def updata_analytical_solution():
"""
updates the analytical solution
"""
x = np.linspace(pde_settings.x_min, pde_settings.x_max, 200)
u_ana_id = get_solver_id()
f0 = pde_functions.parse(initial_condition.value)
u_x[0] = pde_settings.analytical_solutions[u_ana_id](f0, x)
def updata_analytical_solution():
"""
updates the analytical solution
"""
x = np.linspace(pde_settings.x_min, pde_settings.x_max, 200)
u_ana_id = get_solver_id()
f0 = pde_functions.parse(initial_condition.value)
u_x = pde_settings.analytical_solutions[u_ana_id](f0, x)
ana_sol.data = dict({'u_x':u_x})
def update_mesh(h, k):
"""
called if the numerical discretization mesh changed. i.e. if temporal or spatial meshwidth changes. The whole
problem is recomputed and each timestep is saved to the mesh_data. Finally the currently active timestep is plotted.
:param h: spatial meshwidth
:param k: temporal meshwidth
"""
solver_id = get_solver_id()
pde_specs.data = dict(h=[h], k=[k], solver_id=[solver_id])
solver = pde_settings.solvers[solver_id]
# spatial discretization
x0 = pde_settings.x_min
x1 = pde_settings.x_max
x = np.arange(x0, x1+h, h)
# get initial condition
f0 = pde_functions.parse(initial_condition.value)
u = f0(x)
# this enforces neumann BC: u'(t=0)=0
u_old = np.array(u)
# number of timesteps
n_temporal = int(round(pde_settings.t_max / k, 0)) + 1
# setup datastructure for saving each timestep
mesh_dict = dict(x=x)
for i in range(n_temporal): # iterate over all timesteps
key = 'u' + str(i)
mesh_dict[key] = u.tolist() # save result to dict
u_new = solver(u_old, u, k, h) # propagate in time
u_old = u
u = u_new
mesh_data.data = mesh_dict
t = time_slider.value
update_plot(k, t)
def update_mesh(h, k):
"""
called if the numerical discretization mesh changed. i.e. if temporal or spatial meshwidth changes. The whole
problem is recomputed and each timestep is saved to the mesh_data. Finally the currently active timestep is plotted.
:param h: spatial meshwidth
:param k: temporal meshwidth
"""
solver_id = get_solver_id()
pde_specs.data = dict(h=[h], k=[k], solver_id=[solver_id])
solver = pde_settings.solvers[solver_id]
# spatial discretization
x0 = pde_settings.x_min
x1 = pde_settings.x_max
x = np.arange(x0, x1 + h, h)
# get initial condition
f0 = pde_functions.parse(initial_condition.value)
u = f0(x)
# this enforces neumann BC: u'(t=0)=0
u_old = np.array(u)
# number of timesteps
n_temporal = int(round(pde_settings.t_max / k, 0)) + 1
# setup datastructure for saving each timestep
mesh_dict = dict(x=x)
for i in range(n_temporal): # iterate over all timesteps
key = 'u' + str(i)
mesh_dict[key] = u.tolist() # save result to dict
u_new = solver(u_old, u, k, h) # propagate in time
u_old = u
u = u_new
mesh_data.data = mesh_dict
t = time_slider.value
update_plot(k, t)
