def test_ScalarView_mpl_unknown():
mesh = Mesh()
mesh.load(domain_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()
from scipy.sparse.linalg import cg
x, res = cg(A, b)
sln = Solution()
sln.set_fe_solution(space, pss, x)
view = ScalarView("Solution")
def test_ScalarView_mpl_unknown():
mesh = Mesh()
mesh.load(domain_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()
from scipy.sparse.linalg import cg
x, res = cg(A, b)
sln = Solution()
sln.set_fe_solution(space, pss, x)
view = ScalarView("Solution")
def test_example_03():
set_verbose(False)
mesh = Mesh()
mesh.load(domain_mesh)
mesh.refine_element(0)
shapeset = H1Shapeset()
pss = PrecalcShapeset(shapeset)
# create an H1 space
space = H1Space(mesh, shapeset)
space.set_uniform_order(5)
from hermes2d.examples.c03 import set_bc
set_bc(space)
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
sln = Solution()
sys.assemble()
sys.solve_system(sln)
assert abs(sln.l2_norm() - 0.25493) < 1e-4
assert abs(sln.h1_norm() - 0.89534) < 1e-4
def test_example_08():
from hermes2d.examples.c08 import set_bc, set_forms
set_verbose(False)
# The following parameter can be changed:
P_INIT = 4
# Load the mesh file
mesh = Mesh()
mesh.load(get_sample_mesh())
# Perform uniform mesh refinement
mesh.refine_all_elements()
# Create the x- and y- displacement space using the default H1 shapeset
xdisp = H1Space(mesh, P_INIT)
ydisp = H1Space(mesh, P_INIT)
set_bc(xdisp, ydisp)
# Initialize the weak formulation
wf = WeakForm(2)
set_forms(wf)
# Initialize the linear system.
ls = LinSystem(wf)
ls.set_spaces(xdisp, ydisp)
# Assemble and solve the matrix problem
xsln = Solution()
ysln = Solution()
ls.assemble()
ls.solve_system(xsln, ysln, lib="scipy")
def test_example_07():
from hermes2d.examples.c07 import set_bc, set_forms
set_verbose(False)
# The following parameters can be changed:
P_INIT = 2 # Initial polynomial degree of all mesh elements.
INIT_REF_NUM = 4 # Number of initial uniform refinements
# Load the mesh
mesh = Mesh()
mesh.load(get_07_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_matrix():
set_verbose(False)
mesh = Mesh()
mesh.load(domain_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
sln = Solution()
sys.assemble()
A = sys.get_matrix()
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_08():
from hermes2d.examples.c08 import set_bc, set_forms
set_verbose(False)
mesh = Mesh()
mesh.load(cylinder_mesh)
#mesh.refine_element(0)
#mesh.refine_all_elements()
mesh.refine_towards_boundary(5, 3)
shapeset = H1Shapeset()
pss = PrecalcShapeset(shapeset)
# create an H1 space
xvel = H1Space(mesh, shapeset)
yvel = H1Space(mesh, shapeset)
press = H1Space(mesh, shapeset)
xvel.set_uniform_order(2)
yvel.set_uniform_order(2)
press.set_uniform_order(1)
set_bc(xvel, yvel, press)
ndofs = 0
ndofs += xvel.assign_dofs(ndofs)
ndofs += yvel.assign_dofs(ndofs)
ndofs += press.assign_dofs(ndofs)
xprev = Solution()
yprev = Solution()
xprev.set_zero(mesh)
yprev.set_zero(mesh)
# initialize the discrete problem
wf = WeakForm(3)
set_forms(wf, xprev, yprev)
solver = DummySolver()
sys = LinSystem(wf, solver)
sys.set_spaces(xvel, yvel, press)
sys.set_pss(pss)
#dp.set_external_fns(xprev, yprev)
# visualize the solution
EPS_LOW = 0.0014
for i in range(3):
psln = Solution()
sys.assemble()
sys.solve_system(xprev, yprev, psln)
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_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_08():
from hermes2d.examples.c08 import set_bc, set_forms
set_verbose(False)
# The following parameter can be changed:
P_INIT = 4
# Load the mesh file
mesh = Mesh()
mesh.load(get_sample_mesh())
# Perform uniform mesh refinement
mesh.refine_all_elements()
# Create the x- and y- displacement space using the default H1 shapeset
xdisp = H1Space(mesh, P_INIT)
ydisp = H1Space(mesh, P_INIT)
set_bc(xdisp, ydisp)
# Initialize the weak formulation
wf = WeakForm(2)
set_forms(wf)
# Initialize the linear system.
ls = LinSystem(wf)
ls.set_spaces(xdisp, ydisp)
# Assemble and solve the matrix problem
xsln = Solution()
ysln = Solution()
ls.assemble()
ls.solve_system(xsln, ysln, lib="scipy")
def test_example_07():
from hermes2d.examples.c07 import set_bc, set_forms
set_verbose(False)
# The following parameters can be changed:
P_INIT = 2 # Initial polynomial degree of all mesh elements.
INIT_REF_NUM = 4 # Number of initial uniform refinements
# Load the mesh
mesh = Mesh()
mesh.load(get_07_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_09():
from hermes2d.examples.c09 import set_bc, temp_ext, set_forms
# The following parameters can be changed:
INIT_REF_NUM = 4 # number of initial uniform mesh refinements
INIT_REF_NUM_BDY = 1 # number of initial uniform mesh refinements towards the boundary
P_INIT = 4 # polynomial degree of all mesh elements
TAU = 300.0 # time step in seconds
# Problem constants
T_INIT = 10 # temperature of the ground (also initial temperature)
FINAL_TIME = 86400 # length of time interval (24 hours) in seconds
# Global variable
TIME = 0
# Boundary markers.
bdy_ground = 1
bdy_air = 2
# Load the mesh
mesh = Mesh()
mesh.load(get_cathedral_mesh())
# Perform initial mesh refinements
for i in range(INIT_REF_NUM):
mesh.refine_all_elements()
mesh.refine_towards_boundary(bdy_air, INIT_REF_NUM_BDY)
# Create an H1 space with default shapeset
space = H1Space(mesh, P_INIT)
set_bc(space)
# Set initial condition
tsln = Solution()
tsln.set_const(mesh, T_INIT)
# Initialize the weak formulation
wf = WeakForm()
set_forms(wf)
# Initialize the linear system.
ls = LinSystem(wf)
ls.set_spaces(space)
# Time stepping
nsteps = int(FINAL_TIME / TAU + 0.5)
rhsonly = False
# Assemble and solve
ls.assemble()
rhsonly = True
ls.solve_system(tsln, lib="scipy")
def test_example_07():
from hermes2d.examples.c07 import set_bc, set_forms
set_verbose(False)
mesh = Mesh()
mesh.load(sample_mesh)
#mesh.refine_element(0)
#mesh.refine_all_elements()
#mesh.refine_towards_boundary(5, 3)
shapeset = H1Shapeset()
pss = PrecalcShapeset(shapeset)
# create an H1 space
xdisp = H1Space(mesh, shapeset)
ydisp = H1Space(mesh, shapeset)
xdisp.set_uniform_order(8)
ydisp.set_uniform_order(8)
set_bc(xdisp, ydisp)
ndofs = xdisp.assign_dofs(0)
ndofs += ydisp.assign_dofs(ndofs)
# initialize the discrete problem
wf = WeakForm(2)
set_forms(wf)
solver = DummySolver()
sys = LinSystem(wf, solver)
sys.set_spaces(xdisp, ydisp)
sys.set_pss(pss)
xsln = Solution()
ysln = Solution()
old_flag = set_warn_integration(False)
sys.assemble()
set_warn_integration(old_flag)
sys.solve_system(xsln, ysln)
E = float(200e9)
nu = 0.3
stress = VonMisesFilter(xsln, ysln, E / (2*(1 + nu)),
(E * nu) / ((1 + nu) * (1 - 2*nu)))
def test_example_02():
set_verbose(False)
mesh = Mesh()
mesh.load(domain_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)
def test_example_09():
from hermes2d.examples.c09 import set_bc, temp_ext, set_forms
# The following parameters can be changed:
INIT_REF_NUM = 4 # number of initial uniform mesh refinements
INIT_REF_NUM_BDY = 1 # number of initial uniform mesh refinements towards the boundary
P_INIT = 4 # polynomial degree of all mesh elements
TAU = 300.0 # time step in seconds
# Problem constants
T_INIT = 10 # temperature of the ground (also initial temperature)
FINAL_TIME = 86400 # length of time interval (24 hours) in seconds
# Global variable
TIME = 0;
# Boundary markers.
bdy_ground = 1
bdy_air = 2
# Load the mesh
mesh = Mesh()
mesh.load(get_cathedral_mesh())
# Perform initial mesh refinements
for i in range(INIT_REF_NUM):
mesh.refine_all_elements()
mesh.refine_towards_boundary(bdy_air, INIT_REF_NUM_BDY)
# Create an H1 space with default shapeset
space = H1Space(mesh, P_INIT)
set_bc(space)
# Set initial condition
tsln = Solution()
tsln.set_const(mesh, T_INIT)
# Initialize the weak formulation
wf = WeakForm()
set_forms(wf)
# Initialize the linear system.
ls = LinSystem(wf)
ls.set_spaces(space)
# Time stepping
nsteps = int(FINAL_TIME/TAU + 0.5)
rhsonly = False;
# Assemble and solve
ls.assemble()
rhsonly = True
ls.solve_system(tsln, lib="scipy")
def test_example_04():
from hermes2d.examples.c04 import set_bc
set_verbose(False)
mesh = Mesh()
mesh.load(domain_mesh)
# mesh.refine_element(0)
# mesh.refine_all_elements()
mesh.refine_towards_boundary(5, 3)
shapeset = H1Shapeset()
pss = PrecalcShapeset(shapeset)
# create an H1 space
space = H1Space(mesh, shapeset)
space.set_uniform_order(5)
set_bc(space)
space.assign_dofs()
xprev = Solution()
yprev = Solution()
# initialize the discrete problem
wf = WeakForm()
set_forms(wf, -4)
solver = DummySolver()
sys = LinSystem(wf, solver)
sys.set_spaces(space)
sys.set_pss(pss)
# assemble the stiffness matrix and solve the system
sys.assemble()
sln = Solution()
sys.solve_system(sln)
assert abs(sln.l2_norm() - 1.22729) < 1e-4
assert abs(sln.h1_norm() - 2.90006) < 1e-4
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_05():
from hermes2d.examples.c05 import set_bc
from hermes2d.examples.c05 import set_forms as set_forms_surf
set_verbose(False)
mesh = Mesh()
mesh.load(domain_mesh)
mesh.refine_towards_vertex(3, 12)
shapeset = H1Shapeset()
pss = PrecalcShapeset(shapeset)
# create an H1 space
space = H1Space(mesh, shapeset)
space.set_uniform_order(4)
set_bc(space)
space.assign_dofs()
xprev = Solution()
yprev = Solution()
# initialize the discrete problem
wf = WeakForm(1)
set_forms(wf, -1)
set_forms_surf(wf)
sln = Solution()
solver = DummySolver()
sys = LinSystem(wf, solver)
sys.set_spaces(space)
sys.set_pss(pss)
sys.assemble()
sys.solve_system(sln)
assert abs(sln.l2_norm() - 0.535833) < 1e-4
assert abs(sln.h1_norm() - 1.332908) < 1e-4
def poisson_solver(mesh_tuple):
"""
Poisson solver.
mesh_tuple ... a tuple of (nodes, elements, boundary, nurbs)
"""
set_verbose(False)
mesh = Mesh()
mesh.create(*mesh_tuple)
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()
from scipy.sparse.linalg import cg
x, res = cg(A, b)
sln = Solution()
sln.set_fe_solution(space, pss, x)
return sln
def test_example_07():
from hermes2d.examples.c07 import set_bc, set_forms
set_verbose(False)
P_INIT = 2 # Initial polynomial degree of all mesh elements.
mesh = Mesh()
mesh.load(get_07_mesh())
# Initialize the shapeset and the cache
shapeset = H1Shapeset()
pss = PrecalcShapeset(shapeset)
# create finite element space
space = H1Space(mesh, shapeset)
space.set_uniform_order(P_INIT)
set_bc(space)
# Enumerate basis functions
space.assign_dofs()
# weak formulation
wf = WeakForm(1)
set_forms(wf)
# matrix solver
solver = DummySolver()
# Solve the problem
sln = Solution()
ls = LinSystem(wf, solver)
ls.set_spaces(space)
ls.set_pss(pss)
ls.assemble()
ls.solve_system(sln)
def test_matrix():
set_verbose(False)
mesh = Mesh()
mesh.load(domain_mesh)
mesh.refine_element_id(0)
# create an H1 space with default shapeset
space = H1Space(mesh, 1)
# initialize the discrete problem
wf = WeakForm(1)
set_forms(wf)
sys = LinSystem(wf)
sys.set_spaces(space)
# assemble the stiffness matrix and solve the system
sln = Solution()
sys.assemble()
A = sys.get_matrix()
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_matrix():
set_verbose(False)
mesh = Mesh()
mesh.load(domain_mesh)
mesh.refine_element(0)
# create an H1 space with default shapeset
space = H1Space(mesh, 1)
# initialize the discrete problem
wf = WeakForm(1)
set_forms(wf)
sys = LinSystem(wf)
sys.set_spaces(space)
# assemble the stiffness matrix and solve the system
sln = Solution()
sys.assemble()
A = sys.get_matrix()
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)
# Initialize refinement selector
selector = H1ProjBasedSelector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER)
# Initialize the linear system.
ls = LinSystem(wf)
ls.set_spaces(space)
# Adaptivity loop
it = 0
done = False
sln_coarse = Solution()
sln_fine = Solution()
while (not done):
print("\n---- Adaptivity step %d ---------------------------------------------\n" % (it+1))
it += 1
# Assemble and solve the fine mesh problem
rs = RefSystem(ls)
rs.assemble()
set_forms(wf)
sln = Solution()
rsln = Solution()
solver = DummySolver()
view = ScalarView("Solution")
mview = MeshView("Mesh")
graph = []
iter = 0
print "Calculating..."
while 1:
space.assign_dofs()
sys = LinSystem(wf, solver)
sys.set_spaces(space)
sys.set_pss(pss)
sys.assemble()
sys.solve_system(sln)
dofs = sys.get_matrix().shape[0]
if interactive_plotting:
view.show(sln, lib="mayavi", filename="a%02d.png" % iter)
if show_mesh:
mview.show(mesh, lib="mpl", method="orders", filename="b%02d.png" % iter)
rsys = RefSystem(sys)
rsys.assemble()
rsys.solve_system(rsln)
it = 1
ndofs = 0
done = False
cpu = 0.0
sln_coarse = Solution()
sln_fine = Solution()
while(not done):
print("\n---- Adaptivity step %d ---------------------------------------------\n" % it)
it += 1
# Solve the coarse mesh problem
ls = LinSystem(wf, solver)
ls.set_spaces(space)
ls.set_pss(pss)
ls.assemble()
ls.solve_system(sln_coarse)
# View the solution
sview.show(sln_coarse, lib='mayavi')
# View the mesh
mview = MeshView("Example 7", 100, 100, 500, 500)
mview.show(mesh, lib="mpl", method="orders", notebook=False)
# Solve the fine mesh problem
rs = RefSystem(ls)
rs.assemble()
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()
from scipy.sparse.linalg import cg
x, res = cg(A, b)
sln = Solution()
sln.set_fe_solution(space, pss, x)
view = ScalarView("Solution")
view.show(sln, lib="mayavi")
# view.wait()
yprev.set_zero(mesh)
# initialize the discrete problem
wf = WeakForm(3)
set_forms(wf, xprev, yprev)
# visualize the solution
vview = VectorView("velocity [m/s]", 0, 0, 1200, 350)
pview = ScalarView("pressure [Pa]", 0, 500, 1200, 350)
vview.set_min_max_range(0, 1.9)
vview.show_scale(False)
pview.show_scale(False)
pview.show_mesh(False)
solver = DummySolver()
sys = LinSystem(wf, solver)
sys.set_spaces(xvel, yvel, press)
sys.set_pss(pss)
#dp.set_external_fns(xprev, yprev)
EPS_LOW = 0.0014
for i in range(1000):
print "*** Iteration %d ***" % i
psln = Solution()
sys.assemble()
sys.solve_system(xprev, yprev, psln)
vview.show(xprev, yprev, 2*EPS_LOW)
pview.show(psln)
vview.wait()
def test_example_22():
from hermes2d.examples.c22 import set_bc, set_forms
# The following parameters can be changed:
SOLVE_ON_COARSE_MESH = True # if true, coarse mesh FE problem is solved in every adaptivity step
INIT_REF_NUM = 1 # Number of initial uniform mesh refinements
P_INIT = 2 # Initial polynomial degree of all mesh elements.
THRESHOLD = 0.3 # 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 = 0.5
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
# Problem parameters.
SLOPE = 60 # Slope of the layer.
# Load the mesh
mesh = Mesh()
mesh.create([
[0, 0],
[1, 0],
[1, 1],
[0, 1],
], [
[2, 3, 0, 1, 0],
], [
[0, 1, 1],
[1, 2, 1],
[2, 3, 1],
[3, 0, 1],
], [])
# 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 coarse mesh problem
ls = LinSystem(wf)
ls.set_spaces(space)
# Adaptivity loop
iter = 0
done = False
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
def test_example_22():
from hermes2d.examples.c22 import set_bc, set_forms
# The following parameters can be changed:
SOLVE_ON_COARSE_MESH = True # if true, coarse mesh FE problem is solved in every adaptivity step
INIT_REF_NUM = 1 # Number of initial uniform mesh refinements
P_INIT = 2 # Initial polynomial degree of all mesh elements.
THRESHOLD = 0.3 # 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 = 0.5
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
# Problem parameters.
SLOPE = 60 # Slope of the layer.
# Load the mesh
mesh = Mesh()
mesh.create([
[0, 0],
[1, 0],
[1, 1],
[0, 1],
], [
[2, 3, 0, 1, 0],
], [
[0, 1, 1],
[1, 2, 1],
[2, 3, 1],
[3, 0, 1],
], [])
# 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 coarse mesh problem
ls = LinSystem(wf)
ls.set_spaces(space)
# Adaptivity loop
iter = 0
done = False
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
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)
# Visualize the approximation
sln.plot()
# Visualize the mesh
mesh.plot(space=space)
def calc(threshold=0.3,
strategy=0,
h_only=False,
error_tol=1,
interactive_plotting=False,
show_mesh=False,
show_graph=True):
mesh = Mesh()
mesh.create([
[0, 0],
[1, 0],
[1, 1],
[0, 1],
], [
[2, 3, 0, 1, 0],
], [
[0, 1, 1],
[1, 2, 1],
[2, 3, 1],
[3, 0, 1],
], [])
mesh.refine_all_elements()
shapeset = H1Shapeset()
pss = PrecalcShapeset(shapeset)
space = H1Space(mesh, shapeset)
set_bc(space)
space.set_uniform_order(1)
wf = WeakForm(1)
set_forms(wf)
sln = Solution()
rsln = Solution()
solver = DummySolver()
selector = H1ProjBasedSelector(CandList.HP_ANISO, 1.0, -1, shapeset)
view = ScalarView("Solution")
iter = 0
graph = []
while 1:
space.assign_dofs()
sys = LinSystem(wf, solver)
sys.set_spaces(space)
sys.set_pss(pss)
sys.assemble()
sys.solve_system(sln)
dofs = sys.get_matrix().shape[0]
if interactive_plotting:
view.show(sln,
lib=lib,
notebook=True,
filename="a%02d.png" % iter)
rsys = RefSystem(sys)
rsys.assemble()
rsys.solve_system(rsln)
hp = H1Adapt([space])
hp.set_solutions([sln], [rsln])
err_est = hp.calc_error() * 100
err_est = hp.calc_error(sln, rsln) * 100
print "iter=%02d, err_est=%5.2f%%, DOFS=%d" % (iter, err_est, dofs)
graph.append([dofs, err_est])
if err_est < error_tol:
break
hp.adapt(selector, threshold, strategy)
iter += 1
if not interactive_plotting:
view.show(sln, lib=lib, notebook=True)
if show_mesh:
mview = MeshView("Mesh")
mview.show(mesh, lib="mpl", notebook=True, filename="b.png")
if show_graph:
from numpy import array
graph = array(graph)
import pylab
pylab.clf()
pylab.plot(graph[:, 0], graph[:, 1], "ko", label="error estimate")
pylab.plot(graph[:, 0], graph[:, 1], "k-")
pylab.title("Error Convergence for the Inner Layer Problem")
pylab.legend()
pylab.xlabel("Degrees of Freedom")
pylab.ylabel("Error [%]")
pylab.yscale("log")
pylab.grid()
pylab.savefig("graph.png")
# 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 views
sview = ScalarView("Coarse solution", 0, 100, 798, 700)
oview = OrderView("Polynomial orders", 800, 100, 798, 700)
# 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)
# View the solution
sln.plot()
# View the mesh
mesh.plot(space=space)
mesh.load(get_sample_mesh())
# Perform uniform mesh refinement
mesh.refine_all_elements()
# Create the x- and y- displacement space using the default H1 shapeset
xdisp = H1Space(mesh, P_INIT)
ydisp = H1Space(mesh, P_INIT)
set_bc(xdisp, ydisp)
# Initialize the weak formulation
wf = WeakForm(2)
set_forms(wf)
# Initialize the linear system.
ls = LinSystem(wf)
ls.set_spaces(xdisp, ydisp)
# Assemble and solve the matrix problem
xsln = Solution()
ysln = Solution()
ls.assemble()
ls.solve_system(xsln, ysln, lib="scipy")
# Visualize the solution
view = ScalarView("Von Mises stress [Pa]", 50, 50, 1200, 600)
E = float(200e9)
nu = 0.3
l = (E * nu) / ((1 + nu) * (1 - 2 * nu))
mu = E / (2 * (1 + nu))
stress = VonMisesFilter(xsln, ysln, mu, l)
def test_example_11():
from hermes2d.examples.c11 import set_bc, set_wf_forms, set_hp_forms
SOLVE_ON_COARSE_MESH = True # If true, coarse mesh FE problem is solved in every adaptivity step.
P_INIT_U = 2 # Initial polynomial degree for u
P_INIT_V = 2 # Initial polynomial degree for v
INIT_REF_BDY = 3 # Number of initial boundary refinements
MULTI = True # MULTI = true ... use multi-mesh,
# MULTI = false ... use single-mesh.
# Note: In the single mesh option, the meshes are
# forced to be geometrically the same but the
# polynomial degrees can still vary.
THRESHOLD = 0.3 # This is a quantitative parameter of the adapt(...) function and
# it has different meanings for various adaptive strategies (see below).
STRATEGY = 1 # 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 # Default value is 1.0. This parameter influences the selection of
# cancidates in hp-adaptivity. See get_optimal_refinement() for details.
MAX_ORDER = 10 # Maximum allowed element degree
ERR_STOP = 0.5 # 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 mainly 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
# Load the mesh
umesh = Mesh()
vmesh = Mesh()
umesh.load(get_bracket_mesh())
if MULTI == False:
umesh.refine_towards_boundary(1, INIT_REF_BDY)
# Create initial mesh (master mesh).
vmesh.copy(umesh)
# Initial mesh refinements in the vmesh towards the boundary
if MULTI == True:
vmesh.refine_towards_boundary(1, INIT_REF_BDY)
# Create the x displacement space
uspace = H1Space(umesh, P_INIT_U)
vspace = H1Space(vmesh, P_INIT_V)
# Initialize the weak formulation
wf = WeakForm(2)
set_wf_forms(wf)
# Initialize refinement selector
selector = H1ProjBasedSelector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER)
# Initialize the coarse mesh problem
ls = LinSystem(wf)
ls.set_spaces(uspace, vspace)
u_sln_coarse = Solution()
v_sln_coarse = Solution()
u_sln_fine = Solution()
v_sln_fine = Solution()
# Assemble and Solve the fine mesh problem
rs = RefSystem(ls)
rs.assemble()
rs.solve_system(u_sln_fine, v_sln_fine, lib="scipy")
# 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(u_sln_coarse, v_sln_coarse, lib="scipy")
# Calculate element errors and total error estimate
hp = H1Adapt(ls)
hp.set_solutions([u_sln_coarse, v_sln_coarse], [u_sln_fine, v_sln_fine])
set_hp_forms(hp)
err_est = hp.calc_error() * 100
set_bc(space)
space.set_uniform_order(1)
wf = WeakForm(1)
set_forms(wf)
sln = Solution()
rsln = Solution()
solver = DummySolver()
view = ScalarView("Solution")
iter = 0
while 1:
space.assign_dofs()
sys = LinSystem(wf, solver)
sys.set_spaces(space)
sys.set_pss(pss)
sys.assemble()
sys.solve_system(sln)
if interactive_plotting:
view.show(sln)
rsys = RefSystem(sys)
rsys.assemble()
rsys.solve_system(rsln)
hp = H1OrthoHP(space)
error = hp.calc_error(sln, rsln)*100
print "iter=%02d, error=%5.2f%%" % (iter, error)
def test_example_10():
from hermes2d.examples.c10 import set_bc, set_forms
from hermes2d.examples import get_motor_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 = 0.2 # This is a quantitative parameter of the adapt(...) function and
# it has different meanings for various adaptive strategies (see below).
STRATEGY = 1 # 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_H # Predefined list of element refinement candidates.
# Possible values are are attributes of the class CandList:
# H2D_P_ISO, H2D_P_ANISO, H2D_H_ISO, H2D_H_ANISO, H2D_HP_ISO, H2D_HP_ANISO_H, H2D_HP_ANISO_P, H2D_HP_ANISO
# See User Documentation 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.
ERR_STOP = 1.0 # Stopping criterion for adaptivity (rel. error tolerance between the
# fine mesh and coarse mesh solution in percent).
CONV_EXP = 1.0
# Default value is 1.0. This parameter influences the selection of
# cancidates in hp-adaptivity. See get_optimal_refinement() for details.
# 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
# Load the mesh
mesh = Mesh()
mesh.load(get_motor_mesh())
# Create an H1 space with default shapeset
space = H1Space(mesh, P_INIT)
set_bc(space)
# Initialize the discrete problem
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 element errors and total error estimate
hp = H1Adapt(ls)
hp.set_solutions([sln_coarse], [sln_fine])
err_est = hp.calc_error() * 100
mesh.refine_towards_boundary(bdy_air, INIT_REF_NUM_BDY)
# Create an H1 space with default shapeset
space = H1Space(mesh, P_INIT)
set_bc(space)
# Set initial condition
tsln = Solution()
tsln.set_const(mesh, T_INIT)
# Initialize the weak formulation
wf = WeakForm()
set_forms(wf)
# Initialize the linear system.
ls = LinSystem(wf)
ls.set_spaces(space)
# Visualisation
sview = ScalarView("Temperature", 0, 0, 450, 600)
#title = "Time %s, exterior temperature %s" % (TIME, temp_ext(TIME))
#Tview.set_min_max_range(0,20);
#Tview.set_title(title);
#Tview.fix_scale_width(3);
# Time stepping
nsteps = int(FINAL_TIME / TAU + 0.5)
rhsonly = False
for n in range(1, nsteps + 1):
print("\n---- Time %s, time step %s, ext_temp %s ----------" %
def test_example_09():
from hermes2d.examples.c09 import set_bc, temp_ext, set_forms
# The following parameters can be played with:
P_INIT = 1 # polynomial degree of elements
INIT_REF_NUM = 4 # number of initial uniform refinements
TAU = 300.0 # time step in seconds
# Problem constants
T_INIT = 10 # temperature of the ground (also initial temperature)
FINAL_TIME = 86400 # length of time interval (24 hours) in seconds
# Global variable
TIME = 0
# Load the mesh
mesh = Mesh()
mesh.load(get_cathedral_mesh())
# for i in range(INIT_REF_NUM):
# mesh.refine_all_elements()
# mesh.refine_towards_boundary(2, 5)
# Set up shapeset
shapeset = H1Shapeset()
pss = PrecalcShapeset(shapeset)
# Set up spaces
space = H1Space(mesh, shapeset)
set_bc(space)
space.set_uniform_order(P_INIT)
# Enumerate basis functions
space.assign_dofs()
# Set initial condition
tsln = Solution()
tsln.set_const(mesh, T_INIT)
# Weak formulation
wf = WeakForm(1)
set_forms(wf, tsln)
# Matrix solver
solver = DummySolver()
# Linear system
ls = LinSystem(wf, solver)
ls.set_spaces(space)
ls.set_pss(pss)
# Visualisation
sview = ScalarView("Temperature", 0, 0, 450, 600)
# title = "Time %s, exterior temperature %s" % (TIME, temp_ext(TIME))
# Tview.set_min_max_range(0,20);
# Tview.set_title(title);
# Tview.fix_scale_width(3);
# Time stepping
nsteps = int(FINAL_TIME / TAU + 0.5)
rhsonly = False
# Assemble and solve
ls.assemble()
rhsonly = True
ls.solve_system(tsln)
xdisp = H1Space(mesh, shapeset)
ydisp = H1Space(mesh, shapeset)
xdisp.set_uniform_order(8)
ydisp.set_uniform_order(8)
set_bc(xdisp, ydisp)
ndofs = xdisp.assign_dofs(0)
ndofs += ydisp.assign_dofs(ndofs)
# initialize the discrete problem
wf = WeakForm(2)
set_forms(wf)
solver = DummySolver()
sys = LinSystem(wf, solver)
sys.set_spaces(xdisp, ydisp)
sys.set_pss(pss)
xsln = Solution()
ysln = Solution()
sys.assemble()
sys.solve_system(xsln, ysln)
view = ScalarView("Von Mises stress [Pa]", 50, 50, 1200, 600)
E = float(200e9)
nu = 0.3
stress = VonMisesFilter(xsln, ysln, E / (2*(1 + nu)),
(E * nu) / ((1 + nu) * (1 - 2*nu)))
view.show(stress)
def test_example_11():
from hermes2d.examples.c11 import set_bc, set_wf_forms, set_hp_forms
# The following parameters can be changed: In particular, compare hp- and
# h-adaptivity via the ADAPT_TYPE option, and compare the multi-mesh vs. single-mesh
# using the MULTI parameter.
P_INIT = 1 # Initial polynomial degree of all mesh elements.
MULTI = True # MULTI = true ... use multi-mesh,
# MULTI = false ... use single-mesh.
# Note: In the single mesh option, the meshes are
# forced to be geometrically the same but the
# polynomial degrees can still vary.
SAME_ORDERS = True # SAME_ORDERS = true ... when single-mesh is used,
# this forces the meshes for all components to be
# identical, including the polynomial degrees of
# corresponding elements. When multi-mesh is used,
# this parameter is ignored.
THRESHOLD = 0.3 # This is a quantitative parameter of the adapt(...) function and
# it has different meanings for various adaptive strategies (see below).
STRATEGY = 1 # 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.
MAX_ORDER = 10 # Maximum allowed element degree
ERR_STOP = 0.5 # 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 mainly to prevent h-adaptivity to go on forever.
# Problem constants
E = 200e9 # Young modulus for steel: 200 GPa
nu = 0.3 # Poisson ratio
lamda = (E * nu) / ((1 + nu) * (1 - 2 * nu))
mu = E / (2 * (1 + nu))
# Load the mesh
xmesh = Mesh()
ymesh = Mesh()
xmesh.load(get_bracket_mesh())
# initial mesh refinements
xmesh.refine_element(1)
xmesh.refine_element(4)
# Create initial mesh for the vertical displacement component,
# identical to the mesh for the horizontal displacement
# (bracket.mesh becomes a master mesh)
ymesh.copy(xmesh)
# Initialize the shapeset and the cache
shapeset = H1Shapeset()
xpss = PrecalcShapeset(shapeset)
ypss = PrecalcShapeset(shapeset)
# Create the x displacement space
xdisp = H1Space(xmesh, shapeset)
set_bc(xdisp)
xdisp.set_uniform_order(P_INIT)
# Create the x displacement space
ydisp = H1Space(ymesh, shapeset)
set_bc(ydisp)
ydisp.set_uniform_order(P_INIT)
# Enumerate basis functions
ndofs = xdisp.assign_dofs()
ydisp.assign_dofs(ndofs)
# Initialize the weak formulation
wf = WeakForm(2)
set_wf_forms(wf)
# Matrix solver
solver = DummySolver()
# adaptivity loop
it = 1
done = False
cpu = 0.0
x_sln_coarse = Solution()
y_sln_coarse = Solution()
x_sln_fine = Solution()
y_sln_fine = Solution()
# Calculating the number of degrees of freedom
ndofs = xdisp.assign_dofs()
ndofs += ydisp.assign_dofs(ndofs)
# Solve the coarse mesh problem
ls = LinSystem(wf, solver)
ls.set_spaces(xdisp, ydisp)
ls.set_pss(xpss, ypss)
ls.assemble()
ls.solve_system(x_sln_coarse, y_sln_coarse)
# View the solution -- this can be slow; for illustration only
stress_coarse = VonMisesFilter(x_sln_coarse, y_sln_coarse, mu, lamda)
# Solve the fine mesh problem
rs = RefSystem(ls)
rs.assemble()
rs.solve_system(x_sln_fine, y_sln_fine)
# Calculate element errors and total error estimate
hp = H1OrthoHP(xdisp, ydisp)
set_hp_forms(hp)
err_est = hp.calc_error_2(x_sln_coarse, y_sln_coarse, x_sln_fine, y_sln_fine) * 100
# Show the fine solution - this is the final result
stress_fine = VonMisesFilter(x_sln_fine, y_sln_fine, mu, lamda)
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
set_bc(space)
# Initialize the weak formulation
wf = WeakForm()
set_forms(wf)
# Initialize views
sview = ScalarView("Solution")
mview = MeshView("Mesh")
graph = []
# Initialize refinement selector
selector = H1ProjBasedSelector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER)
# Initialize the coarse mesh problem
ls = LinSystem(wf)
ls.set_spaces(space)
# Adaptivity loop
iter = 0
done = False
print "Calculating..."
sln_coarse = Solution()
sln_fine = Solution()
while (not done):
# Assemble and solve the fine mesh problem
rs = RefSystem(ls)
rs.assemble()
rs.solve_system(sln_fine)
# Initialize the weak formulation
wf = WeakForm(2)
set_wf_forms(wf)
# Initialize views
uoview = OrderView("Coarse mesh for u", 0, 0, 360, 300)
voview = OrderView("Coarse mesh for v", 370, 0, 360, 300)
uview = ScalarView("Coarse mesh solution u", 740, 0, 400, 300)
vview = ScalarView("Coarse mesh solution v", 1150, 0, 400, 300)
# Initialize refinement selector
selector = H1ProjBasedSelector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER)
# Initialize the coarse mesh problem
ls = LinSystem(wf)
ls.set_spaces(uspace, vspace)
# adaptivity loop
it = 1
done = False
u_sln_coarse = Solution()
v_sln_coarse = Solution()
u_sln_fine = Solution()
v_sln_fine = Solution()
while(not done):
print ("\n---- Adaptivity step %d ---------------------------------------------\n" % it)
it += 1