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 dictionary produced by e.g. pybamm.battery_geometry() after calling param.process_geometry(geometry).
Maps domain name → submesh class or MeshGenerator instance. Example:{
"negative electrode": pybamm.Uniform1DSubMesh,
"separator": pybamm.Uniform1DSubMesh,
"positive electrode": pybamm.Uniform1DSubMesh,
}
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
Uniformly spaced nodes across the domain.
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
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},
)
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,
}
var_pts = {"x_n": 10, "x_s": 5, "x_p": 10, "r_n": 10, "r_p": 10}
