# their notoriously bad performance. CONV_EXP = 1.0 ERR_STOP = 0.1 # Stopping criterion for adaptivity (rel. error tolerance between the # fine mesh and coarse mesh solution in percent). NDOF_STOP = 60000 # Adaptivity process stops when the number of degrees of freedom grows # over this limit. This is to prevent h-adaptivity to go on forever. H2DRS_DEFAULT_ORDER = -1 # A default order. Used to indicate an unkonwn order or a maximum support order # Boundary markers BDY_DIRICHLET = 1 BDY_NEUMANN = 2 # Load the mesh mesh = Mesh() mesh.load(get_12_mesh()) # Perform initial mesh refinements mesh.refine_all_elements() # Create an H1 space with default shapeset space = H1Space(mesh, P_INIT) set_bc(space) # Initialize the weak formulation wf = WeakForm() set_forms(wf) # Initialize views sview = ScalarView("Coarse solution", 0, 0, 600, 1000) oview = OrderView("Polynomial orders", 1220, 0, 600, 1000)
def test_example_12(): from hermes2d.examples.c12 import set_bc, set_forms from hermes2d.examples import get_12_mesh # The following parameters can be changed: SOLVE_ON_COARSE_MESH = True # if true, coarse mesh FE problem is solved in every adaptivity step P_INIT = 2 # Initial polynomial degree of all mesh elements. THRESHOLD = 0.6 # This is a quantitative parameter of the adapt(...) function and # it has different meanings for various adaptive strategies (see below). STRATEGY = 0 # Adaptive strategy: # STRATEGY = 0 ... refine elements until sqrt(THRESHOLD) times total # error is processed. If more elements have similar errors, refine # all to keep the mesh symmetric. # STRATEGY = 1 ... refine all elements whose error is larger # than THRESHOLD times maximum element error. # STRATEGY = 2 ... refine all elements whose error is larger # than THRESHOLD. # More adaptive strategies can be created in adapt_ortho_h1.cpp. CAND_LIST = CandList.H2D_HP_ANISO # Predefined list of element refinement candidates. # Possible values are are attributes of the class CandList: # P_ISO, P_ANISO, H_ISO, H_ANISO, HP_ISO, HP_ANISO_H, HP_ANISO_P, HP_ANISO # See the Sphinx tutorial (http://hpfem.org/hermes2d/doc/src/tutorial-2.html#adaptive-h-fem-and-hp-fem) for details. MESH_REGULARITY = -1 # Maximum allowed level of hanging nodes: # MESH_REGULARITY = -1 ... arbitrary level hangning nodes (default), # MESH_REGULARITY = 1 ... at most one-level hanging nodes, # MESH_REGULARITY = 2 ... at most two-level hanging nodes, etc. # Note that regular meshes are not supported, this is due to # their notoriously bad performance. CONV_EXP = 1.0 ERR_STOP = 0.1 # Stopping criterion for adaptivity (rel. error tolerance between the # fine mesh and coarse mesh solution in percent). NDOF_STOP = 60000 # Adaptivity process stops when the number of degrees of freedom grows # over this limit. This is to prevent h-adaptivity to go on forever. H2DRS_DEFAULT_ORDER = -1 # A default order. Used to indicate an unkonwn order or a maximum support order # Boundary markers BDY_DIRICHLET = 1 BDY_NEUMANN = 2 # Load the mesh mesh = Mesh() mesh.load(get_12_mesh()) # Perform initial mesh refinements mesh.refine_all_elements() # Create an H1 space with default shapeset space = H1Space(mesh, P_INIT) set_bc(space) # Initialize the weak formulation wf = WeakForm() set_forms(wf) # Initialize refinement selector selector = H1ProjBasedSelector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER) # Initialize the linear system. ls = LinSystem(wf) ls.set_spaces(space) sln_coarse = Solution() sln_fine = Solution() # Assemble and solve the fine mesh problem rs = RefSystem(ls) rs.assemble() rs.solve_system(sln_fine) # Either solve on coarse mesh or project the fine mesh solution # on the coarse mesh. if SOLVE_ON_COARSE_MESH: ls.assemble() ls.solve_system(sln_coarse) # Calculate error estimate wrt. fine mesh solution hp = H1Adapt(ls) hp.set_solutions([sln_coarse], [sln_fine]) err_est = hp.calc_error() * 100