_vars.x_s: 5,
    pybamm.standard_spatial_vars.x_p: 10,
    pybamm.standard_spatial_vars.r_n: 10,
    pybamm.standard_spatial_vars.r_p: 10,
}

submesh_types = model.default_submesh_types

mesh = pybamm.Mesh(geometry, submesh_types, var_pts)

---

pybamm.MeshGenerator

A thin wrapper that pairs a submesh class with any extra keyword arguments needed at construction time.

pybamm.MeshGenerator(submesh_type, submesh_params=None)

# Exponential mesh, clustered symmetrically
generator = pybamm.MeshGenerator(
    pybamm.Exponential1DSubMesh,
    submesh_params={"side": "symmetric", "stretch": 1.5},
)

submesh_types = {
    "negative electrode": generator,
    "separator": pybamm.Uniform1DSubMesh,
    "positive electrode": generator,
}

---

Submesh Types

Uniform1DSubMesh

Uniformly spaced nodes across the domain.

pybamm.Uniform1DSubMesh

Best for homogeneous domains with no boundary layers.

---

Exponential1DSubMesh

Exponentially stretched nodes — concentrated near one or both boundaries.

pybamm.MeshGenerator(
    pybamm.Exponential1DSubMesh,
    submesh_params={"side": "symmetric", "stretch": 1.15},
)

side · str · default: "\"symmetric\""

Which boundary to cluster near: "left", "right", or "symmetric".

stretch · float · default: "1.15 (symmetric) / 2.3 (left or right)"

Stretching factor α. As node count → ∞, the ratio of largest to smallest cell → exp(α).

---

Chebyshev1DSubMesh

Nodes placed at Chebyshev collocation points on (a, b), clustered near both boundaries.

pybamm.Chebyshev1DSubMesh

Useful when you need polynomial interpolation properties or are solving with spectral methods.

---

UserSupplied1DSubMesh

Use your own array of edge locations.

import numpy as np

edges = np.array([0, 0.1, 0.3, 0.6, 1.0])  # custom edge positions

generator = pybamm.MeshGenerator(
    pybamm.UserSupplied1DSubMesh,
    submesh_params={"edges": edges},
)

---

Uniform2DSubMesh

Uniform 2D mesh for current-collector domains. Requires ScikitFiniteElement as the corresponding spatial method.

---

Controlling Resolution with var_pts

The var_pts dictionary is the primary knob for trading accuracy against speed:

# Coarse mesh — fast
var_pts_coarse = {
    pybamm.standard_spatial_vars.x_n: 5,
    pybamm.standard_spatial_vars.x_s: 3,
    pybamm.standard_spatial_vars.x_p: 5,
    pybamm.standard_spatial_vars.r_n: 5,
    pybamm.standard_spatial_vars.r_p: 5,
}

# Fine mesh — accurate
var_pts_fine = {
    pybamm.standard_spatial_vars.x_n: 30,
    pybamm.standard_spatial_vars.x_s: 15,
    pybamm.standard_spatial_vars.x_p: 30,
    pybamm.standard_spatial_vars.r_n: 30,
    pybamm.standard_spatial_vars.r_p: 30,
}

String keys are also accepted:

var_pts = {"x_n": 10, "x_s": 5, "x_p": 10, "r_n": 10, "r_p": 10}