q = 2
if myrank == 0: print '\npolynomial order = {}'.format(q)
alpha = 3.
for Nxy in NN:
h = 1./Nxy
mesh = UnitSquareMesh(Nxy, Nxy)
V = FunctionSpace(mesh, 'Lagrange', q)
Vl = FunctionSpace(mesh, 'Lagrange', 1)
Dt = h/(q*alpha*c)
if myrank == 0: print '\n\th = {} - Dt = {}'.format(h, Dt)
Wave = AcousticWave({'V':V, 'Vl':Vl, 'Vr':Vl})
Wave.timestepper = 'backward'
Wave.lump = True
Wave.exact = interpolate(uex_expr, V)
Wave.bc = DirichletBC(V, ubc, u0_boundary)
Wave.update({'lambda':lam, 'rho':rho, 't0':0.0, 'tf':tf, 'Dt':Dt,\
'u0init':interpolate(u0_expr, V), 'utinit':Function(V)})
sol, error = Wave.solve()
ERROR.append(error)
if myrank == 0: print 'relative error = {:.5e}'.format(error)
if not mycomm == None: MPI.barrier(mycomm)
if myrank == 0:
# Order of convergence:
CONVORDER = []
for ii in range(len(ERROR)-1):
CONVORDER.append(np.log(ERROR[ii+1]/ERROR[ii])/np.log((1./NN[ii+1])/(1./NN[ii])))
print '\n\norder of convergence:', CONVORDER
def source(tt):
return Expression('6*(sqrt(pow(x[0]-0.5,2)+pow(x[1]-0.5,2))<=t)', t=tt)
for Nxy in NN:
h = 1./Nxy
print '\n\th = {}'.format(h)
mesh = UnitSquareMesh(Nxy, Nxy, "crossed")
q = 1 # Polynomial order
V = FunctionSpace(mesh, 'Lagrange', q)
Dt = h/(q*5.*c)
Wave = AcousticWave({'V':V, 'Vl':V, 'Vr':V})
Wave.timestepper = 'backward'
Wave.lump = True
#Wave.verbose = True
Wave.exact = interpolate(exact_expr, V)
Wave.update({'lambda':lam, 'rho':rho, 't0':0.0, 'tf':tf, 'Dt':Dt,\
'u0init':Function(V), 'utinit':Function(V)})
test = TestFunction(V)
def srcterm(tt):
src_expr = source(tt)
src_vect = assemble(src_expr*test*dx)
return src_vect.array()
Wave.ftime = srcterm
sol, error = Wave.solve()
ERROR.append(error)
print 'relative error = {:.5e}'.format(error)
# Convergence order:
CONVORDER = []
for ii in range(len(ERROR)-1):
return on_boundary
for r in RR:
V = FunctionSpace(mesh, 'Lagrange', r)
Pt = PointSources(V, [[.5,.5]])
mydelta = Pt[0].array()
def mysrc(tt):
return Ricker(tt)*mydelta
# Computation:
if myrank == 0: print '\n\th = {}, Dt = {}'.format(h, Dt)
Wave = AcousticWave({'V':V, 'Vl':Vl, 'Vr':Vl})
#Wave.verbose = True
Wave.timestepper = 'centered'
Wave.lump = True
Wave.set_abc(mesh, AllFour(), True)
Wave.exact = Function(V)
Wave.update({'lambda':1.0, 'rho':1.0, 't0':0.0, 'tf':tf, 'Dt':Dt,\
'u0init':Function(V), 'utinit':Function(V)})
Wave.ftime = mysrc
sol, error = Wave.solve()
ERROR.append(error)
if myrank == 0: print 'relative error = {:.5e}'.format(error)
if not mycomm == None: MPI.barrier(mycomm)
# Plots:
try:
boolplot = int(sys.argv[1])
except:
boolplot = 0
if boolplot > 0:
filename, ext = splitext(sys.argv[0])
Pt = PointSources(Vex, [[.5, .5]])
mydelta = Pt[0].array()
def mysrc(tt):
return Ricker(tt) * mydelta
Waveex = AcousticWave({'V': Vex, 'Vm': Vl})
Waveex.timestepper = 'backward'
Waveex.lump = True
Waveex.update({'a':1.0, 'b':1.0, 't0':0.0, 'tf':tf, 'Dt':Dt,\
'u0init':dl.Function(Vex), 'utinit':dl.Function(Vex)})
Waveex.ftime = mysrc
sol, _ = Waveex.solve()
Waveex.exact = dl.Function(Vex)
normex = Waveex.computeabserror()
# plot
myplot.set_varname('u-q' + str(qq))
plotu = dl.Function(Vex)
for index, uu in enumerate(sol):
if index % boolplot == 0:
setfct(plotu, uu[0])
myplot.plot_vtk(plotu, index)
myplot.gather_vtkplots()
print 'Check different spatial sampling'
QQ = [4, 5, 6, 10]
for qq in QQ:
N = int(qq / cmin)
h = 1. / N
for r in RR:
V = FunctionSpace(mesh, 'Lagrange', r)
Pt = PointSources(V, [[.5, .5]])
mydelta = Pt[0].array()
def mysrc(tt):
return Ricker(tt) * mydelta
# Computation:
if myrank == 0: print '\n\th = {}, Dt = {}'.format(h, Dt)
Wave = AcousticWave({'V': V, 'Vm': Vl})
#Wave.verbose = True
Wave.timestepper = 'centered'
Wave.lump = True
Wave.set_abc(mesh, AllFour(), True)
Wave.exact = Function(V)
Wave.update({'b':1.0, 'a':1.0, 't0':0.0, 'tf':tf, 'Dt':Dt,\
'u0init':Function(V), 'utinit':Function(V)})
Wave.ftime = mysrc
sol, error = Wave.solve()
ERROR.append(error)
if myrank == 0: print 'relative error = {:.5e}'.format(error)
if not mycomm == None: MPI.barrier(mycomm)
# Plots:
try:
boolplot = int(sys.argv[1])
except:
boolplot = 0
if boolplot > 0:
filename, ext = splitext(sys.argv[0])
alpha = 5.
for Nxy in NN:
h = 1. / Nxy
mesh = UnitSquareMesh(Nxy, Nxy)
V = FunctionSpace(mesh, 'Lagrange', q)
Vl = FunctionSpace(mesh, 'Lagrange', 1)
Dt = h / (q * alpha * c)
if myrank == 0: print '\n\th = {}, Dt = {}'.format(h, Dt)
Wave = AcousticWave({'V': V, 'Vm': Vl})
#Wave.verbose = True
Wave.timestepper = 'centered'
Wave.lump = True
Wave.set_abc(mesh, LeftRight(), True)
Wave.exact = interpolate(exact_expr, V)
Wave.update({'b':b, 'a':a, 't0':0.0, 'tf':tf, 'Dt':Dt,\
'u0init':interpolate(u0_expr, V), 'utinit':Function(V)})
Wave.ftime = lambda t: 0.0
sol, error = Wave.solve()
ERROR.append(error)
if myrank == 0: print 'relative error = {:.5e}'.format(error)
if not mycomm == None: MPI.barrier(mycomm)
if myrank == 0:
# Order of convergence:
CONVORDER = []
for ii in range(len(ERROR) - 1):
CONVORDER.append(
np.log(ERROR[ii + 1] / ERROR[ii]) / np.log(
(1. / NN[ii + 1]) / (1. / NN[ii])))
h = 1./N
mesh = dl.UnitSquareMesh(N,N)
Vl = dl.FunctionSpace(mesh, 'Lagrange', 1)
Vex = dl.FunctionSpace(mesh, 'Lagrange', r)
Pt = PointSources(Vex, [[.5,.5]])
mydelta = Pt[0].array()
def mysrc(tt):
return Ricker(tt)*mydelta
Waveex = AcousticWave({'V':Vex, 'Vl':Vl, 'Vr':Vl})
Waveex.timestepper = 'backward'
Waveex.lump = True
Waveex.update({'lambda':1.0, 'rho':1.0, 't0':0.0, 'tf':tf, 'Dt':Dt,\
'u0init':dl.Function(Vex), 'utinit':dl.Function(Vex)})
Waveex.ftime = mysrc
sol,_ = Waveex.solve()
Waveex.exact = dl.Function(Vex)
normex = Waveex.computeabserror()
# plot
myplot.set_varname('u-q'+str(qq))
plotu = dl.Function(Vex)
for index, uu in enumerate(sol):
if index%boolplot == 0:
setfct(plotu, uu[0])
myplot.plot_vtk(plotu, index)
myplot.gather_vtkplots()
print 'Check different spatial sampling'
QQ = [4, 5, 6, 10]
for qq in QQ:
N = int(qq/cmin)
h = 1./N
