"""
Defines an explicit solver using multiprocessing via MPI
.. codeauthor:: David Zwicker <david.zwicker@ds.mpg.de>
"""
from typing import Callable, List, Union
import numpy as np
from numba.extending import register_jitable
from ..fields.base import FieldBase
from ..grids._mesh import GridMesh
from ..pdes.base import PDEBase
from ..tools import mpi
from ..tools.math import OnlineStatistics
from .explicit import ExplicitSolver
[docs]class ExplicitMPISolver(ExplicitSolver):
"""class for solving partial differential equations explicitly using MPI
This solver can only be used if MPI is properly installed.
The main idea of the solver is to take the full initial state in the main node
(ID 0) and split the grid into roughly equal subgrids. The main node then
distributes these subfields to all other nodes and each node creates the right hand
side of the PDE for itself (and independently). Each node then advances the PDE
independently, ensuring proper coupling to neighboring nodes via special boundary
conditions, which exchange field values between sub grids. This is implemented by
the :meth:`get_boundary_conditions` method of the sub grids, which takes the
boundary conditions for the full grid and creates conditions suitable for the
specific sub grid on the given node. The trackers (and thus all input and output)
are only handled on the main node.
Warning:
`modify_after_step` can only be used to do local modifications since the field
data supplied to the function is local to each MPI node.
"""
name = "explicit_mpi"
def __init__(
self,
pde: PDEBase,
scheme: str = "euler",
decomposition: Union[int, List[int]] = -1,
*,
backend: str = "auto",
adaptive: bool = False,
tolerance: float = 1e-4,
):
"""
Args:
pde (:class:`~pde.pdes.base.PDEBase`):
The instance describing the pde that needs to be solved
scheme (str):
Defines the explicit scheme to use. Supported values are 'euler' and
'runge-kutta' (or 'rk' for short).
decomposition (list of ints):
Number of subdivision in each direction. Should be a list of length
`grid.num_axes` specifying the number of nodes along this axis. If one
value is `-1`, its value will be determined from the number of available
nodes. The default value decomposed the first axis using all available
nodes.
backend (str):
Determines how the function is created. Accepted values are 'numpy` and
'numba'. Alternatively, 'auto' lets the code decide for the most optimal
backend.
adaptive (bool):
When enabled, the time step is adjusted during the simulation using the
error tolerance set with `tolerance`.
tolerance (float):
The error tolerance used in adaptive time stepping. This is used in
adaptive time stepping to choose a time step which is small enough so
the truncation error of a single step is below `tolerance`.
"""
super().__init__(
pde, scheme=scheme, backend=backend, adaptive=adaptive, tolerance=tolerance
)
self.decomposition = decomposition
def _make_error_synchronizer(self) -> Callable[[float], float]:
"""return helper function that synchronizes errors between multiple processes"""
if mpi.parallel_run:
# in a parallel run, we need to return the maximal error
from numba_mpi import Operator
from ..tools.mpi import mpi_allreduce
operator_max_int = int(Operator.MAX)
@register_jitable
def synchronize_errors(error: float) -> float:
"""return maximal error accross all cores"""
return mpi_allreduce(error, operator_max_int) # type: ignore
return synchronize_errors # type: ignore
else:
return super()._make_error_synchronizer()
[docs] def make_stepper(
self, state: FieldBase, dt=None
) -> Callable[[FieldBase, float, float], float]:
"""return a stepper function using an explicit scheme
Args:
state (:class:`~pde.fields.base.FieldBase`):
An example for the state from which the grid and other information can
be extracted
dt (float):
Time step of the explicit stepping. If `None`, this solver specifies
1e-3 as a default value.
Returns:
Function that can be called to advance the `state` from time `t_start` to
time `t_end`. The function call signature is `(state: numpy.ndarray,
t_start: float, t_end: float)`
"""
if not mpi.parallel_run:
self._logger.warning(
"Using `ExplicitMPISolver` without a proper multiprocessing run. "
"Scripts need to be started with `mpiexec` to profit from multiple cores"
)
if dt is None:
# support `None` as a default value, so the controller can signal that
# the solver should use a default time step
dt = 1e-3
if not self.adaptive:
self._logger.warning(
"Explicit stepper with a fixed time step did not receive any "
f"initial value for `dt`. Using dt={dt}, but specifying a value or "
"enabling adaptive stepping is advisable."
)
self.info["dt"] = dt
self.info["steps"] = 0
self.info["state_modifications"] = 0.0
self.info["use_mpi"] = True
self.info["scheme"] = self.scheme
# decompose the state into multiple cells
self.mesh = GridMesh.from_grid(state.grid, self.decomposition)
sub_state = self.mesh.extract_subfield(state)
self.info["grid_decomposition"] = self.mesh.shape
if self.adaptive:
# create stepper with adaptive steps
self.info["dt_statistics"] = OnlineStatistics()
adaptive_stepper = self._make_adaptive_stepper(sub_state, dt)
def wrapped_stepper(
state: FieldBase, t_start: float, t_end: float
) -> float:
"""advance `state` from `t_start` to `t_end` using adaptive steps"""
nonlocal dt # `dt` stores value for the next call
# distribute the end time and the field to all nodes
t_end = self.mesh.broadcast(t_end)
substate_data = self.mesh.split_field_data_mpi(state.data)
# evolve the sub state
t_last, dt, steps, modifications = adaptive_stepper(
substate_data, t_start, t_end, dt, self.info["dt_statistics"]
)
# check whether dt is the same for all processes
dt_list = self.mesh.allgather(dt)
if not np.isclose(min(dt_list), max(dt_list)):
# abort simulations in all nodes when they went out of sync
raise RuntimeError(f"Processes went out of sync: dt={dt_list}")
# collect the data from all nodes
modification_list = self.mesh.gather(modifications)
self.mesh.combine_field_data_mpi(substate_data, out=state.data)
if mpi.is_main:
self.info["steps"] += steps
self.info["state_modifications"] += sum(modification_list) # type: ignore
return t_last
else:
# create stepper with fixed steps
fixed_stepper = self._make_fixed_stepper(sub_state, dt)
def wrapped_stepper(
state: FieldBase, t_start: float, t_end: float
) -> float:
"""advance `state` from `t_start` to `t_end` using fixed steps"""
# calculate number of steps (which is at least 1)
steps = max(1, int(np.ceil((t_end - t_start) / dt)))
# distribute the number of steps and the field to all nodes
steps = self.mesh.broadcast(steps)
substate_data = self.mesh.split_field_data_mpi(state.data)
# evolve the sub state
t_last, modifications = fixed_stepper(substate_data, t_start, steps)
# check whether t_last is the same for all processes
t_list = self.mesh.gather(t_last)
if t_list is not None and not np.isclose(min(t_list), max(t_list)):
raise RuntimeError(f"Processes went out of sync: t_last={t_list}")
# collect the data from all nodes
modification_list = self.mesh.gather(modifications)
self.mesh.combine_field_data_mpi(substate_data, out=state.data)
# store information in the main node
if mpi.is_main:
self.info["steps"] += steps
self.info["state_modifications"] += sum(modification_list) # type: ignore
return t_last
return wrapped_stepper