def test_example_03():
from hermes2d.examples.c03 import set_bc
set_verbose(False)
P_INIT = 5 # Uniform polynomial degree of mesh elements.
# Problem parameters.
CONST_F = 2.0
# Load the mesh file
mesh = Mesh()
mesh.load(get_example_mesh())
# Sample "manual" mesh refinement
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(1)
set_forms(wf)
# Initialize the linear system
ls = LinSystem(wf)
ls.set_spaces(space)
# Assemble and solve the matrix problem.
sln = Solution()
ls.assemble()
ls.solve_system(sln)
def test_example_05():
from hermes2d.examples.c05 import set_bc
from hermes2d.examples.c05 import set_forms as set_forms_surf
set_verbose(False)
P_INIT = 4 # initial polynomial degree in all elements
CORNER_REF_LEVEL = 12 # number of mesh refinements towards the re-entrant corner
# Load the mesh file
mesh = Mesh()
mesh.load(get_example_mesh())
# Perform initial mesh refinements.
mesh.refine_towards_vertex(3, CORNER_REF_LEVEL)
# 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 the linear system.
ls = LinSystem(wf)
ls.set_spaces(space)
# Assemble and solve the matrix problem
sln = Solution()
ls.assemble()
ls.solve_system(sln)
def test_example_04():
from hermes2d.examples.c04 import set_bc
set_verbose(False)
# Below you can play with the parameters CONST_F, P_INIT, and UNIFORM_REF_LEVEL.
INIT_REF_NUM = 2 # number of initial uniform mesh refinements
P_INIT = 2 # initial polynomial degree in all elements
# Load the mesh file
mesh = Mesh()
mesh.load(get_example_mesh())
# Perform initial mesh refinements
for i in range(INIT_REF_NUM):
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 the linear system
ls = LinSystem(wf)
ls.set_spaces(space)
# Assemble and solve the matrix problem
sln = Solution()
ls.assemble()
ls.solve_system(sln)
def test_example_05():
from hermes2d.examples.c05 import set_bc
from hermes2d.examples.c05 import set_forms as set_forms_surf
set_verbose(False)
P_INIT = 4 # initial polynomial degree in all elements
CORNER_REF_LEVEL = 12 # number of mesh refinements towards the re-entrant corner
# Load the mesh file
mesh = Mesh()
mesh.load(get_example_mesh())
# Perform initial mesh refinements.
mesh.refine_towards_vertex(3, CORNER_REF_LEVEL)
# 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 the linear system.
ls = LinSystem(wf)
ls.set_spaces(space)
# Assemble and solve the matrix problem
sln = Solution()
ls.assemble()
ls.solve_system(sln)
def test_example_04():
from hermes2d.examples.c04 import set_bc
set_verbose(False)
# Below you can play with the parameters CONST_F, P_INIT, and UNIFORM_REF_LEVEL.
INIT_REF_NUM = 2 # number of initial uniform mesh refinements
P_INIT = 2 # initial polynomial degree in all elements
# Load the mesh file
mesh = Mesh()
mesh.load(get_example_mesh())
# Perform initial mesh refinements
for i in range(INIT_REF_NUM):
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 the linear system
ls = LinSystem(wf)
ls.set_spaces(space)
# Assemble and solve the matrix problem
sln = Solution()
ls.assemble()
ls.solve_system(sln)
def test_example_03():
from hermes2d.examples.c03 import set_bc
set_verbose(False)
P_INIT = 5 # Uniform polynomial degree of mesh elements.
# Problem parameters.
CONST_F = 2.0
# Load the mesh file
mesh = Mesh()
mesh.load(get_example_mesh())
# Sample "manual" mesh refinement
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(1)
set_forms(wf)
# Initialize the linear system
ls = LinSystem(wf)
ls.set_spaces(space)
# Assemble and solve the matrix problem.
sln = Solution()
ls.assemble()
ls.solve_system(sln)
def test_example_02():
set_verbose(False)
P_INIT = 3
# Load the mesh file
domain_mesh = get_example_mesh() # Original L-shape domain
mesh = Mesh()
mesh.load(domain_mesh)
# Refine all elements (optional)
mesh.refine_all_elements()
# Create a shapeset and an H1 space
space = H1Space(mesh)
# Assign element orders and initialize the space
space.set_uniform_order(P_INIT) # Set uniform polynomial order
def test_example_02():
set_verbose(False)
P_INIT = 3
# Load the mesh file
domain_mesh = get_example_mesh() # Original L-shape domain
mesh = Mesh()
mesh.load(domain_mesh)
# Refine all elements (optional)
mesh.refine_all_elements()
# Create a shapeset and an H1 space
space = H1Space(mesh)
# Assign element orders and initialize the space
space.set_uniform_order(P_INIT) # Set uniform polynomial order
def test_example_06():
from hermes2d.examples.c06 import set_bc, set_forms
set_verbose(False)
# The following parameters can be changed:
UNIFORM_REF_LEVEL = 2
# Number of initial uniform mesh refinements.
CORNER_REF_LEVEL = 12
# Number of mesh refinements towards the re-entrant corner.
P_INIT = 6
# Uniform polynomial degree of all mesh elements.
# Boundary markers
NEWTON_BDY = 1
# Load the mesh file
mesh = Mesh()
mesh.load(get_example_mesh())
# Perform initial mesh refinements.
for i in range(UNIFORM_REF_LEVEL):
mesh.refine_all_elements()
mesh.refine_towards_vertex(3, CORNER_REF_LEVEL)
# 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 the linear system.
ls = LinSystem(wf)
ls.set_spaces(space)
# Assemble and solve the matrix problem
sln = Solution()
ls.assemble()
ls.solve_system(sln)
def test_example_06():
from hermes2d.examples.c06 import set_bc, set_forms
set_verbose(False)
# The following parameters can be changed:
UNIFORM_REF_LEVEL = 2; # Number of initial uniform mesh refinements.
CORNER_REF_LEVEL = 12; # Number of mesh refinements towards the re-entrant corner.
P_INIT = 6; # Uniform polynomial degree of all mesh elements.
# Boundary markers
NEWTON_BDY = 1
# Load the mesh file
mesh = Mesh()
mesh.load(get_example_mesh())
# Perform initial mesh refinements.
for i in range(UNIFORM_REF_LEVEL):
mesh.refine_all_elements()
mesh.refine_towards_vertex(3, CORNER_REF_LEVEL)
# 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 the linear system.
ls = LinSystem(wf)
ls.set_spaces(space)
# Assemble and solve the matrix problem
sln = Solution()
ls.assemble()
ls.solve_system(sln)
def test_example_12():
from hermes2d.examples.c12 import set_bc, set_forms
from hermes2d.examples import get_example_mesh
# The following parameters can be changed:
P_INIT = 1 # 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.
ADAPT_TYPE = 0 # Type of automatic adaptivity:
# ADAPT_TYPE = 0 ... adaptive hp-FEM (default),
# ADAPT_TYPE = 1 ... adaptive h-FEM,
# ADAPT_TYPE = 2 ... adaptive p-FEM.
ISO_ONLY = False # Isotropic refinement flag (concerns quadrilateral elements only).
# ISO_ONLY = false ... anisotropic refinement of quad elements
# is allowed (default),
# ISO_ONLY = true ... only isotropic refinements of quad elements
# are allowed.
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.
ERR_STOP = 0.01 # Stopping criterion for adaptivity (rel. error tolerance between the
# fine mesh and coarse mesh solution in percent).
NDOF_STOP = 40000 # Adaptivity process stops when the number of degrees of freedom grows
# over this limit. This is to prevent h-adaptivity to go on forever.
# Load the mesh
mesh = Mesh()
mesh.load(get_example_mesh())
# mesh.load("hermes2d/examples/12.mesh")
# Initialize the shapeset and the cache
shapeset = H1Shapeset()
pss = PrecalcShapeset(shapeset)
# Create finite element space
space = H1Space(mesh, shapeset)
set_bc(space)
space.set_uniform_order(P_INIT)
# Enumerate basis functions
space.assign_dofs()
# Initialize the weak formulation
wf = WeakForm(1)
set_forms(wf)
# Matrix solver
solver = DummySolver()
# Adaptivity loop
it = 0
ndofs = 0
done = False
sln_coarse = Solution()
sln_fine = Solution()
# Solve the coarse mesh problem
ls = LinSystem(wf, solver)
ls.set_spaces(space)
ls.set_pss(pss)
ls.assemble()
ls.solve_system(sln_coarse)
# Solve the fine mesh problem
rs = RefSystem(ls)
rs.assemble()
rs.solve_system(sln_fine)
# Calculate element errors and total error estimate
hp = H1OrthoHP(space)
err_est = hp.calc_error(sln_coarse, sln_fine) * 100
FN_DX,
FN_DY,
H1OrthoHP,
RefSystem,
)
from hermes2d.forms import set_forms
from hermes2d.examples import (
get_example_mesh,
get_sample_mesh,
get_cylinder_mesh,
get_07_mesh,
get_cathedral_mesh,
get_bracket_mesh,
)
domain_mesh = get_example_mesh()
sample_mesh = get_sample_mesh()
cylinder_mesh = get_cylinder_mesh()
def test_example_01():
mesh = Mesh()
mesh.load(domain_mesh)
mesh.refine_all_elements()
mesh.refine_all_elements()
mesh.refine_all_elements()
def test_example_02():
set_verbose(False)
#! /usr/bin/env python # This example shows how to load a mesh, perform various types # of "manual" element refinements. # Import modules from hermes2d import Mesh, MeshView from hermes2d.examples import get_example_mesh # Load the mesh file domain_mesh = get_example_mesh() mesh = Mesh() mesh.load(domain_mesh) # Perform some sample initial refinements mesh.refine_all_elements(); # Refines all elements. #mesh.refine_towards_vertex(3, 4); # Refines mesh towards vertex #3 (4x). #mesh.refine_towards_boundary(2, 4); # Refines all elements along boundary 2 (4x). # Display the mesh mesh.plot()
#! /usr/bin/env python
from hermes2d import Mesh, MeshView, H1Shapeset, PrecalcShapeset, H1Space, \
WeakForm, Solution, ScalarView, LinSystem, DummySolver
from hermes2d.forms import set_forms
from hermes2d.examples import get_example_mesh
mesh = Mesh()
mesh.load(get_example_mesh())
mesh.refine_element(0)
shapeset = H1Shapeset()
pss = PrecalcShapeset(shapeset)
# create an H1 space
space = H1Space(mesh, shapeset)
space.set_uniform_order(5)
space.assign_dofs()
# initialize the discrete problem
wf = WeakForm(1)
set_forms(wf)
solver = DummySolver()
sys = LinSystem(wf, solver)
sys.set_spaces(space)
sys.set_pss(pss)
# assemble the stiffness matrix and solve the system
sys.assemble()
A = sys.get_matrix()
b = sys.get_rhs()
# The following parameters can be changed:
UNIFORM_REF_LEVEL = 2
# Number of initial uniform mesh refinements.
CORNER_REF_LEVEL = 12
# Number of mesh refinements towards the re-entrant corner.
P_INIT = 6
# Uniform polynomial degree of all mesh elements.
# Boundary markers
NEWTON_BDY = 1
# Load the mesh file
mesh = Mesh()
mesh.load(get_example_mesh())
# Perform initial mesh refinements.
for i in range(UNIFORM_REF_LEVEL):
mesh.refine_all_elements()
mesh.refine_towards_vertex(3, CORNER_REF_LEVEL)
# 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 the linear system.
#
# You can use this example to visualize all shape functions
# on the reference square and reference triangle domains,
# just load the corresponding mesh at the beginning of the file.
# Import modules
from hermes2d import Mesh, H1Shapeset, PrecalcShapeset, H1Space, \
BaseView
from hermes2d.forms import set_forms
from hermes2d.examples import get_example_mesh
P_INIT = 3
# Load the mesh file
domain_mesh = get_example_mesh() # Original L-shape domain
mesh = Mesh()
mesh.load(domain_mesh)
# Refine all elements (optional)
mesh.refine_all_elements()
# Create a shapeset and an H1 space
space = H1Space(mesh)
# Assign element orders and initialize the space
space.set_uniform_order(P_INIT) # Set uniform polynomial order
# P_INIT to all mesh elements.
# View the basis functions
bview = BaseView()
#
# You can use this example to visualize all shape functions
# on the reference square and reference triangle domains,
# just load the corresponding mesh at the beginning of the file.
# Import modules
from hermes2d import Mesh, H1Shapeset, PrecalcShapeset, H1Space, \
BaseView
from hermes2d.forms import set_forms
from hermes2d.examples import get_example_mesh
P_INIT = 3
# Load the mesh file
domain_mesh = get_example_mesh() # Original L-shape domain
mesh = Mesh()
mesh.load(domain_mesh)
# Refine all elements (optional)
mesh.refine_all_elements()
# Create a shapeset and an H1 space
space = H1Space(mesh)
# Assign element orders and initialize the space
space.set_uniform_order(P_INIT) # Set uniform polynomial order
# P_INIT to all mesh elements.
# View the basis functions
bview = BaseView()
