# 3. Allocate an object of the Stokes class
stokes_problem = Stokes(V, subdomains=subdomains, boundaries=boundaries)
mu_range = [(0.5, 1.5), (0.5, 1.5), (0.5, 1.5), (0.5, 1.5), (0.5, 1.5),
(0., pi / 6.)]
stokes_problem.set_mu_range(mu_range)
# 4. Prepare reduction with a POD-Galerkin method
reduced_basis_method = ReducedBasis(stokes_problem)
reduced_basis_method.set_Nmax(25)
reduced_basis_method.set_tolerance(1e-6)
# 5. Perform the offline phase
first_mu = (0.5, 0.5, 0.5, 0.5, 0.5, 0.)
stokes_problem.set_mu(first_mu)
reduced_basis_method.initialize_training_set(
100, sampling=LinearlyDependentUniformDistribution())
reduced_stokes_problem = reduced_basis_method.offline()
# 6. Perform an online solve
online_mu = (1.0, 1.0, 1.0, 1.0, 1.0, pi / 6.)
reduced_stokes_problem.set_mu(online_mu)
reduced_stokes_problem.solve()
reduced_stokes_problem.export_solution(filename="online_solution")
# 7. Perform an error analysis
reduced_basis_method.initialize_testing_set(
100, sampling=LinearlyDependentUniformDistribution())
reduced_basis_method.error_analysis()
# 8. Perform a speedup analysis
reduced_basis_method.speedup_analysis()
(0.5, 1.5),
(0.5, 1.5),
(0.5, 1.5),
(0.5, 1.5),
(0.5, 1.5),
(0., pi/6.)
]
stokes_problem.set_mu_range(mu_range)
# 4. Prepare reduction with a POD-Galerkin method
pod_galerkin_method = PODGalerkin(stokes_problem)
pod_galerkin_method.set_Nmax(25)
pod_galerkin_method.set_tolerance(1e-6)
# 5. Perform the offline phase
pod_galerkin_method.initialize_training_set(100, sampling=LinearlyDependentUniformDistribution())
reduced_stokes_problem = pod_galerkin_method.offline()
# 6. Perform an online solve
online_mu = (1.0, 1.0, 1.0, 1.0, 1.0, pi/6.)
reduced_stokes_problem.set_mu(online_mu)
reduced_stokes_problem.solve()
reduced_stokes_problem.export_solution(filename="online_solution")
# 7. Perform an error analysis
pod_galerkin_method.initialize_testing_set(100, sampling=LinearlyDependentUniformDistribution())
pod_galerkin_method.error_analysis()
# 8. Perform a speedup analysis
pod_galerkin_method.speedup_analysis()
(0.5, 1.5),
(0.5, 1.5),
(0.5, 1.5),
(0., pi/6.)
]
stokes_problem.set_mu_range(mu_range)
# 4. Prepare reduction with a POD-Galerkin method
reduced_basis_method = ReducedBasis(stokes_problem)
reduced_basis_method.set_Nmax(25)
reduced_basis_method.set_tolerance(1e-6)
# 5. Perform the offline phase
lifting_mu = (1.0, 1.0, 1.0, 1.0, 1.0, 0.0)
stokes_problem.set_mu(lifting_mu)
reduced_basis_method.initialize_training_set(100, sampling=LinearlyDependentUniformDistribution())
reduced_stokes_problem = reduced_basis_method.offline()
# 6. Perform an online solve
online_mu = (1.0, 1.0, 1.0, 1.0, 1.0, pi/6.)
reduced_stokes_problem.set_mu(online_mu)
reduced_stokes_problem.solve()
reduced_stokes_problem.export_solution(filename="online_solution")
# 7. Perform an error analysis
reduced_basis_method.initialize_testing_set(100, sampling=LinearlyDependentUniformDistribution())
reduced_basis_method.error_analysis()
# 8. Perform a speedup analysis
reduced_basis_method.speedup_analysis()
mu_range = [
(0.5, 1.5),
(0.5, 1.5),
(0.5, 1.5),
(0.5, 1.5),
(0.5, 1.5),
(0., pi/6.)
]
stokes_problem.set_mu_range(mu_range)
# 4a. Prepare reduction with a POD-Galerkin method
stokes_pod_galerkin_method = PODGalerkin(stokes_problem)
stokes_pod_galerkin_method.set_Nmax(25)
# 5a. Perform the offline phase
stokes_pod_galerkin_method.initialize_training_set(100, sampling=LinearlyDependentUniformDistribution())
reduced_stokes_problem = stokes_pod_galerkin_method.offline()
# 6a. Perform an online solve
online_mu = (1.0, 1.0, 1.0, 1.0, 1.0, pi/6.)
reduced_stokes_problem.set_mu(online_mu)
reduced_stokes_problem.solve()
reduced_stokes_problem.export_solution(filename="online_solution")
# 2b. Create Finite Element space for advection diffusion problem
element_c = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
C = FunctionSpace(mesh, element_c)
# 3b. Allocate an object of the AdvectionDiffusionProblem class
advection_diffusion_problem = AdvectionDiffusion(C, subdomains=subdomains, boundaries=boundaries, stokes_problem=stokes_problem)
advection_diffusion_problem.set_mu_range(mu_range)
mu_range = [
(0.5, 1.5),
(0.5, 1.5),
(0.5, 1.5),
(0.5, 1.5),
(0.5, 1.5),
(0., pi / 6.)
]
stokes_problem.set_mu_range(mu_range)
# 4a. Prepare reduction with a POD-Galerkin method
stokes_reduction_method = PODGalerkin(stokes_problem)
stokes_reduction_method.set_Nmax(25)
# 5a. Perform the offline phase
stokes_reduction_method.initialize_training_set(100, sampling=LinearlyDependentUniformDistribution())
stokes_reduced_problem = stokes_reduction_method.offline()
# 6a. Perform an online solve
online_mu = (1.0, 1.0, 1.0, 1.0, 1.0, pi / 6.)
stokes_reduced_problem.set_mu(online_mu)
stokes_reduced_problem.solve()
stokes_reduced_problem.export_solution(filename="online_solution")
# 2b. Create Finite Element space for advection diffusion problem
element_c = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
C = FunctionSpace(mesh, element_c)
# 3b. Allocate an object of the AdvectionDiffusionProblem class
advection_diffusion_problem = AdvectionDiffusion(
C, subdomains=subdomains, boundaries=boundaries, stokes_problem=stokes_problem)