hermit.transfer

interpolate / project – transfer a hermit.Field between spaces on the same mesh.

interpolate is collocation: the source basis evaluated at the target dofs’ reference coordinates, a constant sparse matrix and therefore a plain csdl.sparse.matvec. It is fully differentiable in the coefficients and independent of the geometry. This holds for identity-mapped, point-evaluation elements – Lagrange, DG, DQ and Quadrature, which covers every space these builders produce. Piola-mapped families such as RT and Nedelec are rejected, as is the Crouzeix-Raviart rotation space of the CG2CR1 element.

project is the L2 alternative, M c = int(phi_target . src) dx. Both sides carry dx, so it depends on the geometry: it is a custom operation with the mass-matrix quotient-rule VJP, reverse mode only. Its optional geometry= argument defaults to the domain’s reference coordinates, which keeps the mass factorization cached; passing a live geometry enables the shape-derivative branch.

Functions

`interpolate`(→ hermit._field.Field)	Collocate a field at another space's dof points -- the default transfer.
`project`(→ hermit._field.Field)	L2-project a field onto another space, `M c = int(phi_target . src) dx`.

Module Contents

hermit.transfer.interpolate(src_field, space) → hermit._field.Field

Collocate a field at another space’s dof points – the default transfer.

Parameters:

src_fieldField
spacetuple: Target space; its value shape must match the source’s.

Returns:

Field: On the target space, or src_field itself if already there.

Raises:

ValueError: If the value shapes differ, or if either space is not point-evaluation (Lagrange, DG, DQ or Quadrature). Piola-mapped families such as RT and Nedelec drag in the geometric Jacobian and are rejected, as does Crouzeix-Raviart. A Quadrature source has no basis to tabulate – use project().