# -*- coding: utf-8 -*-
from pyfr.integrators.std.base import BaseStdIntegrator
from pyfr.util import memoize
class BaseStdStepper(BaseStdIntegrator):
def collect_stats(self, stats):
super().collect_stats(stats)
# Total number of RHS evaluations
stats.set('solver-time-integrator', 'nfevals', self._stepper_nfevals)
[docs]class StdEulerStepper(BaseStdStepper):
stepper_name = 'euler'
stepper_has_errest = False
stepper_nregs = 2
stepper_order = 1
@property
def _stepper_nfevals(self):
return self.nsteps
[docs] def step(self, t, dt):
add, rhs = self._add, self.system.rhs
ut, f = self._regidx
rhs(t, ut, f)
add(1.0, ut, dt, f)
return ut
[docs]class StdTVDRK3Stepper(BaseStdStepper):
stepper_name = 'tvd-rk3'
stepper_has_errest = False
stepper_nregs = 3
stepper_order = 3
@property
def _stepper_nfevals(self):
return 3*self.nsteps
[docs] def step(self, t, dt):
add, rhs = self._add, self.system.rhs
# Get the bank indices for each register (n, n+1, rhs)
r0, r1, r2 = self._regidx
# Ensure r0 references the bank containing u(t)
if r0 != self._idxcurr:
r0, r1 = r1, r0
# First stage; r2 = -∇·f(r0); r1 = r0 + dt*r2
rhs(t, r0, r2)
add(0.0, r1, 1.0, r0, dt, r2)
# Second stage; r2 = -∇·f(r1); r1 = 0.75*r0 + 0.25*r1 + 0.25*dt*r2
rhs(t + dt, r1, r2)
add(0.25, r1, 0.75, r0, 0.25*dt, r2)
# Third stage; r2 = -∇·f(r1);
# r1 = 1.0/3.0*r0 + 2.0/3.0*r1 + 2.0/3.0*dt*r2
rhs(t + 0.5*dt, r1, r2)
add(2.0/3.0, r1, 1.0/3.0, r0, 2.0/3.0*dt, r2)
# Return the index of the bank containing u(t + dt)
return r1
[docs]class StdRK4Stepper(BaseStdStepper):
stepper_name = 'rk4'
stepper_has_errest = False
stepper_nregs = 3
stepper_order = 4
@property
def _stepper_nfevals(self):
return 4*self.nsteps
[docs] def step(self, t, dt):
add, rhs = self._add, self.system.rhs
# Get the bank indices for each register
r0, r1, r2 = self._regidx
# Ensure r0 references the bank containing u(t)
if r0 != self._idxcurr:
r0, r1 = r1, r0
# First stage; r1 = -∇·f(r0)
rhs(t, r0, r1)
# Second stage; r2 = r0 + dt/2*r1; r2 = -∇·f(r2)
add(0.0, r2, 1.0, r0, dt/2.0, r1)
rhs(t + dt/2.0, r2, r2)
# As no subsequent stages depend on the first stage we can
# reuse its register to start accumulating the solution with
# r1 = r0 + dt/6*r1 + dt/3*r2
add(dt/6.0, r1, 1.0, r0, dt/3.0, r2)
# Third stage; here we reuse the r2 register
# r2 = r0 + dt/2*r2
# r2 = -∇·f(r2)
add(dt/2.0, r2, 1.0, r0)
rhs(t + dt/2.0, r2, r2)
# Accumulate; r1 = r1 + dt/3*r2
add(1.0, r1, dt/3.0, r2)
# Fourth stage; again we reuse r2
# r2 = r0 + dt*r2
# r2 = -∇·f(r2)
add(dt, r2, 1.0, r0)
rhs(t + dt, r2, r2)
# Final accumulation r1 = r1 + dt/6*r2 = u(t + dt)
add(1.0, r1, dt/6.0, r2)
# Return the index of the bank containing u(t + dt)
return r1
class StdRKVdH2RStepper(BaseStdStepper):
# Coefficients
a = []
b = []
bhat = []
def __init__(self, *args, **kwargs):
super().__init__(*args, **kwargs)
# Register our pointwise kernel
self.backend.pointwise.register('pyfr.integrators.std.kernels.rkvdh2')
# Compute the coefficients
self.c = [0.0] + [sum(self.b[:i]) + ai for i, ai in enumerate(self.a)]
self.e = [b - bh for b, bh in zip(self.b, self.bhat)]
self._nstages = len(self.c)
@memoize
def _get_rkvdh2_kerns(self, stage, r1, r2, rold=None, rerr=None):
kerns = []
tplargs = {
'a': self.a, 'b': self.b, 'e': self.e,
'stage': stage, 'nstages': self._nstages,
'nvars': self.system.nvars, 'errest': rold is not None
}
for dims, em in zip(self.system.ele_shapes, self.system.ele_banks):
if rold is not None:
kern = self.backend.kernel(
'rkvdh2', tplargs=tplargs, dims=[dims[0], dims[2]],
r1=em[r1], r2=em[r2], rold=em[rold], rerr=em[rerr],
)
else:
kern = self.backend.kernel(
'rkvdh2', tplargs=tplargs, dims=[dims[0], dims[2]],
r1=em[r1], r2=em[r2],
)
kerns.append(kern)
return kerns
@property
def stepper_has_errest(self):
return self.controller_needs_errest and len(self.bhat)
@property
def _stepper_nfevals(self):
return len(self.b)*self.nsteps
@property
def stepper_nregs(self):
return 4 if self.stepper_has_errest else 2
def step(self, t, dt):
run_kernels, rhs = self.backend.run_kernels, self.system.rhs
r1 = self._idxcurr
r2, *rs = set(self._regidx) - {r1}
# Evaluate the stages in the scheme
for i, ci in enumerate(self.c):
# Compute -∇·f
rhs(t + ci*dt, r2 if i > 0 else r1, r2)
# Fetch the appropriate RK accumulation kernels
kerns = self._get_rkvdh2_kerns(i, r1, r2, *rs)
# Bind the arguments
for k in kerns:
k.bind(dt=dt)
# Execute
run_kernels(kerns)
# Swap
r1, r2 = r2, r1
# Return
return (r2, *rs) if len(rs) else r2
[docs]class StdRK34Stepper(StdRKVdH2RStepper):
stepper_name = 'rk34'
stepper_order = 3
a = [
11847461282814 / 36547543011857,
3943225443063 / 7078155732230,
-346793006927 / 4029903576067
]
b = [
1017324711453 / 9774461848756,
8237718856693 / 13685301971492,
57731312506979 / 19404895981398,
-101169746363290 / 37734290219643
]
bhat = [
15763415370699 / 46270243929542,
514528521746 / 5659431552419,
27030193851939 / 9429696342944,
-69544964788955 / 30262026368149
]
[docs]class StdRK45Stepper(StdRKVdH2RStepper):
stepper_name = 'rk45'
stepper_order = 4
a = [
970286171893 / 4311952581923,
6584761158862 / 12103376702013,
2251764453980 / 15575788980749,
26877169314380 / 34165994151039
]
b = [
1153189308089 / 22510343858157,
1772645290293 / 4653164025191,
-1672844663538 / 4480602732383,
2114624349019 / 3568978502595,
5198255086312 / 14908931495163
]
bhat = [
1016888040809 / 7410784769900,
11231460423587 / 58533540763752,
-1563879915014 / 6823010717585,
606302364029 / 971179775848,
1097981568119 / 3980877426909
]