# Source code for imod.wq.slv

```
from imod.wq.pkgbase import Package
import numpy as np
import pathlib
import pandas as pd
from imod import util
[docs]class PreconditionedConjugateGradientSolver(Package):
"""
The Preconditioned Conjugate Gradient Solver is used to solve the finite
difference equations in each step of a MODFLOW stress period.
Parameters
----------
max_iter: int
is the maximum number of outer iterations - that is, calss to the
solutions routine (MXITER). For a linear problem max_iter should be 1, unless
more than 50 inner iterations are required, when max_iter could be as
large as 10. A larger number (generally less than 100) is required for a
nonlinear problem.
inner_iter: int
is the number of inner iterations (iter1). For nonlinear problems,
inner_iter usually ranges from 10 to 30; a value of 30 will be
sufficient for most linear problems.
rclose: float
is the residual criterion for convergence, in units of cubic length per
time. The units for length and time are the same as established for all
model data. When the maximum absolute value of the residual at all nodes
during an iteration is less than or equal to RCLOSE, and the criterion
for HCLOSE is also satisfied (see below), iteration stops.
Default value: 100.0. **Nota bene**: this is aimed at regional modelling.
For detailed studies (e.g. lab experiments) much smaller values can be
required.
Very general rule of thumb: should be less than 10% of smallest cell volume.
hclose: float
is the head change criterion for convergence, in units of length. When
the maximum absolute value of head change from all nodes during an
iteration is less than or equal to HCLOSE, and the criterion for RCLOSE
is also satisfied (see above), iteration stops.
Default value: 1.0e-4. **Nota bene**: This is aimed at regional modelling, `
for detailed studies (e.g. lab experiments) much smaller values can be
required.
relax: float, optional
is the relaxation parameter used. Usually, RELAX = 1.0, but for some
problems a value of 0.99, 0.98, or 0.97 will reduce the number of
iterations required for convergence.
Default value: 0.98.
damp: float, optional
is the damping factor. It is typically set equal to one, which indicates
no damping. A value less than 1 and greater than 0 causes damping. DAMP
does not affect inner iterations; instead, it affects outer iterations.
Default value: 1.0.
"""
__slots__ = ("max_iter", "inner_iter", "rclose", "hclose", "relax", "damp")
_pkg_id = "pcg"
_template = (
"[pcg]\n"
" mxiter = {max_iter}\n"
" iter1 = {inner_iter}\n"
" npcond = 1\n"
" hclose = {hclose}\n"
" rclose = {rclose}\n"
" relax = {relax}\n"
" iprpcg = 1\n"
" mutpcg = 0\n"
" damp = {damp}"
)
def __init__(
self,
max_iter=150,
inner_iter=100,
rclose=1000.0,
hclose=1.0e-4,
relax=0.98,
damp=1.0,
):
super(__class__, self).__init__()
self["max_iter"] = max_iter
self["inner_iter"] = inner_iter
self["rclose"] = rclose
self["hclose"] = hclose
self["relax"] = relax
self["damp"] = damp
def _pkgcheck(self, ibound=None):
to_check = ["max_iter", "inner_iter", "rclose", "hclose", "damp"]
self._check_positive(to_check)
[docs]class GeneralizedConjugateGradientSolver(Package):
"""
The Generalized Conjugate Gradient Solver solves the matrix equations
resulting from the implicit solution of the transport equation.
Parameters
----------
max_iter: int
is the maximum number of outer iterations (MXITER); it should be set to an
integer greater than one (1) only when a nonlinear sorption isotherm is
included in simulation.
iter1: int
is the maximum number of inner iterations (iter1); a value of 30-50
should be adequate for most problems.
isolve: int
is the type of preconditioners to be used with the Lanczos/ORTHOMIN
acceleration scheme:
isolve = 1: Jacobi
isolve = 2: SSOR
isolve = 3: Modified Incomplete Cholesky (MIC)
(MIC usually converges faster, but it needs significantly more memory)
lump_dispersion: bool
is an integer flag for treatment of dispersion tensor cross terms:
ncrs = 0: lump all dispersion cross terms to the right-hand-side
(approximate but highly efficient).
ncrs = 1: include full dispersion tensor (memory intensive).
cclose: float
is the convergence criterion in terms of relative concentration; a real
value between 10-4 and 10-6 is generally adequate.
"""
__slots__ = (
"max_iter",
"inner_iter",
"cclose",
"preconditioner",
"lump_dispersion",
)
_pkg_id = "gcg"
_template = (
"[gcg]\n"
" mxiter = {max_iter}\n"
" iter1 = {inner_iter}\n"
" isolve = {preconditioner}\n"
" ncrs = {lump_dispersion}\n"
" cclose = {cclose}\n"
" iprgcg = 0"
)
_keywords = {
"preconditioner": {"jacobi": 1, "ssor": 2, "mic": 3},
"lump_dispersion": {True: 0, False: 1},
}
def __init__(
self,
max_iter=1,
inner_iter=50,
cclose=1.0e-6,
preconditioner="mic",
lump_dispersion=True,
):
super(__class__, self).__init__()
self["max_iter"] = max_iter
self["inner_iter"] = inner_iter
self["cclose"] = cclose
self["preconditioner"] = preconditioner
self["lump_dispersion"] = lump_dispersion
def _pkgcheck(self, ibound=None):
to_check = ["max_iter", "inner_iter", "cclose"]
self._check_positive(to_check)
class ParallelSolver(Package):
"""
Base package for the parallel solvers.
"""
__slots__ = ()
def _compute_load_balance_weight(self, ibound):
if self["partition"] == "rcb":
if self["load_balance_weight"].values[()] is None:
self["load_balance_weight"] = (ibound != 0).sum("layer").astype(float)
def _render(self, directory):
d = {k: v.values for k, v in self.data_vars.items()}
if hasattr(self, "_keywords"):
for key in self._keywords.keys():
self._replace_keyword(d, key)
if self["partition"] == "rcb":
d["load_balance_weight"] = self._compose(
{
"directory": directory,
"name": "load_balance_weight",
"extension": ".asc",
}
)
return self._template.format(**d)
def save(self, directory):
"""
Overloaded method to write .asc instead of .idf.
(This is an idiosyncracy of the parallel iMODwq code.)
"""
# TODO: remove this when iMOD_wq accepts idfs for the load grid.
da = self["load_balance_weight"]
if not da.dims == ("y", "x"):
raise ValueError(
"load_balance_weight dimensions must be exactly ('y', 'x')."
)
path = pathlib.Path(directory).joinpath("load_balance_weight.asc")
path.parent.mkdir(exist_ok=True, parents=True)
pd.DataFrame(da.values).to_csv(
path, sep="\t", header=False, index=False, float_format="%8.2f"
)
[docs]class ParallelKrylovFlowSolver(ParallelSolver):
"""
The Parallel Krylov Flow Solver is used for parallel solving of the flow
model.
Parameters
----------
max_iter: int
is the maximum number of outer iterations (MXITER); it should be set to
an integer greater than one (1) only when a nonlinear sorption isotherm
is included in simulation.
inner_iter: int
is the maximum number of inner iterations (INNERIT); a value of 30-50
should be adequate for most problems.
hclose: float
is the head change criterion for convergence (HCLOSEPKS), in units of
length. When the maximum absolute value of head change from all nodes
during an iteration is less than or equal to HCLOSE, and the criterion
for RCLOSE is also satisfied (see below), iteration stops.
rclose: float
is the residual criterion for convergence (RCLOSEPKS), in units of cubic
length per time. The units for length and time are the same as
established for all model data. When the maximum absolute value of the
residual at all nodes during an iteration is less than or equal to
RCLOSE, and the criterion for HCLOSE is also satisfied (see above),
iteration stops.
relax: float
is the relaxation parameter used. Usually, RELAX = 1.0, but for some
problems a value of 0.99, 0.98, or 0.97 will reduce the number of
iterations required for convergence.
h_fstrict: float, optional
is a factor to apply to HCLOSE to set a stricter hclose for the linear
inner iterations (H_FSTRICTPKS). HCLOSE_inner is calculated as follows:
HCLOSEPKS * H_FSTRICTPKS.
r_fstrict: float, optional
is a factor to apply to RCLOSE to set a stricter rclose for the linear
inner iterations (R_FSTRICTPKS). RCLOSE_inner is calculated as follows:
RCLOSEPKS * R_FSTRICTPKS.
partition: {"uniform", "rcb"}, optional
Partitioning option (PARTOPT). "uniform" partitions the model domain
into equally sized subdomains. "rcb" (Recursive Coordinate Bisection)
uses a 2D pointer grid with weights to partition the model domain.
Default value: "uniform"
solver: {"pcg"}, optional
Flag indicating the linear solver to be used (ISOLVER).
Default value: "pcg"
preconditioner: {"ilu"}, optional
Flag inicating the preconditioner to be used (NPC).
Devault value: "ilu"
deflate: {True, False}, optional
Flag for deflation preconditioner.
Default value: False
debug: {True, False}, optional
Debug option.
Default value: False
load_balance_weight: xarray.DataArray, optional
2D grid with load balance weights, used when partition = "rcb"
(Recursive Coordinate Bisection). If None (default), then the module
will create a load balance grid by summing active cells over layers:
`(ibound != 0).sum("layer")`
Note that even though the iMOD-SEAWAT helpfile states .idf is
accepted, it is not. This load balance grid should be a .asc file
(without a header). Formatting is done as follows:
`pd.DataFrame(load_balance_weight.values).to_csv(path, sep='\\t',
header=False, index=False, float_format = "%8.2f")`
"""
__slots__ = ()
_pkg_id = "pksf"
_template = (
"[pksf]\n"
" mxiter = {max_iter}\n"
" innerit = {inner_iter}\n"
" hclosepks = {hclose}\n"
" rclosepks = {rclose}\n"
" relax = {relax}\n"
" h_fstrictpks = {h_fstrict}\n"
" r_fstrictpks = {r_fstrict}\n"
" partopt = {partition}\n"
" isolver = {solver}\n"
" npc = {preconditioner}\n"
" npcdef = {deflate}\n"
" loadptr = {load_balance_weight}\n"
" pressakey = {debug}\n"
)
_keywords = {
"partition": {"uniform": 0, "rcb": 5},
"solver": {"pcg": 1},
"preconditioner": {"ilu": 2},
"deflate": {False: 0, True: 1},
}
def __init__(
self,
max_iter=150,
inner_iter=100,
hclose=1.0e-4,
rclose=1000.0,
relax=0.98,
h_fstrict=1.0,
r_fstrict=1.0,
partition="uniform",
solver="pcg",
preconditioner="ilu",
deflate=False,
debug=False,
load_balance_weight=None,
):
super(__class__, self).__init__()
self["max_iter"] = max_iter
self["inner_iter"] = inner_iter
self["hclose"] = hclose
self["rclose"] = rclose
self["relax"] = relax
self["h_fstrict"] = h_fstrict
self["r_fstrict"] = r_fstrict
self["partition"] = partition
self["solver"] = solver
self["preconditioner"] = preconditioner
self["deflate"] = deflate
self["debug"] = debug
self["load_balance_weight"] = load_balance_weight
def _pkgcheck(self, ibound=None):
to_check = [
"hclose",
"rclose",
"h_fstrict",
"r_fstrict",
"max_iter",
"inner_iter",
"relax",
]
self._check_positive(to_check)
# TODO: fix
## Check whether option is actually an available option
# for opt_arg in self._keywords.keys():
# if self[opt_arg] not in self._keywords[opt_arg].keys():
# raise ValueError(
# "Argument for {} not in {}, instead got {}".format(
# opt_arg, self._keywords[opt_arg].keys(), self[opt_arg]
# )
# )
#
[docs]class ParallelKrylovTransportSolver(ParallelSolver):
"""
The Parallel Krylov Transport Solver is used for parallel solving of the
transport model.
Parameters
----------
max_iter: int
is the maximum number of outer iterations (MXITER); it should be set to
an integer greater than one (1) only when a nonlinear sorption isotherm
is included in simulation.
inner_iter: int
is the maximum number of inner iterations (INNERIT); a value of 30-50
should be adequate for most problems.
cclose: float, optional
is the convergence criterion in terms of relative concentration; a real
value between 10-4 and 10-6 is generally adequate.
Default value: 1.0e-6.
relax: float, optional
is the relaxation parameter used. Usually, RELAX = 1.0, but for some
problems a value of 0.99, 0.98, or 0.97 will reduce the number of
iterations required for convergence.
Default value: 0.98.
partition: {"uniform", "rcb"}, optional
Partitioning option (PARTOPT). "uniform" partitions the model domain
into equally sized subdomains. "rcb" (Recursive Coordinate Bisection)
uses a 2D pointer grid with weights to partition the model domain.
Default value: "uniform".
solver: {"bicgstab", "gmres", "gcr"}, optional
Flag indicating the linear solver to be used (ISOLVER).
Default value: "bicgstab"
preconditioner: {"ilu"}, optional
Flag inicating the preconditioner to be used (NPC).
Devault value: "ilu".
debug: {True, False}, optional
Debug option.
Default value: False
load_balance_weight: xarray.DataArray, optional
2D grid with load balance weights, used when partition = "rcb"
(Recursive Coordinate Bisection). If None (default), then the module
will create a load balance grid by summing active cells over layers:
`(ibound != 0).sum("layer")`
Note that even though the iMOD-SEAWAT helpfile states .idf is
accepted, it is not. This load balance grid should be a .asc file
(without a header). Formatting is done as follows:
`pd.DataFrame(load_balance_weight.values).to_csv(path, sep='\\t',
header=False, index=False, float_format = "%8.2f")`
"""
__slots__ = ()
_pkg_id = "pkst"
_template = (
"[pkst]\n"
" mxiter = {max_iter}\n"
" innerit = {inner_iter}\n"
" cclosepks = {cclose}\n"
" relax = {relax}\n"
" partopt = {partition}\n"
" isolver = {solver}\n"
" npc = {preconditioner}\n"
" loadptr = {load_balance_weight}\n"
" pressakey = {debug}\n"
)
_keywords = {
"partition": {"uniform": 0, "rcb": 5},
"solver": {"bicgstab": 2, "gmres": 3, "gcr": 4},
"preconditioner": {"ilu": 2},
}
def __init__(
self,
max_iter=1,
inner_iter=50,
cclose=1.0e-6,
relax=0.98,
partition="uniform",
solver="bicgstab",
preconditioner="ilu",
debug=False,
load_balance_weight=None,
):
super(__class__, self).__init__()
self["max_iter"] = max_iter
self["inner_iter"] = inner_iter
self["cclose"] = cclose
self["relax"] = relax
self["partition"] = partition
self["solver"] = solver
self["preconditioner"] = preconditioner
self["debug"] = debug
self["load_balance_weight"] = load_balance_weight
def _pkgcheck(self, ibound=None):
to_check = ["cclose", "max_iter", "inner_iter", "relax"]
self._check_positive(to_check)
# TODO: fix
## Check whether option is actually an available option
# for opt_arg in self._keywords.keys():
# if self[opt_arg] not in self._keywords[opt_arg].keys():
# raise ValueError(
# "Argument for {} not in {}, instead got {}".format(
# opt_arg, self._keywords[opt_arg].keys(), self[opt_arg]
# )
# )
```