def test_linearized_mms_ldg_convergence():
# LDG Diffusion should converge at 1st order for 1 basis_cpt
# or at num_basis_cpts - 2 for more basis_cpts
t = 0.0
bc = boundary.Periodic()
p_class = convection_hyper_diffusion.NonlinearHyperDiffusion
p_func = p_class.linearized_manufactured_solution
exact_solution = flux_functions.AdvectingSine(offset=2.0)
for diffusion_function in diffusion_functions:
problem = p_func(exact_solution, diffusion_function)
exact_time_derivative = problem.exact_time_derivative(
exact_solution, t)
for num_basis_cpts in [1] + list(range(5, 6)):
for basis_class in basis.BASIS_LIST:
error_list = []
basis_ = basis_class(num_basis_cpts)
# 10 and 20 elems maybe not in asymptotic regime yet
for num_elems in [20, 40]:
mesh_ = mesh.Mesh1DUniform(0.0, 1.0, num_elems)
dg_solution = basis_.project(exact_solution, mesh_, t)
L = problem.ldg_operator(dg_solution, t, bc, bc)
dg_error = math_utils.compute_dg_error(
L, exact_time_derivative)
error = dg_error.norm()
error_list.append(error)
# plot.plot_dg_1d(L, function=exact_time_derivative)
order = utils.convergence_order(error_list)
# if already at machine precision don't check convergence
if error_list[-1] > tolerance:
if num_basis_cpts == 1:
assert order >= 1
else:
assert order >= num_basis_cpts - 4
def test_linearized_mms_ldg_irk():
# g = functions.Sine(offset=2.0)
# r = -1.0
# exact_solution = flux_functions.ExponentialFunction(g, r)
exact_solution = flux_functions.AdvectingSine(offset=2.0)
t_initial = 0.0
t_final = 0.1
exact_solution_final = lambda x: exact_solution(x, t_final)
bc = boundary.Periodic()
p_class = convection_hyper_diffusion.NonlinearHyperDiffusion
p_func = p_class.linearized_manufactured_solution
for diffusion_function in diffusion_functions:
problem = p_func(exact_solution, diffusion_function)
for num_basis_cpts in range(1, 3):
irk = implicit_runge_kutta.get_time_stepper(num_basis_cpts)
for basis_class in basis.BASIS_LIST:
basis_ = basis_class(num_basis_cpts)
error_list = []
for i in [1, 2]:
if i == 1:
delta_t = 0.01
num_elems = 20
else:
delta_t = 0.005
num_elems = 40
mesh_ = mesh.Mesh1DUniform(0.0, 1.0, num_elems)
dg_solution = basis_.project(problem.initial_condition,
mesh_)
# time_dependent_matrix time does matter
matrix_function = lambda t: problem.ldg_matrix(
dg_solution, t, bc, bc, bc, bc)
rhs_function = problem.get_implicit_operator(
bc, bc, bc, bc)
solve_function = time_stepping.get_solve_function_matrix(
matrix_function)
new_solution = time_stepping.time_step_loop_implicit(
dg_solution,
t_initial,
t_final,
delta_t,
irk,
rhs_function,
solve_function,
)
error = math_utils.compute_error(new_solution,
exact_solution_final)
error_list.append(error)
# plot.plot_dg_1d(new_solution, function=exact_solution_final)
order = utils.convergence_order(error_list)
assert order >= num_basis_cpts
def test_nonlinear_mms_ldg_irk():
exact_solution = flux_functions.AdvectingSine(amplitude=0.1, offset=0.15)
t_initial = 0.0
t_final = 0.1
exact_solution_final = lambda x: exact_solution(x, t_final)
bc = boundary.Periodic()
p_func = thin_film.ThinFilmDiffusion.manufactured_solution
problem = p_func(exact_solution)
for num_basis_cpts in range(1, 3):
irk = implicit_runge_kutta.get_time_stepper(num_basis_cpts)
cfl = 0.5
for basis_class in basis.BASIS_LIST:
basis_ = basis_class(num_basis_cpts)
error_list = []
n = 40
for num_elems in [n, 2 * n]:
mesh_ = mesh.Mesh1DUniform(0.0, 1.0, num_elems)
delta_t = cfl * mesh_.delta_x / exact_solution.wavespeed
dg_solution = basis_.project(problem.initial_condition, mesh_)
# time_dependent_matrix time does matter
matrix_function = lambda t, q: problem.ldg_matrix(q, t, bc, bc, bc, bc)
rhs_function = problem.get_implicit_operator(bc, bc, bc, bc)
solve_function = time_stepping.get_solve_function_picard(
matrix_function, num_basis_cpts, num_elems * num_basis_cpts
)
new_solution = time_stepping.time_step_loop_implicit(
dg_solution,
t_initial,
t_final,
delta_t,
irk,
rhs_function,
solve_function,
)
error = math_utils.compute_error(new_solution, exact_solution_final)
error_list.append(error)
# plot.plot_dg_1d(new_solution, function=exact_solution_final)
with open("thin_film_nonlinear_irk_test.yml", "a") as file:
dict_ = dict()
subdict = dict()
subdict["cfl"] = cfl
subdict["n"] = n
subdict["error0"] = float(error_list[0])
subdict["error1"] = float(error_list[1])
subdict["order"] = float(np.log2(error_list[0] / error_list[1]))
dict_[num_basis_cpts] = subdict
yaml.dump(dict_, file, default_flow_style=False)
order = utils.convergence_order(error_list)
assert order >= num_basis_cpts
def test_mms_operator_zero():
# For manufactured solution the overall operator should be zero
exact_solution = flux_functions.AdvectingSine(offset=2.0)
nonlinear_diffusion_class = convection_hyper_diffusion.NonlinearHyperDiffusion
for diffusion_function in diffusion_functions:
problem = nonlinear_diffusion_class.manufactured_solution(
exact_solution, diffusion_function)
linearized_problem = nonlinear_diffusion_class.linearized_manufactured_solution(
exact_solution, diffusion_function)
assert isinstance(linearized_problem.diffusion_function,
flux_functions.XTFunction)
for t in range(3):
exact_operator = problem.exact_operator(exact_solution, t)
values = [exact_operator(x) for x in np.linspace(-1.0, 1.0)]
assert np.linalg.norm(values) <= tolerance
exact_operator = linearized_problem.exact_operator(
exact_solution, t)
values = [exact_operator(x) for x in np.linspace(-1.0, 1.0)]
assert np.linalg.norm(values) <= tolerance
def test_mms_operator_zero():
# For manufactured solution the overall operator should be zero
exact_solution = flux_functions.AdvectingSine(offset=2.0)
problem_list = []
problem_list.append(thin_film.ThinFilm.manufactured_solution(exact_solution))
problem_list.append(
thin_film.ThinFilm.linearized_manufactured_solution(exact_solution)
)
problem_list.append(
thin_film.ThinFilmDiffusion.linearized_manufactured_solution(exact_solution)
)
problem_list.append(
thin_film.ThinFilmDiffusion.manufactured_solution(exact_solution)
)
assert isinstance(problem_list[1].diffusion_function, flux_functions.XTFunction)
assert isinstance(problem_list[2].diffusion_function, flux_functions.XTFunction)
for t in range(3):
for problem in problem_list:
exact_operator = problem.exact_operator(exact_solution, t)
values = [exact_operator(x) for x in np.linspace(-1.0, 1.0)]
assert np.linalg.norm(values) <= tolerance
from pydogpack.utils import functions
from pydogpack.utils import flux_functions
from pydogpack.basis import basis
from pydogpack.mesh import mesh
from pydogpack.mesh import boundary
from apps.onedimensional.thinfilm import thin_film
import numpy as np
import yaml
if __name__ == "__main__":
exact_solution = flux_functions.AdvectingSine(amplitude=0.1, offset=0.15)
problem = thin_film.ThinFilm.manufactured_solution(exact_solution)
t = 0.0
bc = boundary.Periodic()
n = 10
dict_ = dict()
for bc in [boundary.Periodic(), boundary.Extrapolation()]:
dict_[str(bc)] = dict()
dict_bc = dict_[str(bc)]
for basis_class in basis.BASIS_LIST:
dict_bc[basis_class.string] = dict()
dict_basis = dict_bc[basis_class.string]
for num_basis_cpts in range(1, 4):
dict_basis[num_basis_cpts] = dict()
dict_cpt = dict_basis[num_basis_cpts]
basis_ = basis_class(num_basis_cpts)
for num_elems in range(10, 90, 10):
mesh_ = mesh.Mesh1DUniform(0.0, 1.0, num_elems)
dg_solution = basis_.project(problem.initial_condition, mesh_)
(matrix, vector) = problem.ldg_matrix(
def test_imex_linearized_mms():
# advection with linearized diffusion
# (q_t + q_x = (f(x, t) q_xx + s(x, t))
exact_solution = flux_functions.AdvectingSine(amplitude=0.1, offset=0.15)
p_class = convection_hyper_diffusion.ConvectionHyperDiffusion
p_func = p_class.linearized_manufactured_solution
t_initial = 0.0
bc = boundary.Periodic()
for diffusion_function in [squared]:
problem = p_func(exact_solution, None, diffusion_function)
cfl_list = [0.9, 0.15, 0.1]
for num_basis_cpts in range(2, 4):
imex = imex_runge_kutta.get_time_stepper(num_basis_cpts)
cfl = cfl_list[num_basis_cpts - 1]
n = 20
t_final = cfl * (1.0 / n) / exact_solution.wavespeed
exact_solution_final = lambda x: exact_solution(x, t_final)
for basis_class in [basis.LegendreBasis1D]:
basis_ = basis_class(num_basis_cpts)
error_list = []
for num_elems in [n, 2 * n]:
mesh_ = mesh.Mesh1DUniform(0.0, 1.0, num_elems)
delta_t = cfl * mesh_.delta_x / exact_solution.wavespeed
dg_solution = basis_.project(problem.initial_condition,
mesh_)
# weak dg form with flux_function and source term
explicit_operator = problem.get_explicit_operator(bc)
# ldg discretization of diffusion_function
implicit_operator = problem.get_implicit_operator(
bc, bc, bc, bc, include_source=False)
# this is a constant matrix case
matrix_function = lambda t: problem.ldg_matrix(
dg_solution, t, bc, bc, bc, bc, include_source=False)
solve_operator = time_stepping.get_solve_function_matrix(
matrix_function)
final_solution = time_stepping.time_step_loop_imex(
dg_solution,
t_initial,
t_final,
delta_t,
imex,
explicit_operator,
implicit_operator,
solve_operator,
)
error = math_utils.compute_error(final_solution,
exact_solution_final)
error_list.append(error)
# plot.plot_dg_1d(final_solution, function=exact_solution_final)
order = utils.convergence_order(error_list)
with open("hyper_diffusion_linearized_mms_test.yml",
"a") as file:
dict_ = dict()
subdict = dict()
subdict["cfl"] = cfl
subdict["n"] = n
subdict["error0"] = float(error_list[0])
subdict["error1"] = float(error_list[1])
subdict["order"] = float(
np.log2(error_list[0] / error_list[1]))
dict_[num_basis_cpts] = subdict
yaml.dump(dict_, file, default_flow_style=False)
assert order >= num_basis_cpts
def test_imex_nonlinear_mms():
wavenumber = 1.0 / 20.0
x_left = 0.0
x_right = 40.0
exact_solution = flux_functions.AdvectingSine(
amplitude=0.1, wavenumber=wavenumber, offset=0.15
)
p_func = thin_film.ThinFilm.manufactured_solution
t_initial = 0.0
bc = boundary.Periodic()
problem = p_func(exact_solution)
cfl_list = [0.5, 0.1, 0.1]
n = 40
for num_basis_cpts in range(3, 4):
imex = imex_runge_kutta.get_time_stepper(num_basis_cpts)
cfl = cfl_list[num_basis_cpts - 1]
t_final = 10 * cfl * ((x_right - x_left) / n) / exact_solution.wavespeed
exact_solution_final = lambda x: exact_solution(x, t_final)
for basis_class in [basis.LegendreBasis1D]:
basis_ = basis_class(num_basis_cpts)
error_list = []
for num_elems in [n, 2 * n]:
mesh_ = mesh.Mesh1DUniform(x_left, x_right, num_elems)
delta_t = cfl * mesh_.delta_x / exact_solution.wavespeed
dg_solution = basis_.project(problem.initial_condition, mesh_)
# weak dg form with flux_function and source term
explicit_operator = problem.get_explicit_operator(bc)
# ldg discretization of diffusion_function
implicit_operator = problem.get_implicit_operator(
bc, bc, bc, bc, include_source=False
)
matrix_function = lambda t, q: problem.ldg_matrix(
q, t, bc, bc, bc, bc, include_source=False
)
solve_operator = time_stepping.get_solve_function_picard(
matrix_function, num_basis_cpts, num_elems * num_basis_cpts
)
final_solution = time_stepping.time_step_loop_imex(
dg_solution,
t_initial,
t_final,
delta_t,
imex,
explicit_operator,
implicit_operator,
solve_operator,
)
error = math_utils.compute_error(final_solution, exact_solution_final)
error_list.append(error)
# plot.plot_dg_1d(final_solution, function=exact_solution_final)
with open("thin_film_nonlinear_mms_test.yml", "a") as file:
dict_ = dict()
subdict = dict()
subdict["cfl"] = cfl
subdict["n"] = n
subdict["error0"] = float(error_list[0])
subdict["error1"] = float(error_list[1])
subdict["order"] = float(np.log2(error_list[0] / error_list[1]))
dict_[num_basis_cpts] = subdict
yaml.dump(dict_, file, default_flow_style=False)
order = utils.convergence_order(error_list)
assert order >= num_basis_cpts