description['transfer_params'] = tparams
# quickly generate block of steps
MS = mp.generate_steps(num_procs,sparams,description)
# setup parameters "in time"
t0 = MS[0].levels[0].prob.t0
dt = 0.5
Tend = 8*dt
# get initial values on finest level
P = MS[0].levels[0].prob
uinit = P.u_exact(t0)
# call main function to get things done...
uend,stats = mp.run_pfasst(MS,u0=uinit,t0=t0,dt=dt,Tend=Tend)
# df.plot(uend.values,interactive=True)
# compute exact solution and compare
uex = P.u_exact(Tend)
print('(classical) error at time %s: %s' %(Tend,abs(uex-uend)/abs(uex)))
uex = df.Expression('sin(a*x[0]) * cos(t)',a=np.pi,t=Tend)
print('(fenics-style) error at time %s: %s' %(Tend,df.errornorm(uex,uend.values)))
extract_stats = grep_stats(stats,iter=-1,type='residual')
sortedlist_stats = sort_stats(extract_stats,sortby='step')
print(extract_stats,sortedlist_stats)
# setup parameters "in time"
t0 = 0
dt = 1/16*np.pi
Tend = 16*dt#np.pi
# get initial values on finest level
P = MS[0].levels[0].prob
uinit = P.u_exact(t0)
print('Init:',uinit.pos.values,uinit.vel.values)
# call main function to get things done...
uend,stats = mp.run_pfasst(MS,u0=uinit,t0=t0,dt=dt,Tend=Tend)
extract_stats = grep_stats(stats,type='energy')
sortedlist_stats = sort_stats(extract_stats,sortby='time')
R0 = np.linalg.norm(uinit.pos.values[:])
H0 = 1/2*np.dot(uinit.vel.values[:],uinit.vel.values[:])+0.02/R0
energy_err = [abs(entry[1]-H0)/H0 for entry in sortedlist_stats]
fig = plt.figure()
plt.plot(energy_err,'bo--')
plt.show()
# rc('text', usetex=True)
# rc('font', family='serif', size=20)
# rc('legend', fontsize='small')
# rc('xtick', labelsize='small')
MS = mp.generate_steps(num_procs, sparams, description)
# setup parameters "in time"
t0 = 0
dt = 0.1
Tend = 2
P = MS[0].levels[0].prob
uinit = P.u_exact(t0)
print('Init:', uinit.values)
# call main function to get things done...
uend, stats = mp.run_pfasst_serial(MS, u0=uinit, t0=t0, dt=dt, Tend=Tend)
# get stats and error
extract_stats = grep_stats(stats, type='niter')
sortedlist_stats = sort_stats(extract_stats, sortby='time')
uex = P.u_exact(Tend)
print(
'Error:',
np.linalg.norm(uex.values - uend.values, np.inf) /
np.linalg.norm(uex.values, np.inf))
print('Min/Max/Sum number of iterations: %s/%s/%s' %
(min(entry[1] for entry in sortedlist_stats),
max(entry[1] for entry in sortedlist_stats),
sum(entry[1] for entry in sortedlist_stats)))
description['num_nodes'] = 3
description['sweeper_class'] = imex_1st_order
description['level_params'] = lparams
description['transfer_class'] = mesh_to_mesh_1d
description['transfer_params'] = tparams
# quickly generate block of steps
MS = mp.generate_steps(num_procs, sparams, description)
# setup parameters "in time"
t0 = 0
dt = 0.125
Tend = 4 * dt
# get initial values on finest level
P = MS[0].levels[0].prob
uinit = P.u_exact(t0)
# call main function to get things done...
uend, stats = mp.run_pfasst_serial(MS, u0=uinit, t0=t0, dt=dt, Tend=Tend)
# compute exact solution and compare
uex = P.u_exact(Tend)
print('error at time %s: %s' %
(Tend, np.linalg.norm(uex.values - uend.values, np.inf) /
np.linalg.norm(uex.values, np.inf)))
extract_stats = grep_stats(stats, iter=-1, type='residual')
sortedlist_stats = sort_stats(extract_stats, sortby='step')
print(extract_stats, sortedlist_stats)
# quickly generate block of steps
MS = mp.generate_steps(num_procs,sparams,description)
# setup parameters "in time"
t0 = 0
dt = 0.1
Tend = 4*dt
# get initial values on finest level
P = MS[0].levels[0].prob
uinit = P.u_exact(t0)
# call main function to get things done...
uend,stats = mp.run_pfasst(MS,u0=uinit,t0=t0,dt=dt,Tend=Tend)
# compute exact solution and compare
uex = P.u_exact(Tend)
print('error at time %s: %s' %(Tend,np.linalg.norm(uex.values-uend.values,np.inf)/np.linalg.norm(
uex.values,np.inf)))
# Get residual at last step (being the max of all residuals.. most likely) on the fine level
extract_stats = grep_stats(stats,step=3,level=-1,type='residual')
sortedlist_stats = sort_stats(extract_stats,sortby='iter')[1:] # remove '-1' entry
print(sortedlist_stats)
# Get the error against the analytical solution at the last step
extract_stats = grep_stats(stats,step=3,level=-1,type='error')
sortedlist_stats = sort_stats(extract_stats,sortby='iter')
print(sortedlist_stats)
# setup parameters "in time"
t0 = 0
dt = 0.1
Tend = 2
P = MS[0].levels[0].prob
uinit = P.u_exact(t0)
print("Init:", uinit.values)
# call main function to get things done...
uend, stats = mp.run_pfasst(MS, u0=uinit, t0=t0, dt=dt, Tend=Tend)
# get stats and error
extract_stats = grep_stats(stats, type="niter")
sortedlist_stats = sort_stats(extract_stats, sortby="time")
uex = P.u_exact(Tend)
print("Error:", np.linalg.norm(uex.values - uend.values, np.inf) / np.linalg.norm(uex.values, np.inf))
print(
"Min/Max/Sum number of iterations: %s/%s/%s"
% (
min(entry[1] for entry in sortedlist_stats),
max(entry[1] for entry in sortedlist_stats),
sum(entry[1] for entry in sortedlist_stats),
)
)