def export_mesh(self, lib="hermes2d"):
"""
Exports the mesh in various FE solver formats.
lib == "hermes2d" ... returns the hermes2d Mesh
Currently only hermes2d is implemented.
Example:
>>> m = Mesh([[0.0,1.0],[1.0,1.0],[1.0,0.0],[0.0,0.0],],[[1,0,2],[2,0,3],],[[3,2,1],[2,1,2],[1,0,3],[0,3,4],],[])
>>> h = m.export_mesh()
>>> h
<hermes2d._hermes2d.Mesh object at 0x7f07284721c8>
"""
if lib == "hermes2d":
from hermes2d import Mesh
m = Mesh()
nodes = self._nodes
elements = [list(e)+[0] for e in self._elements]
boundaries = self._boundaries
curves = self._curves
m.create(nodes, elements, boundaries, curves)
return m
else:
raise NotImplementedError("unknown library")
def test_mesh_create1():
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],
], [])
assert compare(mesh.nodes, [[0, 0], [1, 0], [1, 1], [0, 1]])
assert mesh.elements_markers == [[2, 3, 0, 1, 0]]
assert mesh.elements == [[2, 3, 0, 1]]
# not yet implemented:
#assert mesh.boundaries == [[0, 1, 1], [1, 2, 1], [2, 3, 1], [3, 0, 1]]
#assert mesh.nurbs is None
mesh.refine_all_elements()
assert compare(mesh.nodes, [(0, 0), (1, 0), (1, 1), (0, 1),
(1, 0.5), (0.5, 0), (0, 0.5), (0.5, 1), (0.5, 0.5)])
assert mesh.elements == [[2, 7, 8, 4], [7, 3, 6, 8], [8, 6, 0, 5],
[4, 8, 5, 1]]
mesh.refine_all_elements()
assert mesh.nodes_dict == {0: (0.0, 0.0), 1: (1.0, 0.0), 2: (1.0, 1.0), 3:
(0.0, 1.0), 4: (1.0, 0.5), 5: (0.5, 0.0), 6: (0.0, 0.5), 7: (0.5,
1.0), 8: (0.5, 0.5), 9: (0.5, 0.75), 10: (0.25, 1.0), 12:
(0.75, 1.0), 13: (0.25, 0.5), 14: (0.0, 0.75), 15: (0.5, 0.25), 16:
(0.25, 0.0), 17: (0.0, 0.25), 18: (0.75, 0.25), 19: (1.0, 0.25),
20: (0.75, 0.0), 21: (0.75, 0.5), 22: (1.0, 0.75), 23: (0.75,
0.75), 36: (0.25, 0.75), 47: (0.25, 0.25)}
assert mesh.elements == [[2, 12, 23, 22], [12, 7, 9, 23], [23, 9, 8, 21],
[22, 23, 21, 4], [7, 10, 36, 9], [10, 3, 14, 36], [36, 14, 6, 13],
[9, 36, 13, 8], [8, 13, 47, 15], [13, 6, 17, 47], [47, 17, 0, 16],
[15, 47, 16, 5], [4, 21, 18, 19], [21, 8, 15, 18], [18, 15, 5, 20],
[19, 18, 20, 1]]
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
) from hermes2d.examples.c22 import set_bc, set_forms threshold = 0.3 strategy = 0 h_only = False error_tol = 1 interactive_plotting = False # should the plot be interactively updated # during the calculation? (slower) show_mesh = True show_graph = True set_verbose(False) 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()
def test_mesh_create2():
m = Mesh()
m.create([
[0, -1],
[1, -1],
[-1, 0],
[0, 0],
[1, 0],
[-1, 1],
[0, 1],
[0.707106781, 0.707106781],
], [
[0, 1, 4, 3, 0],
[3, 4, 7, 0],
[3, 7, 6, 0],
[2, 3, 6, 5, 0],
], [
[0, 1, 1],
[1, 4, 2],
[3, 0, 4],
[4, 7, 2],
[7, 6, 2],
[2, 3, 4],
[6, 5, 2],
[5, 2, 3],
], [
[4, 7, 45],
[7, 6, 45],
])
assert compare(m.nodes, [
[0, -1],
[1, -1],
[-1, 0],
[0, 0],
[1, 0],
[-1, 1],
[0, 1],
[0.707106781, 0.707106781],
], eps=1e-4)
assert m.elements_markers == [
[0, 1, 4, 3, 0],
[3, 4, 7, 0],
[3, 7, 6, 0],
[2, 3, 6, 5, 0],
]
assert m.elements == [
[0, 1, 4, 3],
[3, 4, 7],
[3, 7, 6],
[2, 3, 6, 5],
]
# This is not yet implemented:
#assert m.boundaries == [
# [0, 1, 1],
# [1, 4, 2],
# [3, 0, 4],
# [4, 7, 2],
# [7, 6, 2],
# [2, 3, 4],
# [6, 5, 2],
# [5, 2, 3],
# ]
#assert mesh.nurbs == ...
m.refine_all_elements()
assert m.elements == [
[0, 11, 20, 19], [11, 1, 9, 20], [20, 9, 4, 8], [19, 20, 8, 3],
[3, 8, 34], [8, 4, 33], [34, 33, 7], [33, 34, 8], [3, 34, 10],
[34, 7, 12], [10, 12, 6], [12, 10, 34], [2, 18, 16, 15],
[18, 3, 10, 16], [16, 10, 6, 17], [15, 16, 17, 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")
# 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
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
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")
def get_mesh(self):
from hermes2d import Mesh
m = Mesh()
m.create(self._nodes, self._elements, self._boundaries, self._curves)
return m
