NEOPAX._fem

Classes

FVMScheme

Functions

cell_centered_from_faces(face_values)	Average face values to cell centers.
faces_from_cell_centered(cell_values)	Average cell values to faces (interfaces).
conservative_update(flux, dx[, Vprime, Vprime_half, ...])	Update cell values using net flux and optional source, with optional volume weighting.
apply_dirichlet_flux(flux, left_bc, right_bc)	Set left/right boundary fluxes for Dirichlet BCs.
apply_neumann_flux(flux, grad_value, dr[, side])	Set boundary face flux for a Neumann BC: dQ/dr = grad_value at the boundary.
apply_robin_flux(flux, cell_value, decay_length, dr[, ...])	Set boundary face flux for a Robin/decay BC: dQ/dr = -Q/decay_length at the boundary.
set_dirichlet_ghosts(u, left_value, right_value)	Set Dirichlet BCs by assigning ghost cell values.
set_neumann_ghosts(u, grad_left, grad_right, dr)	Set Neumann BCs by assigning ghost cell values using gradients and dr.

Module Contents

NEOPAX._fem.cell_centered_from_faces(face_values)

Average face values to cell centers.

NEOPAX._fem.faces_from_cell_centered(cell_values)

Average cell values to faces (interfaces).

NEOPAX._fem.conservative_update(flux, dx, Vprime=None, Vprime_half=None, source=None)

Update cell values using net flux and optional source, with optional volume weighting. If Vprime and Vprime_half are provided, use stellarator volume form:

update = -1/(Vprime*dx) * (Vprime_half[1:] * flux[1:] - Vprime_half[:-1] * flux[:-1])

Otherwise, defaults to simple FVM.

Notes: - dx can be scalar (uniform spacing) or a per-cell array of shape (n_r,). - JAX broadcasting handles both modes.

NEOPAX._fem.apply_dirichlet_flux(flux, left_bc, right_bc)

Set left/right boundary fluxes for Dirichlet BCs.

NEOPAX._fem.apply_neumann_flux(flux, grad_value, dr, side='right')

Set boundary face flux for a Neumann BC: dQ/dr = grad_value at the boundary. For the right (edge) boundary, set flux[-1] so that:

(Q_edge - Q_interior)/dr = grad_value Q_edge = Q_interior + grad_value * dr

NEOPAX._fem.apply_robin_flux(flux, cell_value, decay_length, dr, side='right')

Set boundary face flux for a Robin/decay BC: dQ/dr = -Q/decay_length at the boundary. For the right (edge) boundary, set flux[-1] so that:

(Q_edge - Q_interior)/dr = -Q_edge/decay_length

Solving for Q_edge:

Q_edge = Q_interior / (1 + dr/decay_length)

NEOPAX._fem.set_dirichlet_ghosts(u, left_value, right_value)

Set Dirichlet BCs by assigning ghost cell values.

NEOPAX._fem.set_neumann_ghosts(u, grad_left, grad_right, dr)

Set Neumann BCs by assigning ghost cell values using gradients and dr.

class NEOPAX._fem.FVMScheme(field)

field

dr

Vprime

Vprime_half

conservative_update(flux)

extend_with_ghosts(arr)

apply_dirichlet_ghosts(arr)

faces_from_cell_centered(arr)