def generate_mesh(self, mesh_size=5):
"""Setup Mesh Object and Properties
Go through generation Builder -> MeshInfo -> Mesh"""
# TODO Look into section-properties on github?
# TODO Are the values from meshpy.triangle accurate?
mesh_info = MeshInfo()
self.builder.set(mesh_info)
self.mesh = build(mesh_info, max_volume=mesh_size)
# Calculate Element Centroids
# C = [(x1+x2+x3)/3 , (y1+y2+y3)/3]
for i, e in enumerate(self.mesh.elements):
p1 = self.mesh.points[e[0]]
p2 = self.mesh.points[e[1]]
p3 = self.mesh.points[e[2]]
self.mesh_centroids[i] = ((p1[0] + p2[0] + p3[0]) / 3,
(p1[1] + p2[1] + p3[1]) / 3)
# Calculate Element Areas
# A = abs(x1*y2 + x2*y3 + x3*y1 - y1*x2 - y2*x3 - y3*x1)/2
for i, e in enumerate(self.mesh.elements):
p1 = self.mesh.points[e[0]]
p2 = self.mesh.points[e[1]]
p3 = self.mesh.points[e[2]]
self.mesh_areas[i] = abs(p1[0] * p2[1] + p2[0] * p3[1] +
p3[0] * p1[1] - p1[1] * p2[0] -
p2[1] * p3[0] - p3[1] * p1[0]) / 2
# Assign material ids to elements
# A bit verbose just to show calculations - might change later
# this only accounts for circle assignments
for primitive in self.ele_mat_primitive:
r = primitive[0]
prim_c = primitive[1]
mat_id = primitive[2]
for n, c in self.mesh_centroids.items():
if hypot(c[0] - prim_c[0], c[1] - prim_c[1]) < r:
self.ele_mat[n] = mat_id
def triangulate(self, options=None):
if options is None:
options = self._get_triangle_options()
mesh_info = MeshInfo()
mesh_info.set_points(self.vertices)
if self.boundary is not None:
segments = []
for b in self.boundary:
segments += self.get_segments(b)
mesh_info.set_facets(segments)
if self.holes is not None:
mesh_info.set_holes(self.holes)
try:
import locale
except ImportError:
use_locale = False
else:
use_locale = True
prev_num_locale = locale.getlocale(locale.LC_NUMERIC)
locale.setlocale(locale.LC_NUMERIC, "C")
try:
mesh = MeshInfo()
internals.triangulate(options, mesh_info, mesh, MeshInfo(), None)
finally:
# restore previous locale if we've changed it
if use_locale:
locale.setlocale(locale.LC_NUMERIC, prev_num_locale)
return mesh
def make_mesh(max_volume):
def round_trip_connect(seq):
result = []
for i in range(len(seq)):
result.append((i, (i+1)%len(seq)))
return result
shapes = read_shape()
#from matplotlib.pyplot import plot,show
#plot(shapes[0][:,0], shapes[0][:,1])
#show()
from meshpy.geometry import GeometryBuilder, Marker
builder = GeometryBuilder()
for shape in shapes:
from meshpy.geometry import make_box
points = shape
facets = round_trip_connect(range(len(points)))
builder.add_geometry(points=points, facets=facets,
facet_markers=Marker.FIRST_USER_MARKER)
points, facets, facet_markers = make_box((-200, -600), (400, -300))
builder.add_geometry(points=points, facets=facets,
facet_markers=facet_markers)
def transform(pt):
x, y = pt
return -0.01*x, -0.01*y
builder.apply_transform(transform)
from meshpy.triangle import MeshInfo, build
mi = MeshInfo()
builder.set(mi)
holes = []
for shape, sign, frac in zip(shapes, [1, 1, -1, 1, 1, 1], [0.5, 0, 0, 0, 0, 0]):
avg = np.average(shape, axis=0)
start_idx = int(frac*shape.shape[0])
start = shape[start_idx]
holes.append(transform(start + sign*0.01*(avg-start)))
mi.set_holes(holes)
mesh = build(mi,
allow_boundary_steiner=True,
generate_faces=True,
max_volume=max_volume)
return mesh
def domain(self, domaintype='meshpy'):
if domaintype is 'meshpy':
from meshpy.triangle import MeshInfo
domain = MeshInfo()
points = np.zeros((16, 2), dtype=np.float)
points[0:4, :] = np.array([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0),
(0.0, 1.0)],
dtype=np.float)
idx = np.arange(5, -1, -1)
points[4:10, 0] = 0.25 + 0.1 * np.cos(idx * np.pi / 3)
points[4:10, 1] = 0.75 + 0.1 * np.sin(idx * np.pi / 3)
points[10:, 0] = 0.6 + 0.1 * np.cos(idx * np.pi / 3)
points[10:, 1] = 0.4 + 0.1 * np.sin(idx * np.pi / 3)
facets = np.zeros((16, 2), dtype=np.int)
facets[0:4, :] = np.array([(0, 1), (1, 2), (2, 3), (3, 0)],
dtype=np.int)
facets[4:10, :] = np.array([(4, 5), (5, 6), (6, 7), (7, 8), (8, 9),
(9, 4)],
dtype=np.int)
facets[10:, :] = np.array([(10, 11), (11, 12), (12, 13), (13, 14),
(14, 15), (15, 10)],
dtype=np.int)
domain.set_points(points)
domain.set_facets(facets)
domain.set_holes([(0.25, 0.75), (0.6, 0.4)])
return domain
def get_mesh_example(): area = rect((0.,0.),(1.,1.)) init = rect((0.1,0.1),(0.2,0.2)) goal1 = rect((0.8,0.8),(0.9,0.9)) goal2 = rect((0.2,0.8),(0.3,0.9)) env = area + goal1 + goal2 + init info = MeshInfo() info.set_points(env) info.set_facets(loop(0,4) + loop(4,8) + loop(8,12) + loop(12,16), facet_markers = [0]*4 + [1]*4 + [2]*4 + [3]*4) # Create 8 facets and apply markers 1-8 on them info.regions.resize(4) s = 0.05 info.regions[0] = [0.15, 0.15, 0, s] # Replace 0.1 by a smaller value to produce a finer mesh info.regions[1] = [0.25, 0.85, 1, s] # Fourth item specifies maximum area of triangles as a region attribute info.regions[2] = [0.85, 0.85, 2, s] # Replace 0.1 by a smaller value to produce a finer mesh info.regions[3] = [0.5, 0.5, 3, s] # Fourth item specifies maximum area of triangles as a region attribute mesh = build(info, volume_constraints=True, attributes=True, generate_faces=True, min_angle=20, mesh_order=1) return mesh
def par_mesh(h, n):
mesh_info = MeshInfo()
# Set the vertices of the domain [0, 1]^2
mesh_info.set_points([
(0,0), (1,0), (1,1), (0,1)])
# Set the facets of the domain [0, 1]^2
mesh_info.set_facets([
[0,1],
[1,2],
[2,3],
[3,0]
])
# Generate the tet mesh
mesh = build(mesh_info, max_volume=(h)**2)
node = np.array(mesh.points, dtype=np.float)
cell = np.array(mesh.elements, dtype=np.int)
tmesh = TriangleMesh(node, cell)
# Partition the mesh cells into n parts
if n > 1:
edgecuts, parts = metis.part_mesh(tmesh, nparts=n, entity='node')
else:
NN = tmesh.number_of_nodes()
parts = np.zeros(NN, dtype=np.int)
tmesh.nodedata['partition'] = parts
return tmesh
def triangle(box, h):
from meshpy.triangle import MeshInfo, build
mesh_info = MeshInfo()
mesh_info.set_points([(box[0], box[2]), (box[1], box[2]), (box[1], box[3]),
(box[0], box[3])])
mesh_info.set_facets([[0, 1], [1, 2], [2, 3], [3, 0]])
mesh = build(mesh_info, max_volume=h**2)
point = np.array(mesh.points, dtype=np.float)
cell = np.array(mesh.elements, dtype=np.int)
return TriangleMesh(point, cell)
def domain(self, domaintype='meshpy'):
if domaintype == 'meshpy':
from meshpy.triangle import MeshInfo
domain = MeshInfo()
points = np.array([(0, 0), (48, 44), (48, 60), (0, 44)],
dtype=np.float)
facets = np.array([(0, 1), (1, 2), (2, 3), (3, 0)], dtype=np.int)
domain.set_points(points)
domain.set_facets(facets)
return domain
if domaintype == 'halfedge':
return None
def triangle(box, h, meshtype='tri'):
from meshpy.triangle import MeshInfo, build
mesh_info = MeshInfo()
mesh_info.set_points([(box[0], box[2]), (box[1], box[2]), (box[1], box[3]), (box[0], box[3])])
mesh_info.set_facets([[0,1], [1,2], [2,3], [3,0]])
mesh = build(mesh_info, max_volume=h**2)
node = np.array(mesh.points, dtype=np.float)
cell = np.array(mesh.elements, dtype=np.int)
if meshtype is 'tri':
return TriangleMesh(node, cell)
elif meshtype is 'polygon':
mesh = TriangleMeshWithInfinityNode(TriangleMesh(node, cell))
pnode, pcell, pcellLocation = mesh.to_polygonmesh()
return PolygonMesh(pnode, pcell, pcellLocation)
def triangle_polygon_domain(points, facets, h, meshtype='tri'):
from meshpy.triangle import MeshInfo, build
mesh_info = MeshInfo()
mesh_info.set_points(points)
mesh_info.set_facets(facets)
mesh = build(mesh_info, max_volume=h**2)
node = np.array(mesh.points, dtype=np.float)
cell = np.array(mesh.elements, dtype=np.int)
if meshtype is 'tri':
return TriangleMesh(node, cell)
elif meshtype is 'polygon':
mesh = TriangleMeshWithInfinityNode(TriangleMesh(node, cell))
pnode, pcell, pcellLocation = mesh.to_polygonmesh()
return PolygonMesh(pnode, pcell, pcellLocation)
def make_mesh_triangle_trimesh(self, **params):
"""make_mesh_triangle_trimesh
create mesh using trimesh.Trimesh
"""
c = params['c']
mesh_info = MeshInfo()
# generate vertices and facets
if params['obj'] == 'line':
points, facets, faces = make_vertex_facets_line(params)
elif params['obj'] == 'hexagon':
points, facets, faces = make_vertex_facets_hexagon(params)
elif params['obj'] == 'rect':
points, facets, faces = make_vertex_facets_rect_trimesh(params)
print('points = {0}\nfacets = {1}'.format(pformat(points),
pformat(facets)))
# mesh = trimesh.Trimesh(vertices=[[0, 0, 0], [0, 0, 1], [0, 1, 0]],
# faces=[[0, 1, 2]])
face_attributes = {
'color': len(faces) * [0],
'state': [],
'freq': [],
}
print('face_attributes = {0}'.format(face_attributes))
mesh = trimesh.Trimesh(vertices=points, faces=faces)
# print('mesh.edges = {0}'.format(mesh.edges))
# writing objects
# mesh.write_vtk("trigrid.vtk")
# f = open('trigrid.pkl', 'wb')
# pickle.dump(mesh, f)
# f.close()
# joblib.dump(mesh, 'trigrid.pkl')
# sys.exit()
return mesh
def test_2d_gauss_theorem(actx_factory):
"""Verify Gauss's theorem explicitly on a mesh"""
pytest.importorskip("meshpy")
from meshpy.geometry import make_circle, GeometryBuilder
from meshpy.triangle import MeshInfo, build
geob = GeometryBuilder()
geob.add_geometry(*make_circle(1))
mesh_info = MeshInfo()
geob.set(mesh_info)
mesh_info = build(mesh_info)
from meshmode.mesh.io import from_meshpy
from meshmode.mesh import BTAG_ALL
mesh = from_meshpy(mesh_info, order=1)
actx = actx_factory()
dcoll = DiscretizationCollection(actx, mesh, order=2)
volm_disc = dcoll.discr_from_dd(dof_desc.DD_VOLUME)
x_volm = thaw(volm_disc.nodes(), actx)
def f(x):
return flat_obj_array(
actx.np.sin(3 * x[0]) + actx.np.cos(3 * x[1]),
actx.np.sin(2 * x[0]) + actx.np.cos(x[1]))
f_volm = f(x_volm)
int_1 = op.integral(dcoll, "vol", op.local_div(dcoll, f_volm))
prj_f = op.project(dcoll, "vol", BTAG_ALL, f_volm)
normal = thaw(dcoll.normal(BTAG_ALL), actx)
int_2 = op.integral(dcoll, BTAG_ALL, prj_f.dot(normal))
assert abs(int_1 - int_2) < 1e-13
def test_2d_gauss_theorem(actx_factory):
"""Verify Gauss's theorem explicitly on a mesh"""
pytest.importorskip("meshpy")
from meshpy.geometry import make_circle, GeometryBuilder
from meshpy.triangle import MeshInfo, build
geob = GeometryBuilder()
geob.add_geometry(*make_circle(1))
mesh_info = MeshInfo()
geob.set(mesh_info)
mesh_info = build(mesh_info)
from meshmode.mesh.io import from_meshpy
mesh = from_meshpy(mesh_info, order=1)
actx = actx_factory()
discr = DGDiscretizationWithBoundaries(actx, mesh, order=2)
def f(x):
return flat_obj_array(
sym.sin(3*x[0])+sym.cos(3*x[1]),
sym.sin(2*x[0])+sym.cos(x[1]))
gauss_err = bind(discr,
sym.integral((
sym.nabla(2) * f(sym.nodes(2))
).sum())
- # noqa: W504
sym.integral(
sym.project("vol", sym.BTAG_ALL)(f(sym.nodes(2)))
.dot(sym.normal(sym.BTAG_ALL, 2)),
dd=sym.BTAG_ALL)
)(actx)
assert abs(gauss_err) < 1e-13
def make_mesh_triangle_meshpy(self, **params):
"""make_mesh_meshpy_triangle
create mesh using meshpy.triangle.MeshInfo
"""
c = params['c']
mesh_info = MeshInfo()
# generate vertices and facets
if params['obj'] == 'line':
points, facets, faces = make_vertex_facets_line(params)
elif params['obj'] == 'hexagon':
points, facets, faces = make_vertex_facets_hexagon(params)
elif params['obj'] == 'rect':
points, facets = make_vertex_facets_rect(params)
print('points = {0}\nfacets = {1}'.format(pformat(points),
pformat(facets)))
# print('mesh_info.unit = {0}'.format(mesh_info.unit))
# copy points data into mesh
mesh_info.set_points(points)
# copy facets data into mesh
mesh_info.set_facets(facets)
# build the mesh
mesh = build(mesh_info)
# writing objects
# mesh.write_vtk("trigrid.vtk")
# f = open('trigrid.pkl', 'wb')
# pickle.dump(mesh, f)
# f.close()
# joblib.dump(mesh, 'trigrid.pkl')
# sys.exit()
return mesh
def make_squaremesh():
def round_trip_connect(seq):
result = []
for i in range(len(seq)):
result.append((i, (i + 1) % len(seq)))
return result
def needs_refinement(vertices, area):
x = sum(numpy.array(v) for v in vertices) / 3
max_area_volume = 0.7e-2 + 0.03 * (0.05 * x[1]**2 +
0.3 * min(x[0] + 1, 0)**2)
max_area_corners = 1e-3 + 0.001 * max(
la.norm(x - corner)**4 for corner in obstacle_corners)
return bool(area > 2.5 * min(max_area_volume, max_area_corners))
from meshpy.geometry import make_box
points, facets, _, _ = make_box((-0.5, -0.5), (0.5, 0.5))
obstacle_corners = points[:]
from meshpy.geometry import GeometryBuilder, Marker
profile_marker = Marker.FIRST_USER_MARKER
builder = GeometryBuilder()
builder.add_geometry(points=points,
facets=facets,
facet_markers=profile_marker)
points, facets, _, facet_markers = make_box((-16, -22), (25, 22))
builder.add_geometry(points=points,
facets=facets,
facet_markers=facet_markers)
from meshpy.triangle import MeshInfo, build
mi = MeshInfo()
builder.set(mi)
mi.set_holes([(0, 0)])
mesh = build(mi,
refinement_func=needs_refinement,
allow_boundary_steiner=True,
generate_faces=True)
print("%d elements" % len(mesh.elements))
from meshpy.triangle import write_gnuplot_mesh
write_gnuplot_mesh("mesh.dat", mesh)
fvi2fm = mesh.face_vertex_indices_to_face_marker
face_marker_to_tag = {
profile_marker: "noslip",
Marker.MINUS_X: "inflow",
Marker.PLUS_X: "outflow",
Marker.MINUS_Y: "inflow",
Marker.PLUS_Y: "inflow"
}
def bdry_tagger(fvi, el, fn, all_v):
face_marker = fvi2fm[fvi]
return [face_marker_to_tag[face_marker]]
from grudge.mesh import make_conformal_mesh_ext
vertices = numpy.asarray(mesh.points, dtype=float, order="C")
from grudge.mesh.element import Triangle
return make_conformal_mesh_ext(vertices, [
Triangle(i, el_idx, vertices) for i, el_idx in enumerate(mesh.elements)
], bdry_tagger)
import numpy as np
import matplotlib.pyplot as plt
from meshpy.triangle import MeshInfo, build
# Utility function to create lists of the form [(1,2), (2,3), (3,4),
# (4,1)], given two numbers 1 and 4
from itertools import islice, cycle
def loop(a, b):
return list(
zip(list(range(a, b)), islice(cycle(list(range(a, b))), 1, None)))
info = MeshInfo()
info.set_points([(0, 0), (1, 0), (1, 1), (0, 1), (2, 0), (3, 0), (3, 1),
(2, 1)])
info.set_facets(loop(0, 4) + loop(4, 8), list(range(
1, 9))) # Create 8 facets and apply markers 1-8 on them
info.regions.resize(2)
info.regions[0] = [
0.5,
0.5,
1,
0.1,
] # Fourth item specifies maximum area of triangles as a region attribute
info.regions[1] = [
2.5,
0.5,
2,
# Quadratic element demo, by Aravind Alwan from numpy import * from matplotlib.pyplot import * from meshpy.triangle import MeshInfo, build # Utility function to create lists of the form [(1,2), (2,3), (3,4), # (4,1)], given two numbers 1 and 4 from itertools import islice, cycle from six.moves import range from six.moves import zip loop = lambda a, b: list(zip(list(range(a, b)), islice(cycle(list(range(a, b))), 1, None))) info = MeshInfo() info.set_points([(0, 0), (1, 0), (1, 1), (0, 1), (2, 0), (3, 0), (3, 1), (2, 1)]) info.set_facets(loop(0, 4) + loop(4, 8), list(range(1, 9))) # Create 8 facets and apply markers 1-8 on them info.regions.resize(2) info.regions[0] = [0.5, 0.5, 1, 0.1] # Fourth item specifies maximum area of triangles as a region attribute info.regions[1] = [2.5, 0.5, 2, 0.1] # Replace 0.1 by a smaller value to produce a finer mesh mesh = build(info, volume_constraints=True, attributes=True, generate_faces=True, min_angle=33, mesh_order=2) pts = vstack(mesh.points) # (npoints, 2)-array of points elements = vstack(mesh.elements) # (ntriangles, 6)-array specifying element connectivity # Matplotlib's Triangulation module uses only linear elements, so use only first 3 columns when plotting triplot(pts[:, 0], pts[:, 1], elements[:, :3]) plot(pts[:, 0], pts[:, 1], "ko") # Manually plot all points including the ones at the midpoints of triangle faces
def make_squaremesh():
def round_trip_connect(seq):
result = []
for i in range(len(seq)):
result.append((i, (i+1)%len(seq)))
return result
def needs_refinement(vertices, area):
x = sum(numpy.array(v) for v in vertices)/3
max_area_volume = 0.7e-2 + 0.03*(0.05*x[1]**2 + 0.3*min(x[0]+1,0)**2)
max_area_corners = 1e-3 + 0.001*max(
la.norm(x-corner)**4 for corner in obstacle_corners)
return bool(area > 2.5*min(max_area_volume, max_area_corners))
from meshpy.geometry import make_box
points, facets, _, _ = make_box((-0.5,-0.5), (0.5,0.5))
obstacle_corners = points[:]
from meshpy.geometry import GeometryBuilder, Marker
profile_marker = Marker.FIRST_USER_MARKER
builder = GeometryBuilder()
builder.add_geometry(points=points, facets=facets,
facet_markers=profile_marker)
points, facets, _, facet_markers = make_box((-16, -22), (25, 22))
builder.add_geometry(points=points, facets=facets,
facet_markers=facet_markers)
from meshpy.triangle import MeshInfo, build
mi = MeshInfo()
builder.set(mi)
mi.set_holes([(0,0)])
mesh = build(mi, refinement_func=needs_refinement,
allow_boundary_steiner=True,
generate_faces=True)
print "%d elements" % len(mesh.elements)
from meshpy.triangle import write_gnuplot_mesh
write_gnuplot_mesh("mesh.dat", mesh)
fvi2fm = mesh.face_vertex_indices_to_face_marker
face_marker_to_tag = {
profile_marker: "noslip",
Marker.MINUS_X: "inflow",
Marker.PLUS_X: "outflow",
Marker.MINUS_Y: "inflow",
Marker.PLUS_Y: "inflow"
}
def bdry_tagger(fvi, el, fn, all_v):
face_marker = fvi2fm[fvi]
return [face_marker_to_tag[face_marker]]
from hedge.mesh import make_conformal_mesh_ext
vertices = numpy.asarray(mesh.points, dtype=float, order="C")
from hedge.mesh.element import Triangle
return make_conformal_mesh_ext(
vertices,
[Triangle(i, el_idx, vertices)
for i, el_idx in enumerate(mesh.elements)],
bdry_tagger)
def test_convergence_advec(ctx_factory,
mesh_name,
mesh_pars,
op_type,
flux_type,
order,
visualize=False):
"""Test whether 2D advection actually converges"""
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
for mesh_par in mesh_pars:
if mesh_name == "segment":
from meshmode.mesh.generation import generate_box_mesh
mesh = generate_box_mesh([np.linspace(-1.0, 1.0, mesh_par)],
order=order)
dim = 1
dt_factor = 1.0
elif mesh_name == "disk":
pytest.importorskip("meshpy")
from meshpy.geometry import make_circle, GeometryBuilder
from meshpy.triangle import MeshInfo, build
geob = GeometryBuilder()
geob.add_geometry(*make_circle(1))
mesh_info = MeshInfo()
geob.set(mesh_info)
mesh_info = build(mesh_info, max_volume=mesh_par)
from meshmode.mesh.io import from_meshpy
mesh = from_meshpy(mesh_info, order=1)
dim = 2
dt_factor = 4
elif mesh_name.startswith("rect"):
dim = int(mesh_name[4:])
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
n=(mesh_par, ) * dim,
order=4)
if dim == 2:
dt_factor = 4
elif dim == 3:
dt_factor = 2
else:
raise ValueError("dt_factor not known for %dd" % dim)
else:
raise ValueError("invalid mesh name: " + mesh_name)
v = np.array([0.27, 0.31, 0.1])[:dim]
norm_v = la.norm(v)
def f(x):
return sym.sin(10 * x)
def u_analytic(x):
return f(-v.dot(x) / norm_v + sym.var("t", sym.DD_SCALAR) * norm_v)
from grudge.models.advection import (StrongAdvectionOperator,
WeakAdvectionOperator)
discr = DGDiscretizationWithBoundaries(actx, mesh, order=order)
op_class = {
"strong": StrongAdvectionOperator,
"weak": WeakAdvectionOperator,
}[op_type]
op = op_class(v,
inflow_u=u_analytic(sym.nodes(dim, sym.BTAG_ALL)),
flux_type=flux_type)
bound_op = bind(discr, op.sym_operator())
u = bind(discr, u_analytic(sym.nodes(dim)))(actx, t=0)
def rhs(t, u):
return bound_op(t=t, u=u)
if dim == 3:
final_time = 0.1
else:
final_time = 0.2
h_max = bind(discr, sym.h_max_from_volume(discr.ambient_dim))(actx)
dt = dt_factor * h_max / order**2
nsteps = (final_time // dt) + 1
dt = final_time / nsteps + 1e-15
from grudge.shortcuts import set_up_rk4
dt_stepper = set_up_rk4("u", dt, u, rhs)
last_u = None
from grudge.shortcuts import make_visualizer
vis = make_visualizer(discr, vis_order=order)
step = 0
for event in dt_stepper.run(t_end=final_time):
if isinstance(event, dt_stepper.StateComputed):
step += 1
logger.debug("[%04d] t = %.5f", step, event.t)
last_t = event.t
last_u = event.state_component
if visualize:
vis.write_vtk_file("fld-%s-%04d.vtu" % (mesh_par, step),
[("u", event.state_component)])
error_l2 = bind(discr,
sym.norm(2,
sym.var("u") - u_analytic(sym.nodes(dim))))(
t=last_t, u=last_u)
logger.info("h_max %.5e error %.5e", h_max, error_l2)
eoc_rec.add_data_point(h_max, error_l2)
logger.info(
"\n%s", eoc_rec.pretty_print(abscissa_label="h",
error_label="L2 Error"))
assert eoc_rec.order_estimate() > order
def discretise_faces(vertices, faces, target, min_angle=15, factor=3):
""" Make discretised triangles from input coarse triangles data.
Parameters
----------
vertices : list
Co-ordinates of coarse vertices.
faces : list
Vertex indices of each face of the coarse triangles.
target : float
Target edge length of each triangle.
min_angle : float
Minimum internal angle of triangles.
factor : float
Factor on the maximum area of each triangle.
Returns
-------
list
Vertices of the discretised trianlges.
list
Vertex numbers of the discretised trianlges.
Notes
-----
- An experimental script.
"""
points_all = []
faces_all = []
Amax = factor * 0.5 * target**2
for count, face in enumerate(faces):
# Seed
face.append(face[0])
points = []
facets = []
for u, v in zip(face[:-1], face[1:]):
sp = vertices[u]
ep = vertices[v]
vec = subtract_vectors(ep, sp)
l = length_vector(vec)
div = l / target
n = max([1, int(div)])
for j in range(n):
points.append(add_vectors(sp, scale_vector(vec, j / n)))
facets = [[i, i + 1] for i in range(len(points) - 1)]
facets.append([len(points) - 1, 0])
# Starting orientation
cent = centroid_points(points)
vec1 = subtract_vectors(points[1], points[0])
vec2 = subtract_vectors(cent, points[0])
vecn = cross_vectors(vec1, vec2)
# Rotate about x
points = array(points).transpose()
phi = -arctan2(vecn[2], vecn[1]) + 0.5 * pi
Rx = array([[1, 0, 0], [0, cos(phi), -sin(phi)],
[0, sin(phi), cos(phi)]])
vecn_x = dot(Rx, array(vecn)[:, newaxis])
points_x = dot(Rx, points)
Rx_inv = inv(Rx)
# Rotate about y
psi = +arctan2(vecn_x[2, 0], vecn_x[0, 0]) - 0.5 * pi
Ry = array([[cos(psi), 0, sin(psi)], [0, 1, 0],
[-sin(psi), 0, cos(psi)]])
points_y = dot(Ry, points_x)
Ry_inv = inv(Ry)
V = points_y.transpose()
try:
new_points = [list(i) for i in list(V[:, :2])]
info = MeshInfo_tri()
info.set_points(new_points)
info.set_facets(facets)
tris = build_tri(info,
allow_boundary_steiner=False,
min_angle=min_angle,
max_volume=Amax)
new_points = [list(j) + [V[0, 2]] for j in tris.points]
new_tris = [list(j) for j in tris.elements]
V = array(new_points)
points = dot(Ry_inv, V.transpose())
points_all.append(
[list(i) for i in list(dot(Rx_inv, points).transpose())])
faces_all.append(new_tris)
except:
print('***** ERROR discretising face {0} *****'.format(count))
return points_all, faces_all
axis=1)
newParent[:, 0] = np.repeat(idx, 4)
newParent[:, 1] = ranges(4 * np.ones(NCC, dtype=np.int))
child[idx, :] = np.arange(NC, NC + 4 * NCC).reshape(NCC, 4)
cell = np.concatenate((cell, newCell), axis=0)
self.node = np.concatenate((node, edgeCenter, cellCenter), axis=0)
self.parent = np.concatenate((parent, newParent), axis=0)
self.child = np.concatenate((child, newChild), axis=0)
self.ds.reinit(N + NEC + NCC, cell)
return True
else:
return False
mesh_info = MeshInfo()
mesh_info.set_points([(-1, -1), (0, -1), (0, 0), (1, 0), (1, 1), (0, 1),
(1, 1), (-1, 0)])
mesh_info.set_facets([[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7],
[7, 0]])
h = 0.05
mesh = build(mesh_info, max_volume=h**2)
node = np.array(mesh.points, dtype=np.float)
cell = np.array(mesh.elements, dtype=np.int)
ttree = Tritree(node, cell)
mesh = ttree.to_mesh()
pde = LShapeRSinData()
integrator = mesh.integrator(3)
fem = PoissonFEMModel(pde, mesh, 1, integrator)
#find one of the nodes in the element
nodes_remove_ID = np.unique(elements.simplices[coarsenIds][0])
#redraw the delaunay triangles
return findDelaunayTriangles(nodepts)
if __name__ == '__main__':
#Create the intial mesh node pts
nodepts = createInitialTriGridPts(4, 4)
#Define the element triangles that link the nodes
elements = defineElementConnectivity(nodepts)
mesh_info = MeshInfo()
print(nodepts)
mesh_info.set_points(nodepts)
print(elements.simplices)
mesh_info.set_facets(elements.simplices)
mesh = build(mesh_info)
#mesh.triangle.
write_gnuplot_mesh("test.vtk", mesh_info.points, facets=False)
#triangle=showMesh(nodepts,elements.simplices)
print(elements)
print(elements.simplices)
print(elements.points)
nodepts, elements = refineMesh(nodepts, elements, 7)
nodepts, elements = refineMesh(nodepts, elements, 20)
from meshpy.triangle import MeshInfo, build
import numpy as np
import matplotlib.pyplot as plt
from fealpy.mesh import TriangleMesh
domain = MeshInfo()
domain.set_points([(0,0),(1,0),(1,1),(0,1)])
domain.set_facets([(0,1),(1,2),(2,3),(3,0)], facet_markers=[1, 2, 3, 4])
mesh = build(domain, max_volume = 0.1**2, attributes=True)
node = np.array(mesh.points, dtype = np.float)
cell = np.array(mesh.elements, dtype = np.int)
tmesh = TriangleMesh(node, cell)
fig = plt.figure()
axes = fig.gca()
tmesh.add_plot(axes)
cell = tmesh.entity('cell')
node = tmesh.entity('node')
NN = tmesh.number_of_nodes()
isBdNode = tmesh.ds.boundary_node_flag()
newNode = np.zeros((NN, 2), dtype=np.float)
degree = np.zeros(NN, dtype=np.int)
np.add.at(degree, cell, 1)
for i in range(10):
#bc = tmesh.entity_barycenter('cell')
bc, R = tmesh.circumcenter()
np.add.at(newNode, (cell, np.s_[:]), bc[:, np.newaxis, :])
newNode /= degree[:, np.newaxis]
node[~isBdNode] = newNode[~isBdNode]
newNode[:] = 0
from fealpy.mesh.TriangleMesh import TriangleMesh
from fealpy.functionspace.mixed_fem_space import RaviartThomasFiniteElementSpace2d
from fealpy.functionspace.mixed_fem_space import BDMFiniteElementSpace2d
from fealpy.functionspace.mixed_fem_space import FirstNedelecFiniteElement2d
def mesh_2dpy(mesh_info, h):
mesh = build(mesh_info, max_volume=(h)**2)
point = np.array(mesh.points, dtype=np.float)
cell = np.array(mesh.elements, dtype=np.int)
tmesh = TriangleMesh(point, cell)
return tmesh
mesh_info = MeshInfo()
mesh_info.set_points([(0, 0), (1, 0), (1, 1), (0, 1)])
mesh_info.set_facets([[0, 1], [1, 2], [2, 3], [3, 0]])
h = 0.5
tmesh = mesh_2dpy(mesh_info, h)
#point = np.array([
# (0, 0),
# (1, 0),
# (1, 1),
# (0, 1)], dtype=np.float)
#cell = np.array([
# (1, 2, 0),
# (3, 0, 2)], dtype=np.int)
#tmesh = TriangleMesh(point, cell)
def make_nacamesh():
def round_trip_connect(seq):
result = []
for i in range(len(seq)):
result.append((i, (i + 1) % len(seq)))
return result
pt_back = numpy.array([1, 0])
# def max_area(pt):
# max_area_front = 1e-2*la.norm(pt)**2 + 1e-5
# max_area_back = 1e-2*la.norm(pt-pt_back)**2 + 1e-4
# return min(max_area_front, max_area_back)
def max_area(pt):
x = pt[0]
if x < 0:
return 1e-2 * la.norm(pt) ** 2 + 1e-5
elif x > 1:
return 1e-2 * la.norm(pt - pt_back) ** 2 + 1e-5
else:
return 1e-2 * pt[1] ** 2 + 1e-5
def needs_refinement(vertices, area):
barycenter = sum(numpy.array(v) for v in vertices) / 3
return bool(area > max_area(barycenter))
from meshpy.naca import get_naca_points
points = get_naca_points(naca_digits="2412", number_of_points=80)
from meshpy.geometry import GeometryBuilder, Marker
from meshpy.triangle import write_gnuplot_mesh
profile_marker = Marker.FIRST_USER_MARKER
builder = GeometryBuilder()
builder.add_geometry(points=points, facets=round_trip_connect(points), facet_markers=profile_marker)
builder.wrap_in_box(4, (10, 8))
from meshpy.triangle import MeshInfo, build
mi = MeshInfo()
builder.set(mi)
mi.set_holes([builder.center()])
mesh = build(
mi,
refinement_func=needs_refinement,
# allow_boundary_steiner=False,
generate_faces=True,
)
write_gnuplot_mesh("mesh.dat", mesh)
print "%d elements" % len(mesh.elements)
fvi2fm = mesh.face_vertex_indices_to_face_marker
face_marker_to_tag = {
profile_marker: "noslip",
Marker.MINUS_X: "inflow",
Marker.PLUS_X: "outflow",
Marker.MINUS_Y: "inflow",
Marker.PLUS_Y: "inflow"
# Marker.MINUS_Y: "minus_y",
# Marker.PLUS_Y: "plus_y"
}
def bdry_tagger(fvi, el, fn, all_v):
face_marker = fvi2fm[fvi]
return [face_marker_to_tag[face_marker]]
from hedge.mesh import make_conformal_mesh_ext
vertices = numpy.asarray(mesh.points, order="C")
from hedge.mesh.element import Triangle
return make_conformal_mesh_ext(
vertices,
[Triangle(i, el_idx, vertices) for i, el_idx in enumerate(mesh.elements)],
bdry_tagger,
# periodicity=[None, ("minus_y", "plus_y")]
)
def make_nacamesh():
def round_trip_connect(seq):
result = []
for i in range(len(seq)):
result.append((i, (i + 1) % len(seq)))
return result
pt_back = numpy.array([1, 0])
#def max_area(pt):
#max_area_front = 1e-2*la.norm(pt)**2 + 1e-5
#max_area_back = 1e-2*la.norm(pt-pt_back)**2 + 1e-4
#return min(max_area_front, max_area_back)
def max_area(pt):
x = pt[0]
if x < 0:
return 1e-2 * la.norm(pt)**2 + 1e-5
elif x > 1:
return 1e-2 * la.norm(pt - pt_back)**2 + 1e-5
else:
return 1e-2 * pt[1]**2 + 1e-5
def needs_refinement(vertices, area):
barycenter = sum(numpy.array(v) for v in vertices) / 3
return bool(area > max_area(barycenter))
from meshpy.naca import get_naca_points
points = get_naca_points(naca_digits="2412", number_of_points=80)
from meshpy.geometry import GeometryBuilder, Marker
from meshpy.triangle import write_gnuplot_mesh
profile_marker = Marker.FIRST_USER_MARKER
builder = GeometryBuilder()
builder.add_geometry(points=points,
facets=round_trip_connect(points),
facet_markers=profile_marker)
builder.wrap_in_box(4, (10, 8))
from meshpy.triangle import MeshInfo, build
mi = MeshInfo()
builder.set(mi)
mi.set_holes([builder.center()])
mesh = build(
mi,
refinement_func=needs_refinement,
#allow_boundary_steiner=False,
generate_faces=True)
write_gnuplot_mesh("mesh.dat", mesh)
print("%d elements" % len(mesh.elements))
fvi2fm = mesh.face_vertex_indices_to_face_marker
face_marker_to_tag = {
profile_marker: "noslip",
Marker.MINUS_X: "inflow",
Marker.PLUS_X: "outflow",
Marker.MINUS_Y: "inflow",
Marker.PLUS_Y: "inflow"
#Marker.MINUS_Y: "minus_y",
#Marker.PLUS_Y: "plus_y"
}
def bdry_tagger(fvi, el, fn, all_v):
face_marker = fvi2fm[fvi]
return [face_marker_to_tag[face_marker]]
from grudge.mesh import make_conformal_mesh_ext
vertices = numpy.asarray(mesh.points, order="C")
from grudge.mesh.element import Triangle
return make_conformal_mesh_ext(
vertices,
[
Triangle(i, el_idx, vertices)
for i, el_idx in enumerate(mesh.elements)
],
bdry_tagger,
#periodicity=[None, ("minus_y", "plus_y")]
)
def uniform_refine_triangles(points, elements, factor=2):
new_points = points[:]
new_elements = []
old_face_to_new_faces = {}
face_point_dict = {}
points_per_edge = factor + 1
def get_refined_face(a, b):
if a > b:
a, b = b, a
flipped = True
else:
flipped = False
try:
face_points = face_point_dict[a, b]
except KeyError:
a_pt, b_pt = [points[idx] for idx in [a, b]]
dx = (b_pt - a_pt) / factor
# build subdivided facet
face_points = [a]
for i in range(1, points_per_edge - 1):
face_points.append(len(new_points))
new_points.append(a_pt + dx * i)
face_points.append(b)
face_point_dict[a, b] = face_points
# build old_face_to_new_faces
old_face_to_new_faces[frozenset([a, b])] = [
(face_points[i], face_points[i + 1]) for i in range(factor)
]
if flipped:
return face_points[::-1]
else:
return face_points
for a, b, c in elements:
a_pt, b_pt, c_pt = [points[idx] for idx in [a, b, c]]
dr = (b_pt - a_pt) / factor
ds = (c_pt - a_pt) / factor
ab_refined, bc_refined, ac_refined = [
get_refined_face(*pt_indices)
for pt_indices in [(a, b), (b, c), (a, c)]
]
el_point_dict = {}
# fill out edges of el_point_dict
for i in range(points_per_edge):
el_point_dict[i, 0] = ab_refined[i]
el_point_dict[0, i] = ac_refined[i]
el_point_dict[points_per_edge - 1 - i, i] = bc_refined[i]
# fill out interior of el_point_dict
for i in range(1, points_per_edge - 1):
for j in range(1, points_per_edge - 1 - i):
el_point_dict[i, j] = len(new_points)
new_points.append(a_pt + dr * i + ds * j)
# generate elements
for i in range(0, points_per_edge - 1):
for j in range(0, points_per_edge - 1 - i):
new_elements.append((
el_point_dict[i, j],
el_point_dict[i + 1, j],
el_point_dict[i, j + 1],
))
if i + 1 + j + 1 <= factor:
new_elements.append((
el_point_dict[i + 1, j + 1],
el_point_dict[i + 1, j],
el_point_dict[i, j + 1],
))
from meshpy.triangle import MeshInfo
mi = MeshInfo()
mi.set_points(new_points)
mi.elements.resize(len(new_elements))
for i, el in enumerate(new_elements):
mi.elements[i] = el
from meshpy.triangle import write_gnuplot_mesh
write_gnuplot_mesh("mesh.dat", mi)
return new_points, new_elements, old_face_to_new_faces
def test_convergence_advec(actx_factory,
mesh_name,
mesh_pars,
op_type,
flux_type,
order,
visualize=False):
"""Test whether 2D advection actually converges"""
actx = actx_factory()
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
for mesh_par in mesh_pars:
if mesh_name == "segment":
mesh = mgen.generate_box_mesh([np.linspace(-1.0, 1.0, mesh_par)],
order=order)
dim = 1
dt_factor = 1.0
elif mesh_name == "disk":
pytest.importorskip("meshpy")
from meshpy.geometry import make_circle, GeometryBuilder
from meshpy.triangle import MeshInfo, build
geob = GeometryBuilder()
geob.add_geometry(*make_circle(1))
mesh_info = MeshInfo()
geob.set(mesh_info)
mesh_info = build(mesh_info, max_volume=mesh_par)
from meshmode.mesh.io import from_meshpy
mesh = from_meshpy(mesh_info, order=1)
dim = 2
dt_factor = 4
elif mesh_name.startswith("rect"):
dim = int(mesh_name[-1:])
mesh = mgen.generate_regular_rect_mesh(
a=(-0.5, ) * dim,
b=(0.5, ) * dim,
nelements_per_axis=(mesh_par, ) * dim,
order=4)
if dim == 2:
dt_factor = 4
elif dim == 3:
dt_factor = 2
else:
raise ValueError("dt_factor not known for %dd" % dim)
elif mesh_name.startswith("warped"):
dim = int(mesh_name[-1:])
mesh = mgen.generate_warped_rect_mesh(dim,
order=order,
nelements_side=mesh_par)
if dim == 2:
dt_factor = 4
elif dim == 3:
dt_factor = 2
else:
raise ValueError("dt_factor not known for %dd" % dim)
else:
raise ValueError("invalid mesh name: " + mesh_name)
v = np.array([0.27, 0.31, 0.1])[:dim]
norm_v = la.norm(v)
def f(x):
return actx.np.sin(10 * x)
def u_analytic(x, t=0):
return f(-v.dot(x) / norm_v + t * norm_v)
from grudge.models.advection import (StrongAdvectionOperator,
WeakAdvectionOperator)
from meshmode.mesh import BTAG_ALL
dcoll = DiscretizationCollection(actx, mesh, order=order)
op_class = {
"strong": StrongAdvectionOperator,
"weak": WeakAdvectionOperator
}[op_type]
adv_operator = op_class(dcoll,
v,
inflow_u=lambda t: u_analytic(
thaw(dcoll.nodes(dd=BTAG_ALL), actx), t=t),
flux_type=flux_type)
nodes = thaw(dcoll.nodes(), actx)
u = u_analytic(nodes, t=0)
def rhs(t, u):
return adv_operator.operator(t, u)
if dim == 3:
final_time = 0.1
else:
final_time = 0.2
from grudge.dt_utils import h_max_from_volume
h_max = h_max_from_volume(dcoll, dim=dcoll.ambient_dim)
dt = dt_factor * h_max / order**2
nsteps = (final_time // dt) + 1
dt = final_time / nsteps + 1e-15
from grudge.shortcuts import set_up_rk4
dt_stepper = set_up_rk4("u", dt, u, rhs)
last_u = None
from grudge.shortcuts import make_visualizer
vis = make_visualizer(dcoll)
step = 0
for event in dt_stepper.run(t_end=final_time):
if isinstance(event, dt_stepper.StateComputed):
step += 1
logger.debug("[%04d] t = %.5f", step, event.t)
last_t = event.t
last_u = event.state_component
if visualize:
vis.write_vtk_file("fld-%s-%04d.vtu" % (mesh_par, step),
[("u", event.state_component)])
error_l2 = op.norm(dcoll, last_u - u_analytic(nodes, t=last_t), 2)
logger.info("h_max %.5e error %.5e", h_max, error_l2)
eoc_rec.add_data_point(h_max, actx.to_numpy(error_l2))
logger.info(
"\n%s", eoc_rec.pretty_print(abscissa_label="h",
error_label="L2 Error"))
if mesh_name.startswith("warped"):
# NOTE: curvilinear meshes are hard
assert eoc_rec.order_estimate() > order - 0.5
else:
assert eoc_rec.order_estimate() > order
def uniform_refine_triangles(points, elements, factor=2):
new_points = points[:]
new_elements = []
old_face_to_new_faces = {}
face_point_dict = {}
points_per_edge = factor+1
def get_refined_face(a, b):
if a > b:
a, b = b, a
flipped = True
else:
flipped = False
try:
face_points = face_point_dict[a, b]
except KeyError:
a_pt, b_pt = [points[idx] for idx in [a, b]]
dx = (b_pt - a_pt)/factor
# build subdivided facet
face_points = [a]
for i in range(1, points_per_edge-1):
face_points.append(len(new_points))
new_points.append(a_pt + dx*i)
face_points.append(b)
face_point_dict[a, b] = face_points
# build old_face_to_new_faces
old_face_to_new_faces[frozenset([a, b])] = [
(face_points[i], face_points[i+1])
for i in range(factor)]
if flipped:
return face_points[::-1]
else:
return face_points
for a, b, c in elements:
a_pt, b_pt, c_pt = [points[idx] for idx in [a, b, c]]
dr = (b_pt - a_pt)/factor
ds = (c_pt - a_pt)/factor
ab_refined, bc_refined, ac_refined = [
get_refined_face(*pt_indices)
for pt_indices in [(a, b), (b, c), (a, c)]]
el_point_dict = {}
# fill out edges of el_point_dict
for i in range(points_per_edge):
el_point_dict[i, 0] = ab_refined[i]
el_point_dict[0, i] = ac_refined[i]
el_point_dict[points_per_edge-1-i, i] = bc_refined[i]
# fill out interior of el_point_dict
for i in range(1, points_per_edge-1):
for j in range(1, points_per_edge-1-i):
el_point_dict[i, j] = len(new_points)
new_points.append(a_pt + dr*i + ds*j)
# generate elements
for i in range(0, points_per_edge-1):
for j in range(0, points_per_edge-1-i):
new_elements.append((
el_point_dict[i, j],
el_point_dict[i+1, j],
el_point_dict[i, j+1],
))
if i+1+j+1 <= factor:
new_elements.append((
el_point_dict[i+1, j+1],
el_point_dict[i+1, j],
el_point_dict[i, j+1],
))
from meshpy.triangle import MeshInfo
mi = MeshInfo()
mi.set_points(new_points)
mi.elements.resize(len(new_elements))
for i, el in enumerate(new_elements):
mi.elements[i] = el
from meshpy.triangle import write_gnuplot_mesh
write_gnuplot_mesh("mesh.dat", mi)
return new_points, new_elements, old_face_to_new_faces
from meshpy.triangle import MeshInfo, build, refine
import numpy as np
mesh_info = MeshInfo()
mesh_info.set_points([
(0,0),
(0,1),
(1,1),
(1,0)
])
mesh_info.set_facets([
[0,1],
[1,2],
[2,3],
[3,0]
])
def refinement_func(tri_points, area):
max_area=0.001
return bool(area>max_area);
mesh = build(mesh_info, refinement_func = refinement_func)
'''
print "Mesh Points:"
for i, p in enumerate(mesh.points):
print i, p
print "Point numbers in tetrahedra:"