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Basis Conversion (Rebase)

rebase() converts a mesh from one set of basis functions to another by:

  1. Computing the new node positions from the current geometry.
  2. Sampling a dense xi grid on the current mesh.
  3. Linearly fitting the new nodal parameters to match the sampled geometry.

This is the recommended way to build high-order meshes: start with a coarse Lagrange mesh that is easy to set up manually, then rebase to a higher-order or Hermite basis.

Trilinear → Cubic Hermite Conversion

import numpy as np
from HOMER import Mesh, MeshNode, MeshElement, L1Basis, H3Basis

# 1. Create a coarse trilinear mesh (L1 × L1 × L1)
nodes = [MeshNode(loc=[x, y, z])
         for x in [0., 1.] for y in [0., 1.] for z in [0., 1.]]
element = MeshElement(node_indexes=list(range(8)),
                      basis_functions=(L1Basis, L1Basis, L1Basis))
seed = Mesh(nodes=nodes, elements=element)

# 2. Rebase to cubic Hermite
mesh = seed.rebase([H3Basis, H3Basis, H3Basis])

# The resulting mesh has the same shape but smooth H3 interpolation
mesh.plot()

Converting a 2-D Manifold Mesh

The same workflow applies to 2-D surface meshes:

from HOMER import L1Basis, H3Basis

# Linear seed
seed_2d = Mesh(nodes=four_nodes, elements=MeshElement(
    node_indexes=[0,1,2,3], basis_functions=(L1Basis, L1Basis)))

# Convert to cubic Hermite surface
smooth_2d = seed_2d.rebase([H3Basis, H3Basis])

Rebase to Lagrange Basis

You can also rebase from Hermite to Lagrange (e.g. for export or compatibility with other solvers):

from HOMER import L3Basis

lagrange_mesh = hermite_mesh.rebase([L3Basis, L3Basis, L3Basis])

Resolution Control

The res parameter of rebase() controls how many xi samples are used for the linear fit. Increase it for better accuracy when rebasing to a significantly different basis:

mesh = seed.rebase([H3Basis]*3, res=20)  # default res=10

Notes

  • rebase() always returns a new MeshField object. The original mesh is not modified.