def p_convergence(config: ConfigParser, solver: Solver, sol: GridFunction, var: str) -> None:
"""
Function to check p (interpolat polynomial order) convergence and print results.
Args:
config: Config file from which to grab
solver: The solver used
sol: Gridfunction that contains the current solution
var: The variable of interest.
"""
num_refinements = config.get_item(['ERROR ANALYSIS', 'num_refinements'], int)
average_lst = config.get_list(['ERROR ANALYSIS', 'error_average'], str, quiet=True)
component = solver.model.model_components[var]
average = component in average_lst
# Reload the model's mesh and finite element space so convergence tests can be chained and don't affect each other.
solver.model.load_mesh_fes(mesh=True, fes=True)
# First solve used the default settings.
if component is None:
err = norm('l2_norm', sol, solver.model.ref_sol['ref_sols'][var],
solver.model.mesh, solver.model.fes, average)
else:
err = norm('l2_norm', sol.components[component], solver.model.ref_sol['ref_sols'][var],
solver.model.mesh, solver.model.fes.components[component], average)
# Track the convergence information.
num_dofs_lst = [solver.model.fes.ndof]
interp_ord_lst = [solver.model.interp_ord[var]]
error_lst = [err]
# Then run through a series of interpolant refinements.
for n in range(num_refinements):
solver.model.interp_ord = {key: val + 1 for key, val in solver.model.interp_ord.items()}
solver.model.load_mesh_fes(mesh=False, fes=True)
solver.reset_model()
sol = solver.solve()
if component is None:
err = norm('l2_norm', sol, solver.model.ref_sol['ref_sols'][var],
solver.model.mesh, solver.model.fes, average)
else:
err = norm('l2_norm', sol.components[component], solver.model.ref_sol['ref_sols'][var],
solver.model.mesh, solver.model.fes.components[component], average)
num_dofs_lst.append(solver.model.fes.ndof)
interp_ord_lst.append(solver.model.interp_ord[var])
error_lst.append(err)
print('L2 norm at refinement {0}: {1}'.format(n, err))
# Display the results nicely.
convergence_table = [['Interpolant Order', 'DOFs', 'Error', 'Convergence Rate']]
convergence_table.append([interp_ord_lst[0], num_dofs_lst[0], error_lst[0], 0])
for n in range(num_refinements):
# TODO: Not sure if this is the correct equation for p-convergence.
convergence_rate = math.log(error_lst[n] / error_lst[n + 1]) / math.log(num_dofs_lst[n + 1] / num_dofs_lst[n])
convergence_table.append([interp_ord_lst[n + 1], num_dofs_lst[n + 1], error_lst[n + 1], convergence_rate])
print(tabulate.tabulate(convergence_table, headers='firstrow', floatfmt=['.1f', '.1f', '.3e', '.2f']))
def h_convergence(config: ConfigParser, solver: Solver, sol: GridFunction, var: str) -> None:
"""
Function to check h (mesh element size) convergence and print results.
Args:
config: Config file from which to grab
solver: The solver used
sol: Gridfunction that contains the current solution
var: The variable of interest.
"""
num_refinements = config.get_item(['ERROR ANALYSIS', 'num_refinements'], int)
average_lst = config.get_list(['ERROR ANALYSIS', 'error_average'], str, quiet=True)
component = solver.model.model_components[var]
average = component in average_lst
# Reload the model's mesh and finite element space so convergence tests can be chained and don't affect each other.
solver.model.load_mesh_fes(mesh=True, fes=True)
# First solve used the default settings.
if component is None:
err = norm('l2_norm', sol, solver.model.ref_sol['ref_sols'][var],
solver.model.mesh, solver.model.fes, average)
else:
err = norm('l2_norm', sol.components[component], solver.model.ref_sol['ref_sols'][var],
solver.model.mesh, solver.model.fes.components[component], average)
# Track the convergence information.
num_dofs_lst = [solver.model.fes.ndof]
error_lst = [err]
# Then run through a series of mesh refinements and resolve on each
# refined mesh.
for n in range(num_refinements):
solver.model.mesh.Refine()
solver.model.fes.Update()
solver.reset_model()
sol = solver.solve()
if component is None:
err = norm('l2_norm', sol, solver.model.ref_sol['ref_sols'][var],
solver.model.mesh, solver.model.fes, average)
else:
err = norm('l2_norm', sol.components[component], solver.model.ref_sol['ref_sols'][var],
solver.model.mesh, solver.model.fes.components[component], average)
num_dofs_lst.append(solver.model.fes.ndof)
error_lst.append(err)
print('L2 norm at refinement {0}: {1}'.format(n, err))
# Display the results nicely.
convergence_table = [['Refinement Level', 'DOFs', 'Error', 'Convergence Rate']]
convergence_table.append([1, num_dofs_lst[0], error_lst[0], 0])
for n in range(num_refinements):
ref_level = '1/{}'.format(int(2 ** (n + 1)))
convergence_rate = math.log(error_lst[n] / error_lst[n + 1]) / \
(math.log(num_dofs_lst[n + 1] / (num_dofs_lst[n] * 2.0 ** (solver.model.mesh.dim - 1))))
convergence_table.append([ref_level, num_dofs_lst[n + 1], error_lst[n + 1], convergence_rate])
print(tabulate.tabulate(convergence_table, headers='firstrow', floatfmt=('.1f', '.1f', '.3e', '.2f')))