"""Basic code for the templated integrators.
Currently we only support two-step integrators.
These classes are used to generate the code for the actual integrators
from the `sph_eval` module.
"""
from numpy import sqrt
# Local imports.
from .integrator_step import IntegratorStep
###############################################################################
# `Integrator` class
###############################################################################
[docs]class Integrator(object):
r"""Generic class for multi-step integrators in PySPH for a system of
ODES of the form :math:`\frac{dy}{dt} = F(y)`.
"""
def __init__(self, **kw):
"""Pass fluid names and suitable `IntegratorStep` instances.
For example::
>>> integrator = Integrator(fluid=WCSPHStep(), solid=WCSPHStep())
where "fluid" and "solid" are the names of the particle arrays.
"""
for array_name, integrator_step in kw.iteritems():
if not isinstance(integrator_step, IntegratorStep):
msg='Stepper %s must be an instance of IntegratorStep'%(integrator_step)
raise ValueError(msg)
self.steppers = kw
self.parallel_manager = None
# This is set later when the underlying compiled integrator is created
# by the SPHCompiler.
self.c_integrator = None
##########################################################################
# Public interface.
##########################################################################
[docs] def set_fixed_h(self, fixed_h):
# compute h_minimum once for constant smoothing lengths
if fixed_h:
self.compute_h_minimum()
self.fixed_h=fixed_h
[docs] def set_nnps(self, nnps):
self.c_integrator.set_nnps(nnps)
[docs] def compute_h_minimum(self):
a_eval = self.c_integrator.acceleration_eval
hmin = 1.0
for pa in a_eval.particle_arrays:
h = pa.get_carray('h')
h.update_min_max()
if h.minimum < hmin:
hmin = h.minimum
self.h_minimum = hmin
[docs] def compute_time_step(self, dt, cfl):
"""If there are any adaptive timestep constraints, the appropriate
timestep is returned, else None is returned.
"""
a_eval = self.c_integrator.acceleration_eval
# different time step controls
dt_cfl_factor = a_eval.dt_cfl
dt_visc_factor = a_eval.dt_viscous
# force factor is acceleration squared
dt_force_factor = a_eval.dt_force
# iterate over particles and find hmin if using vatialbe h
if not self.fixed_h:
self.compute_h_minimum()
hmin = self.h_minimum
# default time steps set to some large value
dt_cfl = dt_force = dt_viscous = 1e20
# stable time step based on courant condition
if dt_cfl_factor > 0:
dt_cfl = hmin/dt_cfl_factor
# stable time step based on force criterion
if dt_force_factor > 0:
dt_force = sqrt( hmin/sqrt(dt_force_factor) )
# stable time step based on viscous condition
if dt_visc_factor > 0:
dt_viscous = hmin/dt_visc_factor
# minimum of all three
dt_min = min( dt_cfl, dt_force, dt_viscous )
# return the computed time steps. If dt factors aren't
# defined, the default dt is returned
if dt_min <= 0.0:
return None
else:
return cfl*dt_min
[docs] def one_timestep(self, t, dt):
"""User written function that actually does one timestep.
This function is used in the high-performance Cython implementation.
The assumptions one may make are the following:
- t and dt are passed.
- the following methods are available:
- self.initialize()
- self.stage1(), self.stage2() etc. depending on the number of
stages available.
- self.compute_accelerations(t, dt)
- self.do_post_stage(stage_dt, stage_count_from_1)
Please see any of the concrete implementations of the Integrator class
to study. By default the Integrator implements a
predict-evaluate-correct method, the same as PECIntegrator.
"""
self.initialize()
# Predict
self.stage1()
# Call any post-stage functions.
self.do_post_stage(0.5*dt, 1)
self.compute_accelerations()
# Correct
self.stage2()
# Call any post-stage functions.
self.do_post_stage(dt, 2)
[docs] def set_compiled_object(self, c_integrator):
"""Set the high-performance compiled object to call internally.
"""
self.c_integrator = c_integrator
[docs] def set_parallel_manager(self, pm):
self.c_integrator.set_parallel_manager(pm)
[docs] def set_post_stage_callback(self, callback):
"""This callback is called when the particles are moved, i.e
one stage of the integration is done.
This callback is passed the current time value, the timestep and the
stage.
The current time value is t + stage_dt, for example this would be
0.5*dt for a two stage predictor corrector integrator.
"""
self.c_integrator.set_post_stage_callback(callback)
[docs] def step(self, time, dt):
"""This function is called by the solver.
To implement the integration step please override the
``one_timestep`` method.
"""
self.c_integrator.step(time, dt)
###############################################################################
# `EulerIntegrator` class
###############################################################################
[docs]class EulerIntegrator(Integrator):
[docs] def one_timestep(self, t, dt):
self.compute_accelerations()
self.stage1()
self.do_post_stage(dt, 1)
###############################################################################
# `PECIntegrator` class
###############################################################################
[docs]class PECIntegrator(Integrator):
r"""
In the Predict-Evaluate-Correct (PEC) mode, the system is advanced using:
.. math::
y^{n+\frac{1}{2}} = y^n + \frac{\Delta t}{2}F(y^{n-\frac{1}{2}}) --> Predict
F(y^{n+\frac{1}{2}}) --> Evaluate
y^{n + 1} = y^n + \Delta t F(y^{n+\frac{1}{2}})
"""
[docs] def one_timestep(self, t, dt):
self.initialize()
# Predict
self.stage1()
# Call any post-stage functions.
self.do_post_stage(0.5*dt, 1)
self.compute_accelerations()
# Correct
self.stage2()
# Call any post-stage functions.
self.do_post_stage(dt, 2)
###############################################################################
# `EPECIntegrator` class
###############################################################################
[docs]class EPECIntegrator(Integrator):
r"""
Predictor corrector integrators can have two modes of
operation.
In the Evaluate-Predict-Evaluate-Correct (EPEC) mode, the
system is advanced using:
.. math::
F(y^n) --> Evaluate
y^{n+\frac{1}{2}} = y^n + F(y^n) --> Predict
F(y^{n+\frac{1}{2}}) --> Evaluate
y^{n+1} = y^n + \Delta t F(y^{n+\frac{1}{2}}) --> Correct
Notes:
The Evaluate stage of the integrator forces a function
evaluation. Therefore, the PEC mode is much faster but relies on
old accelertions for the Prediction stage.
In the EPEC mode, the final corrector can be modified to:
:math:`y^{n+1} = y^n + \frac{\Delta t}{2}\left( F(y^n) + F(y^{n+\frac{1}{2}}) \right)`
This would require additional storage for the accelerations.
"""
[docs] def one_timestep(self, t, dt):
self.initialize()
self.compute_accelerations()
# Predict
self.stage1()
# Call any post-stage functions.
self.do_post_stage(0.5*dt, 1)
self.compute_accelerations()
# Correct
self.stage2()
# Call any post-stage functions.
self.do_post_stage(dt, 2)
###############################################################################
# `TVDRK3Integrator` class
###############################################################################
[docs]class TVDRK3Integrator(Integrator):
r"""
In the TVD-RK3 integrator, the system is advanced using:
.. math::
y^{n + \frac{1}{3}} = y^n + \Delta t F( y^n )
y^{n + \frac{2}{3}} = \frac{3}{4}y^n + \frac{1}{4}(y^{n + \frac{1}{3}} + \Delta t F(y^{n + \frac{1}{3}}))
y^{n + 1} = \frac{1}{3}y^n + \frac{2}{3}(y^{n + \frac{2}{3}} + \Delta t F(y^{n + \frac{2}{3}}))
"""
[docs] def one_timestep(self, t, dt):
self.initialize()
# stage 1
self.compute_accelerations()
self.stage1()
self.do_post_stage(1./3*dt, 1)
# stage 2
self.compute_accelerations()
self.stage2()
self.do_post_stage(2./3*dt, 2)
# stage 3 and end
self.compute_accelerations()
self.stage3()
self.do_post_stage(dt, 3)
###############################################################################
[docs]class LeapFrogIntegrator(PECIntegrator):
r"""A leap-frog integrator.
"""
[docs] def one_timestep(self, t, dt):
self.stage1()
self.do_post_stage(0.5*dt, 1)
self.compute_accelerations()
self.stage2()
self.do_post_stage(dt, 2)
###############################################################################
[docs]class PEFRLIntegrator(Integrator):
r"""A Position-Extended Forest-Ruth-Like integrator [Omeylan2002]_
References
----------
.. [Omeylan2002] I.M. Omelyan, I.M. Mryglod and R. Folk, "Optimized
Forest-Ruth- and Suzuki-like algorithms for integration of motion
in many-body systems", Computer Physics Communications 146, 188 (2002)
http://arxiv.org/abs/cond-mat/0110585
"""
[docs] def one_timestep(self, t, dt):
self.stage1()
self.do_post_stage(0.1786178958448091*dt, 1)
self.compute_accelerations()
self.stage2()
self.do_post_stage(0.1123533131749906*dt, 2)
self.compute_accelerations()
self.stage3()
self.do_post_stage(0.8876466868250094*dt, 3)
self.compute_accelerations()
self.stage4()
self.do_post_stage(0.8213821041551909*dt, 4)
self.compute_accelerations()
self.stage5()
self.do_post_stage(dt, 5)