"""
This module provides some parameters sets that are good defaults
for particular kinds of system.
"""
from gusto.core.function_spaces import is_cg
__all__ = ['mass_parameters', 'hydrostatic_parameters']
[docs]
def mass_parameters(V, spaces=None, ignore_vertical=True):
"""
PETSc solver parameters for mass matrices.
Currently this sets to a monolithic CG+ILU.
TODO: implement field-by-field parameters that choose
preonly for discontinuous fields and CG for continuous
fields - see docstring below.
================= FUTURE DOCSTRING =================
Any fields which are discontinuous will have block diagonal
mass matrices, so are solved directly using:
'ksp_type': 'preonly'
'pc_type': 'ilu'
All continuous fields are solved with CG, with the preconditioner
being ILU independently on each field. By solving all continuous fields
"monolithically", the total number of inner products is minimised, which
is beneficial for scaling to large core counts because it minimises the
total number of MPI_Allreduce calls.
'ksp_type': 'cg'
'pc_type': 'fieldsplit'
'pc_fieldsplit_type': 'additive'
'fieldsplit_ksp_type': 'preonly'
'fieldsplit_pc_type': 'ilu'
Args:
spaces: Optional `Spaces` object. If present, any subspace
of V that came from the `Spaces` object will use the
continuity information from `spaces`.
If not present, continuity is checked with `is_cg`.
ignore_vertical: whether to include the vertical direction when checking
field continuity on extruded meshes. If True, only the horizontal
continuity will be considered, e.g. the standard theta space will
be treated as discontinuous.
"""
return {
'ksp_type': 'cg',
'pc_type': 'bjacobi',
'sub_pc_type': 'ilu'
}
extruded = hasattr(V.mesh, "_base_mesh")
continuous_fields = set()
for i, Vsub in enumerate(V.subfunctions):
# field = Vsub.name or str(i)
field = str(i)
if spaces is not None:
continuous = spaces.continuity.get(field, is_cg(Vsub))
else:
continuous = is_cg(Vsub)
# For extruded meshes the continuity is recorded
# separately for the horizontal and vertical directions.
if extruded and spaces is not None:
if ignore_vertical:
continuous = continuous['horizontal']
else:
continuous = (continuous['horizontal']
or continuous['vertical'])
if continuous:
continuous_fields.add(field)
if len(V.subfunctions) == 1:
parameters = {
'ksp_type': 'cg' if all(continuous_fields) else 'preonly',
'pc_type': 'bjacobi',
'sub_pc_type': 'ilu',
}
else:
parameters = {
'ksp_type': 'preonly',
'pc_type': 'fieldsplit',
'pc_fieldsplit_type': 'additive',
'pc_fieldsplit_0_fields': ','.join(continuous_fields),
'fieldsplit': {
'ksp_type': 'preonly',
'pc_type': 'bjacobi',
'sub_pc_type': 'ilu'
},
'fieldsplit_0_ksp_type': 'cg',
}
return parameters
hydrostatic_parameters = {
'mat_type': 'matfree',
'ksp_type': 'preonly',
'pc_type': 'python',
'pc_python_type': 'firedrake.SCPC',
# Velocity mass operator is singular in the hydrostatic case.
# So for reconstruction, we eliminate rho into u
'pc_sc_eliminate_fields': '1, 0',
'condensed_field': {
'ksp_type': 'fgmres',
'ksp_rtol': 1.0e-8,
'ksp_atol': 1.0e-8,
'ksp_max_it': 100,
'pc_type': 'gamg',
'pc_gamg_sym_graph': True,
'mg_levels': {
'ksp_type': 'gmres',
'ksp_max_it': 5,
'pc_type': 'bjacobi',
'sub_pc_type': 'ilu'
}
}
}