Refactor of FESpaceWithLinearConstraints

docs/src/dev-notes/constraints.md

@@ -0,0 +1,31 @@
+
+# FESpaceWithLinearConstraints
+
+This is a space built from an initial FESpace plus a set of linear constraints.
+The initial FESpace may also be a `FESpaceWithLinearConstraints`.
+
+## Assumptions
+
+- A constrained dof depends only on master dofs, i.e., only one level of constraints. This can be easily relaxed in the future.
+- Free dofs can be constrained both by free and Dirichlet dofs. Dirichlet dofs can be constrained by Dirichlet dofs only.
+- All constrained dofs belong to the original space. Master dofs will generally also belong to the original space, but they may be external. This allows us to have, e.g.
+  - External master Dirichlet dofs, to implement affine constraints.
+  - In distributed context, masters may belong to other processors and therefore NOT be local (and thus not belong to the original local space).
+
+## Notation
+
+We will setup some notation to differentiate between the different dof numberings that appear throughout the implementation:
+
+We have two ways of numbering dofs:
+
+- We will refer to `dof` in non-capital letters to refer to signed dof indices.
+  The sign will indicate if the dof is free (positive) or Dirichlet (negative).
+- We will refer to `DOF` in capital letters to refer to unsigned dof indices. In this case, Dirichlet dofs are also represented with a positive id "pas the end" of free dof ids. I.e., we have `DOF = dof` if `dof > 0` and `DOF = -dof + n_fdofs` if `dof < 0`, where `n_fdofs` is the number of free dofs in the original space.
+
+We will differentiate between three different sets of dofs:
+
+- First, DoFs in the original space will be denoted by `dof`/`DOF`. They can either be free (`fdof`) or Dirichlet (`ddof`).
+- Master DoFs are the non-constrained degrees of freedom. They will be denoted by `mdof`/`mDOF`. They can either be free (`fmdof`) or Dirichlet (`dmdof`).
+- Slave DoFs are the constrained degrees of freedom. They will be denoted by `sdof`/`sDOF`.
+
+Moreover, we will sometimes need to refer to local dofs in a cell, for which we will use `ldof` for the original space and `lmdof` for the constrained space.

src/FESpaces/FESpaces.jl

@@ -12,6 +12,7 @@ using SparseArrays
 using LinearAlgebra
 using StaticArrays
 using ForwardDiff
+using DataStructures
 
 using Gridap.Helpers
 using Gridap.Algebra