Quadratic complexity of dense matrix allocation (e.g., on Real space)

[Jan Blechta]

Quadratic complexity of sparsity pattern allocation has already been resolved by pull request #255. It remains to allocate PETSc matrix using full sparsity pattern data (full pattern mode) as distinct from using just number of non-zeros (num nonzeros mode) in rows which is efficient for sparse matrices. There are few options:

1. Have both num nonzeros and full pattern modes and allow switching them by parameter/argument/TensorLayout interface/SparsityPatternBuilder interface, etc.

2. Have both num nonzeros and full pattern modes and detect a need for using latter automatically.

3. Drop num nonzeros mode and use full pattern mode exclusively. This has been tested by pull request #255 and seemed to have no serious regression.

Investigate the situation with other backends as well.

[Jan Blechta]

@garth-wells, what's the current status of PETScMatrix? Can it be touched now? (You asked me to postpone the fix before as you had MatNest plans with @chris_richardson.)

[Jan Blechta]

Insert dense rows in increasing column order before assembly

This avoid dense rows being inserted in random colun index order during asembly resulting in quadraric complexity. Resolves issue #713.

→ <<cset c8f999c8a87e>>

[Jan Blechta]

Not in master. Possible fix in either in pull request #368 or pull request #369.

[Jan Blechta]

Fixed by pull request #369, commit 2f6a32f.