def solver_r(I,
f,
c,
U_L,
L,
n,
dt,
tstop,
graphics=None,
user_action=None,
version='scalar'):
"""
1D wave equation as in wave1D_func1.solver, but the present
function models spherical waves. The physical solution is v=u/r.
The boundary condition at r=0 is u=0 because of symmetry
so u(L)=U_L is the only free boundary condition.
This version is implemented as a wrapper of the solver
in wave1D_func1.
We compute v and display it through solver's user_action
function before calling the supplied user's user_action
function.
"""
v = None # bring v=u/r into play
def U_0(t):
return 0
solutions = [] # store all u fields at all time levels
def action_with_plot(u, x, t):
v = u.copy() # get right length and type
r = x # radial coordinates
v[1:] = u[1:] / r[1:] # in-place modification
v[0] = v[1] # from the b.c. dv/dr=0 at r=0
solutions.append(v.copy())
if graphics is not None:
graphics.configure(coor=x)
graphics.plotcurve(v, legend='v(x,t=%9.4E)' % t, ps=0)
if user_action is not None:
user_action(v, x, t) # call user's function with v
dt, r, cpu = solver(I, f, c, U_0, U_L, L, n, dt, tstop, action_with_plot,
version)
return dt, r, solutions, cpu
def solver_r(I, f, c, U_L, L, n, dt, tstop,
graphics=None, user_action=None, version='scalar'):
"""
1D wave equation as in wave1D_func1.solver, but the present
function models spherical waves. The physical solution is v=u/r.
The boundary condition at r=0 is u=0 because of symmetry
so u(L)=U_L is the only free boundary condition.
This version is implemented as a wrapper of the solver
in wave1D_func1.
We compute v and display it through solver's user_action
function before calling the supplied user's user_action
function.
"""
v = None # bring v=u/r into play
def U_0(t):
return 0
solutions = [] # store all u fields at all time levels
def action_with_plot(u, x, t):
v = u.copy() # get right length and type
r = x # radial coordinates
v[1:] = u[1:]/r[1:] # in-place modification
v[0] = v[1] # from the b.c. dv/dr=0 at r=0
solutions.append(v.copy())
if graphics is not None:
graphics.configure(coor=x)
graphics.plotcurve(v, legend='v(x,t=%9.4E)' % t, ps=0)
if user_action is not None:
user_action(v, x, t) # call user's function with v
dt, r, cpu = solver(I, f, c, U_0, U_L, L, n, dt, tstop,
action_with_plot, version)
return dt, r, solutions, cpu
solutions = []
time_level_counter = 0
version = 'scalar'
N = int(sys.argv[1])
def action(u, x, t):
global time_level_counter
if time_level_counter % N == 0:
solutions.append(u.copy())
time_level_counter += 1
n = 100
tstop = 6
L = 10
dt, x, cpu = solver(I,
f,
1.0,
lambda t: 0,
lambda t: 0,
L,
n,
0,
tstop,
user_action=action,
version=version)
print 'CPU time:', cpu
from wave1D_func1 import solver
from numpy import sin, pi
def I(x): return sin(2*x*pi/L)
def f(x,t): return 0
solutions = []
time_level_counter = 0
version = 'scalar'
N = int(sys.argv[1])
def action(u, x, t):
global time_level_counter
if time_level_counter % N == 0:
solutions.append(u.copy())
time_level_counter += 1
n = 100; tstop = 6; L = 10
dt, x, cpu = solver(I, f, 1.0, lambda t: 0, lambda t: 0,
L, n, 0, tstop,
user_action=action, version=version)
print 'CPU time:', cpu