def euler_explicit(initial, ival, D=1.0):
alpha = ival.ALPHA_DIFFUSION * D
matrix = make_bc(
np.diag(np.ones(ival.N_X)*(1.0-2.0*alpha)) + \
np.diag(np.ones(ival.N_X-1)*alpha,k=1) + \
np.diag(np.ones(ival.N_X-1)*alpha,k=-1),
ival.BoundaryType)
return np.linalg.matrix_power(matrix, ival.N_T) @ initial
def lax_friedrichs(initial, ival, c=1.0):
alpha = c * ival.ALPHA_HOPF
t = ival.N_T
matrix = make_bc(
0.5*(np.diag(np.ones(ival.N_X-1)*(1-alpha),k=1) + \
np.diag(np.ones(ival.N_X-1)*(1+alpha),-1)),
ival.BoundaryType)
return np.linalg.matrix_power(matrix, t) @ initial
def euler_implicit(initial, ival, D=1.0):
alpha = ival.ALPHA_DIFFUSION * D
matrix = make_bc(
np.diag(np.ones(ival.N_X)*(1.0+2.0*alpha)) - \
np.diag(np.ones(ival.N_X-1)*alpha,k=1) - \
np.diag(np.ones(ival.N_X-1)*alpha,k=-1),
ival.BoundaryType)
result = np.linalg.matrix_power(np.linalg.inv(matrix), ival.N_T) @ initial
return result
def lax_wendroff(initial, ival, c=1.0):
alpha = c * ival.ALPHA_HOPF
t = ival.N_T
matrix = make_bc(
(1.-alpha**2)*np.diag(np.ones(ival.N_X)) + \
np.diag(np.ones(ival.N_X-1)*0.5*(alpha**2-alpha),1) + \
np.diag(np.ones(ival.N_X-1)*0.5*(alpha**2+alpha),-1),
ival.BoundaryType)
return np.linalg.matrix_power(matrix, t) @ initial
def downwind(initial, ival, c=1.0):
alpha = c * ival.ALPHA_HOPF
t = ival.N_T
matrix = make_bc(
np.diag(np.ones(ival.N_X)*(1.0+alpha)) - \
np.diag(np.ones(ival.N_X-1),1)*alpha,
ival.BoundaryType)
result = np.linalg.matrix_power(matrix, t) @ initial
return result
def implicit_centered(initial, ival, c=1.0):
alpha = c * ival.ALPHA_HOPF / 2.0
t = ival.N_T
matrix = make_bc(
np.diag(np.ones(ival.N_X)) + \
np.diag(np.ones(ival.N_X-1)*alpha,1) - \
np.diag(np.ones(ival.N_X-1)*alpha,-1),
ival.BoundaryType)
result = np.linalg.matrix_power(np.linalg.inv(matrix), t) @ initial
return result
def crank_nicolson(initial, ival, D=1.0):
alpha = ival.ALPHA_DIFFUSION * D
Bmat = make_bc(
np.diag(np.ones(ival.N_X))*2 - \
np.diag(np.ones(ival.N_X-1),k=1) - \
np.diag(np.ones(ival.N_X-1),k=-1),
ival.BoundaryType)
left_mat = (2 * np.diag(np.ones(ival.N_X)) + alpha * Bmat)
right_mat = (2 * np.diag(np.ones(ival.N_X)) - alpha * Bmat)
#if CHECK_CRANK_COMMUTE:
# closemat = np.isclose(
# np.linalg.inv(left_mat) @ right_mat - \
# right_mat @ np.linalg.inv(left_mat),
# np.zeros_like(right_mat))
# if not closemat.sum() == closemat.shape[0]**2:
# # check if matrices commute to only solve the problem once, not
# # recursively
# warnings.warn('Matrices do not commute. Wrong result.',RuntimeWarning)
#result = sc_la.solve(np.linalg.matrix_power(left_mat,ival.N_T),
# np.dot(np.linalg.matrix_power(right_mat,ival.N_T),initial),
# assume_a="sym")
result = np.linalg.matrix_power(
np.linalg.inv(left_mat) @ right_mat, ival.N_T) @ initial
return result