Python type FieldsplitSNES

[JHopeCollins]

Description

A nonlinear version of PCFieldsplit, this came out of a discussion on slack with @ScottMacLachlan, @pbrubeck, and Matt.

It can use either additive (Jacobi) or multiplicative (Gauss-Seidel) versions, exactly analogous to the linear version.

• Additive solves each "diagonal" block of the nonlinear problem for each field, with all other fields held at the current value.
• Multiplicative solves each "diagonal" block of the nonlinear problem for each field, and uses the updated values when solving for subsequent fields. Currently solves one field at a time, in the order they appear in the mixed space.

Still to do (mostly adding options to match PCFieldsplit):

• Allow grouping fields together with snes_fieldsplit_%d_fields.
• Allow setting the order of the field solves with snes_fieldsplit_%d_fields.
• Default fields with snes_fieldsplit_default.
• Default options with fieldsplit prefix. If we collect them in initialize and pass them as a dictionary to the NLVS of each field, they will take lower priority than any fieldsplit_%d options in the global dictionary (including those put there by the parent NLVS).
• view method.
• Does the update method need to contain anything?
• Documentation and demo.
• Proper test. The one I added now just checks that it runs without crashing.