hermit.fenics.assembly
======================

.. py:module:: hermit.fenics.assembly

.. autoapi-nested-parse::

   Thin PETSc/UFL assembly helpers for DOLFINx (0.9 / 0.11).

   Slim port of the pieces of ``femo_alpha/fea/utils_dolfinx.py`` that Hermit's custom
   operations actually need. No CSDL here.

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Functions
---------

.. autoapisummary::

   hermit.fenics.assembly.assemble_matrix
   hermit.fenics.assembly.assemble_scalar
   hermit.fenics.assembly.assemble_vector
   hermit.fenics.assembly.derivative
   hermit.fenics.assembly.get_array
   hermit.fenics.assembly.ksp_mumps
   hermit.fenics.assembly.matvec
   hermit.fenics.assembly.owned_entry_mask
   hermit.fenics.assembly.owning_cell
   hermit.fenics.assembly.project
   hermit.fenics.assembly.rmatvec
   hermit.fenics.assembly.set_array
   hermit.fenics.assembly.transpose


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

.. py:function:: assemble_matrix(a, bcs=()) -> petsc4py.PETSc.Mat

   
   Assemble a 2-form to an assembled PETSc matrix.
















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.. py:function:: assemble_scalar(f) -> float

   
   Assemble a scalar UFL form to a float.
















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.. py:function:: assemble_vector(f) -> numpy.ndarray

   
   Assemble a 1-form to a numpy array.
















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.. py:function:: derivative(f, u, du=None)

   
   d f / d u as a UFL form (or w.r.t. a coefficient / SpatialCoordinate).
















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.. py:function:: get_array(f: dolfinx.fem.Function) -> numpy.ndarray

   
   Local array of a Function (owned + ghost).
















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.. py:function:: ksp_mumps(A: petsc4py.PETSc.Mat) -> petsc4py.PETSc.KSP

   
   A preonly + LU(MUMPS) KSP for the (already assembled) operator ``A``.
















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.. py:function:: matvec(A: petsc4py.PETSc.Mat, x: dolfinx.fem.Function) -> numpy.ndarray

   
   A @ x  (x a Function, result a numpy array of A's row layout).
















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.. py:function:: owned_entry_mask(dofmap_list, n_scalar_dofs)

   
   ``(n_cells, n_local_nodes)`` bool -- True where the cell owns that dof.
















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.. py:function:: owning_cell(dofmap_list, n_scalar_dofs)

   
   ``scalar dof -> the cell that writes it last`` in ascending cell order.

   ``Function.interpolate`` scatters a point evaluation per cell, so a shared
   (continuous) target dof is written once per adjacent cell and the last writer
   wins. The interpolation *Jacobian* must therefore carry only the owning cell's
   row -- taking the union of every adjacent cell's contribution (which is what a
   plain COO scatter does, since each cell contributes on its own source columns)
   over-counts it. Deduplicating (row, col) pairs is not enough: the columns
   mostly differ, so the duplicates never collide.

   Same construction as ``hermit._field._Tabulation.dof_cell``, and a no-op on DG
   (every dof has exactly one cell).















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.. py:function:: project(expr, target: dolfinx.fem.Function, lump_mass: bool = False) -> None

   
   L2-project a UFL expression onto ``target``'s space (used for field outputs).
















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.. py:function:: rmatvec(A: petsc4py.PETSc.Mat, x: dolfinx.fem.Function) -> numpy.ndarray

   
   A.T @ x.
















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.. py:function:: set_array(f: dolfinx.fem.Function, values) -> None

   
   Set a Function from a flat array and sync ghosts.
















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.. py:function:: transpose(A: petsc4py.PETSc.Mat) -> petsc4py.PETSc.Mat