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#!/usr/bin/env python3
import sys, petsc4py
petsc4py.init(sys.argv)
from petsc4py import PETSc
import numpy as np
try:
from matplotlib import pylab
except ImportError:
pylab = None
# this user class is an application
# context for the nonlinear problem
# at hand; it contains some parameters
# and knows how to compute residuals
class AppCtx:
def __init__(self, nx, ny, nz):
self.n = np.array([nx, ny, nz], dtype='i')
self.h = np.array([1.0/(n-1) for n in self.n], dtype='d')
from App import formFunction
from App import formInitial
self._formFunction = formFunction
self._formInitial = formInitial
def formInitial(self, t, X):
xx = X.getArray(readonly=0).reshape(self.n, order='f')
self._formInitial(self.h, t, xx)
def formFunction(self, ts, t, X, Xdot, F):
n = self.n
h = self.h
x = X.getArray(readonly=1).reshape(n, order='f')
xdot = Xdot.getArray(readonly=1).reshape(n, order='f')
f = F[...].reshape(n, order='f')
self._formFunction(h, t, x, xdot, f)
def plot(self, t, x):
nx, ny, nz = self.n
from numpy import mgrid
#
U = x.getArray(readonly=1).reshape(nx,ny,nz, order='f')
#
X, Y = mgrid[0:1:1j*nx,0:1:1j*ny]
Z = U[:,:,nz//2]
pylab.figure(0)
pylab.contourf(X,Y,Z)
pylab.colorbar()
pylab.plot(X.ravel(),Y.ravel(),'.k')
pylab.title('z=0.50')
pylab.xlabel('x')
pylab.ylabel('y')
pylab.axis('equal')
#
X, Y = mgrid[0:1:1j*nx,0:1:1j*nz]
Z = U[:,ny//4,:]
pylab.figure(1)
pylab.contourf(X,Y,Z)
pylab.colorbar()
pylab.plot(X.ravel(),Y.ravel(),'.k')
pylab.title('y=0.25')
pylab.xlabel('x')
pylab.ylabel('z')
pylab.axis('equal')
#
X, Y = mgrid[0:1:1j*ny,0:1:1j*nz]
Z = U[nx//2,:,:]
pylab.figure(2)
pylab.contourf(X,Y,Z)
pylab.colorbar()
pylab.plot(X.ravel(),Y.ravel(),'.k')
pylab.title('x=0.50')
pylab.xlabel('y')
pylab.ylabel('z')
pylab.axis('equal')
def run_test(nx,ny,nz,samples,plot=False):
ts = PETSc.TS().create()
ts.setType('theta')
ts.setTheta(1.0)
ts.setTimeStep(0.01)
ts.setTime(0.0)
ts.setMaxTime(1.0)
ts.setMaxSteps(10)
eft = PETSc.TS.ExactFinalTime.STEPOVER
ts.setExactFinalTime(eft)
x = PETSc.Vec().createSeq(nx*ny*nz)
ts.setSolution(x)
app = AppCtx(nx, ny, nz)
f = PETSc.Vec().createSeq(nx*ny*nz)
ts.setIFunction(app.formFunction, f)
ts.snes.setUseMF(1)
ts.snes.ksp.setType('cg')
ts.setFromOptions()
ts.setUp()
wt = 1e300
for i in range(samples):
app.formInitial(0, x)
t1 = PETSc.Log.getTime()
ts.solve(x)
t2 = PETSc.Log.getTime()
wt = min(wt,t2-t1)
if plot and pylab:
app.plot(ts.time, x)
return wt
OptDB = PETSc.Options()
start = OptDB.getInt('start', 12)
step = OptDB.getInt('step', 4)
stop = OptDB.getInt('stop', start)
samples = OptDB.getInt('samples', 1)
plot = OptDB.getBool('plot', False)
if plot and not pylab:
PETSc.Sys.Print("matplotlib not available")
for n in range(start, stop+step, step):
nx = ny = nz = n+1
wt = run_test(nx,ny,nz,samples,plot)
PETSc.Sys.Print("Grid %3d x %3d x %3d -> %f seconds (%2d samples)"
% (nx,ny,nz,wt,samples))
if plot and pylab:
pylab.show()
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