def u_exact(self,t):
"""
Routine to compute the exact solution at time t
Args:
t: current time
Returns:
exact solution
"""
me = mesh(self.nvars)
for i in range(self.lambda_s.size):
for j in range(self.lambda_f.size):
me.values[i,j] = self.u0*np.exp((self.lambda_f[j]+self.lambda_s[i])*t)
return me
def __eval_fexpl(self,u,t):
"""
Helper routine to evaluate the explicit part of the RHS
Args:
u: current values
t: current time (not used here)
Returns:
explicit part of RHS
"""
fexpl = mesh(self.nvars)
for i in range(self.lambda_s.size):
for j in range(self.lambda_f.size):
fexpl.values[i,j] = self.lambda_s[i]*u.values[i,j]
return fexpl
def __eval_fexpl(self, u, t):
"""
Helper routine to evaluate the explicit part of the RHS
Args:
u: current values
t: current time (not used here)
Returns:
explicit part of RHS
"""
fexpl = mesh(self.nvars)
for i in range(self.lambda_s.size):
for j in range(self.lambda_f.size):
fexpl.values[i, j] = self.lambda_s[i] * u.values[i, j]
return fexpl
def u_exact(self, t):
"""
Routine to compute the exact solution at time t
Args:
t: current time
Returns:
exact solution
"""
me = mesh(self.nvars)
for i in range(self.lambda_s.size):
for j in range(self.lambda_f.size):
me.values[i, j] = self.u0 * np.exp(
(self.lambda_f[j] + self.lambda_s[i]) * t)
return me
def solve_system(self,rhs,factor,u0,t):
"""
Simple linear solver for (I-dtA)u = rhs
Args:
rhs: right-hand side for the nonlinear system
factor: abbrev. for the node-to-node stepsize (or any other factor required)
u0: initial guess for the iterative solver (not used here so far)
t: current time (e.g. for time-dependent BCs)
Returns:
solution as mesh
"""
me = mesh(self.nvars)
for i in range(self.lambda_s.size):
for j in range(self.lambda_f.size):
me.values[i,j] = rhs.values[i,j]/(1.0-factor*self.lambda_f[j])
return me
def solve_system(self, rhs, factor, u0):
"""
Simple linear solver for (I-dtA)u = rhs
Args:
rhs: right-hand side for the nonlinear system
factor: abbrev. for the node-to-node stepsize (or any other factor required)
u0: initial guess for the iterative solver (not used here so far)
Returns:
solution as mesh
"""
me = mesh(self.nvars)
for i in range(self.lambda_s.size):
for j in range(self.lambda_f.size):
me.values[i,
j] = rhs.values[i,
j] / (1 - factor * self.lambda_f[j])
return me
