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_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_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_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_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_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_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()
# 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)
# 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)
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")
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")
# Visualize the solution
view = ScalarView("Von Mises stress [Pa]", 50, 50, 1200, 600)
E = float(200e9)
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_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
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
# 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) # Visualize the solution sln.plot() # Visualize the mesh