Fix _SNESContext.options_prefix

[pbrubeck]

Description

Adds options prefix in _SNESContext.split in order to support
-mat_type matfree -fieldsplit_0_mg_coarse_mat_type aij

[JHopeCollins]

One comment about using the FunctionSpace name for components. Once we've sorted that this is good to go.

[pbrubeck]

One comment about using the FunctionSpace name for components. Once we've sorted that this is good to go.

What is enforcing it only using V.name if V has a single component?

The name of each single field subspace now gets propagated when we split the problem (this wasn't the case before). But if we split into a multi-field subspace we need to create a MixedFunctionSpace, and we never set the name kwarg for that case

[JHopeCollins]

One comment about using the FunctionSpace name for components. Once we've sorted that this is good to go.

What is enforcing it only using V.name if V has a single component?

The name of each single field subspace now gets propagated when we split the problem (this wasn't the case before). But if we split into a multi-field subspace we need to create a MixedFunctionSpace, and we never set the name kwarg for that case

But if we don't manually set the name of a MixedFunctionSpace then it gets set according to the names of the component spaces here:

firedrake/firedrake/functionspaceimpl.py

Line 1055 in ee52b41

self.name = name or "_".join(str(s.name) for s in spaces)

Addressed

[JHopeCollins]

LGTM