dragonfly_sim.core.wall_distance
================================

.. py:module:: dragonfly_sim.core.wall_distance

.. autoapi-nested-parse::

   Distance to the wall, as a CG1 DerivedField with an exact mesh derivative.

   d at every CG1 node is the distance to the nearest wall facet: the exact
   point-to-segment distance for the straight 2D wall facets, the distance to
   the nearest wall vertex in 3D (an over-estimate between vertices). The
   nearest facets are found with a KD-tree over the facet midpoints (2D) or
   the wall vertices (3D).

   mesh_jacobian() is the analytic derivative of every nodal distance with
   respect to the coordinates of the node itself and of the wall vertices of
   its nearest facet. With P the nearest point on segment AB, t its parameter
   and r = (x - P)/d,

       dd/dx = r,    dd/dA = -(1 - t) r,    dd/dB = -t r

   (t is stationary at an interior foot point, so it does not move to first
   order; at a clipped end, t = 0 or 1, the same formula holds). On the wall
   itself, d = 0 and the node moves with the wall, so the row is zero. The
   derivative is exact wherever the nearest facet does not switch, i.e.
   almost everywhere.

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Classes
-------

.. autoapisummary::

   dragonfly_sim.core.wall_distance.WallDistance


Functions
---------

.. autoapisummary::

   dragonfly_sim.core.wall_distance._nearest_segments


Module Contents
---------------

.. py:class:: WallDistance(mesh_obj, wall_tags)

   Bases: :py:obj:`dragonfly_sim.utils.derived_fields.DerivedField`


   
   Interface. `function` is the dolfinx Function the forms read.

   update()                 recompute the field at the current state and mesh
   update_geometry()        refresh whatever depends on the mesh only (called
                            after mesh motion, before update())
   state_jacobian()         PETSc Mat d(field)/dU (only if depends_on_state)
   alpha_vector()           PETSc Vec d(field)/dalpha, or None
   mesh_jacobian()          PETSc Mat d(field)/dx, columns in the mesh's
                            coordinate_space, or None















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   .. py:method:: _geometry_node_to_dof()

      
      Local geometry node -> local coordinate_space block (both ghosted).
















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   .. py:method:: _wall_geometry()

      
      Wall segment endpoints (2D) or vertices (3D) on every rank, with the
      global coordinate_space block index of each endpoint.
















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   .. py:method:: mesh_jacobian()


   .. py:method:: update_geometry()


   .. py:attribute:: function


   .. py:attribute:: mesh_obj


   .. py:attribute:: wall_tags


.. py:function:: _nearest_segments(x, A, B, k=16)

   
   Index of the nearest segment, foot parameter t and foot point, per point.
















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