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# Oregonator: stiff 3-variable oscillatory ODE system from chemical reactions,
# problem OREGO in Hairer&Wanner volume 2
# See also http://www.scholarpedia.org/article/Oregonator
import sys
import petsc4py
petsc4py.init(sys.argv)
from petsc4py import PETSc
class Orego:
n = 3
comm = PETSc.COMM_SELF
def evalSolution(self, t, x):
if t != 0.0:
raise ValueError('Only for t=0')
x.setArray([1, 2, 3])
def evalFunction(self, ts, t, x, xdot, f):
f.setArray(
[
xdot[0] - 77.27 * (x[1] + x[0] * (1 - 8.375e-6 * x[0] - x[1])),
xdot[1] - 1 / 77.27 * (x[2] - (1 + x[0]) * x[1]),
xdot[2] - 0.161 * (x[0] - x[2]),
]
)
def evalJacobian(self, ts, t, x, xdot, a, A, B):
B[:, :] = [
[
a - 77.27 * ((1 - 8.375e-6 * x[0] - x[1]) - 8.375e-6 * x[0]),
-77.27 * (1 - x[0]),
0,
],
[1 / 77.27 * x[1], a + 1 / 77.27 * (1 + x[0]), -1 / 77.27],
[-0.161, 0, a + 0.161],
]
B.assemble()
if A != B:
A.assemble()
OptDB = PETSc.Options()
ode = Orego()
J = PETSc.Mat().createDense([ode.n, ode.n], comm=ode.comm)
J.setUp()
x = PETSc.Vec().createSeq(ode.n, comm=ode.comm)
f = x.duplicate()
ts = PETSc.TS().create(comm=ode.comm)
ts.setType(ts.Type.ROSW) # Rosenbrock-W. ARKIMEX is a nonlinearly implicit alternative.
ts.setIFunction(ode.evalFunction, f)
ts.setIJacobian(ode.evalJacobian, J)
history = []
def monitor(ts, i, t, x):
xx = x[:].tolist()
history.append((i, t, xx))
ts.setMonitor(monitor)
ts.setTime(0.0)
ts.setTimeStep(0.1)
ts.setMaxTime(360)
ts.setMaxSteps(2000)
ts.setExactFinalTime(PETSc.TS.ExactFinalTime.INTERPOLATE)
ts.setMaxSNESFailures(
-1
) # allow an unlimited number of failures (step will be rejected and retried)
# Set a different tolerance on each variable. Can use a scalar or a vector for either or both atol and rtol.
vatol = x.duplicate(array=[1e-2, 1e-1, 1e-4])
ts.setTolerances(
atol=vatol, rtol=1e-3
) # adaptive controller attempts to match this tolerance
snes = ts.getSNES() # Nonlinear solver
snes.setTolerances(
max_it=10
) # Stop nonlinear solve after 10 iterations (TS will retry with shorter step)
ksp = snes.getKSP() # Linear solver
ksp.setType(ksp.Type.PREONLY) # Just use the preconditioner without a Krylov method
pc = ksp.getPC() # Preconditioner
pc.setType(pc.Type.LU) # Use a direct solve
ts.setFromOptions() # Apply run-time options, e.g. -ts_adapt_monitor -ts_type arkimex -snes_converged_reason
ode.evalSolution(0.0, x)
ts.solve(x)
print(
'steps %d (%d rejected, %d SNES fails), nonlinear its %d, linear its %d'
% (
ts.getStepNumber(),
ts.getStepRejections(),
ts.getSNESFailures(),
ts.getSNESIterations(),
ts.getKSPIterations(),
)
)
if OptDB.getBool('plot_history', True):
from matplotlib import pylab
from matplotlib import rc
import numpy as np
ii = np.asarray([v[0] for v in history])
tt = np.asarray([v[1] for v in history])
xx = np.asarray([v[2] for v in history])
rc('text', usetex=True)
pylab.suptitle('Oregonator: TS \\texttt{%s}' % ts.getType())
pylab.subplot(2, 2, 1)
pylab.subplots_adjust(wspace=0.3)
pylab.semilogy(
ii[:-1],
np.diff(tt),
)
pylab.xlabel('step number')
pylab.ylabel('timestep')
for i in range(3):
pylab.subplot(2, 2, i + 2)
pylab.semilogy(tt, xx[:, i], 'rgb'[i])
pylab.xlabel('time')
pylab.ylabel('$x_%d$' % i)
# pylab.savefig('orego-history.png')
pylab.show()
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