def __init__(self, nodes, elements, edges, mesh_files):
"""
Test case for a Lagrange mesh. Tries to test an Argyris mesh.
"""
for mesh_file in mesh_files:
self.nodes = nodes
# The mesh classes try to flatten nodes if possible. Do it here too.
if np.all(self.nodes[:, -1] == self.nodes[0, -1]):
self.nodes = self.nodes[:, 0:-1]
self.elements = elements
self.edges = edges
mesh = meshes.mesh_factory(*mesh_file)
parsed_mesh = parsers.parser_factory(*mesh_file)
npt.assert_equal(self.nodes, mesh.nodes)
npt.assert_equal(self.elements, mesh.elements)
if parsed_mesh.edges:
assert set(self.edges) == reduce(
lambda a, b: a + b, mesh.edge_collections.values())
npt.assert_almost_equal(meshtools.project_nodes(
lambda x: x[0:2], self.elements, self.nodes),
self.nodes[:, 0:2],
decimal=10)
if parsed_mesh.edges:
assert set(map(lambda x : x[0:-1], self.edges)) == \
set(map(lambda x : x[0:-1],
meshtools.extract_boundary_edges(self.elements)))
# Test Argyris stuff.
if self.elements.shape[1] == 6:
TestArgyrisCase(mesh_file, parsed_mesh)
def __init__(self, nodes, elements, edges, mesh_files):
"""
Test case for a Lagrange mesh. Tries to test an Argyris mesh.
"""
for mesh_file in mesh_files:
self.nodes = nodes
# The mesh classes try to flatten nodes if possible. Do it here too.
if np.all(self.nodes[:, -1] == self.nodes[0, -1]):
self.nodes = self.nodes[:,0:-1]
self.elements = elements
self.edges = edges
mesh = meshes.mesh_factory(*mesh_file)
parsed_mesh = parsers.parser_factory(*mesh_file)
npt.assert_equal(self.nodes, mesh.nodes)
npt.assert_equal(self.elements, mesh.elements)
if parsed_mesh.edges:
assert set(self.edges) == reduce(lambda a, b : a + b,
mesh.edge_collections.values())
npt.assert_almost_equal(meshtools.project_nodes(lambda x : x[0:2],
self.elements, self.nodes),
self.nodes[:,0:2], decimal=10)
if parsed_mesh.edges:
assert set(map(lambda x : x[0:-1], self.edges)) == \
set(map(lambda x : x[0:-1],
meshtools.extract_boundary_edges(self.elements)))
# Test Argyris stuff.
if self.elements.shape[1] == 6:
TestArgyrisCase(mesh_file, parsed_mesh)
def __init__(self, mesh_file, parsed_mesh):
argyris_mesh = meshes.mesh_factory(*mesh_file, argyris=True)
lagrange_mesh = meshes.mesh_factory(*mesh_file)
assert argyris_mesh.elements.shape == (parsed_mesh.elements.shape[0],
21)
stacked_nodes = dict()
edges_by_midpoint = dict()
for element in argyris_mesh.elements:
for local_number, global_number in enumerate(element[0:3]):
corner_nodes = (element[3 + 2 * local_number],
element[3 + 2 * local_number + 1],
element[9 + 3 * local_number],
element[9 + 3 * local_number + 1],
element[9 + 3 * local_number + 2])
if stacked_nodes.has_key(global_number):
assert corner_nodes == stacked_nodes[global_number]
else:
stacked_nodes[global_number] = corner_nodes
for node in corner_nodes:
npt.assert_almost_equal(
argyris_mesh.nodes[global_number - 1, :],
argyris_mesh.nodes[node - 1, :])
for midpoint_number, local_edge in enumerate([[0, 1], [0, 2],
[1, 2]]):
midpoint = element[18 + midpoint_number]
if edges_by_midpoint.has_key(midpoint):
npt.assert_equal(edges_by_midpoint[midpoint],
element[local_edge])
else:
edges_by_midpoint[midpoint] = element[local_edge]
# Ensure that the Argyris mesh and the Lagrange mesh come up with the
# same edges.
for name, collection in lagrange_mesh.edge_collections.items():
argyris_collection = \
map(lambda x : x.edge,
filter(lambda x : x.name == name,
argyris_mesh.node_collections)[0].edges)
for edge in collection:
argyris_edge = (min(edge[0:2]), max(edge[0:2]), edge[2])
assert argyris_edge in argyris_collection
def __init__(self, mesh_file, parsed_mesh):
argyris_mesh = meshes.mesh_factory(*mesh_file, argyris=True)
lagrange_mesh = meshes.mesh_factory(*mesh_file)
assert argyris_mesh.elements.shape == (parsed_mesh.elements.shape[0],21)
stacked_nodes = dict()
edges_by_midpoint = dict()
for element in argyris_mesh.elements:
for local_number, global_number in enumerate(element[0:3]):
corner_nodes = (element[3 + 2*local_number],
element[3 + 2*local_number + 1],
element[9 + 3*local_number],
element[9 + 3*local_number + 1],
element[9 + 3*local_number + 2])
if stacked_nodes.has_key(global_number):
assert corner_nodes == stacked_nodes[global_number]
else:
stacked_nodes[global_number] = corner_nodes
for node in corner_nodes:
npt.assert_almost_equal(
argyris_mesh.nodes[global_number - 1, :],
argyris_mesh.nodes[node - 1, :])
for midpoint_number, local_edge in enumerate([[0,1], [0,2], [1,2]]):
midpoint = element[18 + midpoint_number]
if edges_by_midpoint.has_key(midpoint):
npt.assert_equal(edges_by_midpoint[midpoint],
element[local_edge])
else:
edges_by_midpoint[midpoint] = element[local_edge]
# Ensure that the Argyris mesh and the Lagrange mesh come up with the
# same edges.
for name, collection in lagrange_mesh.edge_collections.items():
argyris_collection = \
map(lambda x : x.edge,
filter(lambda x : x.name == name,
argyris_mesh.node_collections)[0].edges)
for edge in collection:
argyris_edge = (min(edge[0:2]), max(edge[0:2]), edge[2])
assert argyris_edge in argyris_collection
x2, y2 = coordinates[1]
x3, y3 = coordinates[2]
return np.linalg.inv(np.array([[x1 - x3, x2 - x3],
[y1 - y3, y2 - y3]]))
if __name__ == '__main__':
eps = sys.float_info.epsilon
# USER SET PARAMETERS
reynolds = 1
eps = 0.01
mesh_file = './files/box.mesh'
print "Loading and parsing the mesh..."
domain = msh.mesh_factory(mesh_file)
elements = domain.elements
nodes = np.unique(elements)
pnodes = np.unique(elements.T[:3])
interior_nodes = domain.interior_nodes
coordinates = domain.nodes
n, m = len(nodes), len(pnodes)
k = len(interior_nodes)
weight = 1 / 6.0
gauss_pts = np.array([[0.5, 0.0],
[0.0, 0.5],
[0.5, 0.5]])
A = sp.lil_matrix((n, n))
Bup = sp.lil_matrix((n, m))
from cfem import *
sys.path.append(os.path.expanduser("~/Documents/Code/ArgyrisPack"))
sys.path.append(os.path.expanduser("~/Documents/Code/PODSUPG"))
import ap.mesh.meshes as m
import supg.core.gmsh as gmsh
import supg.core.supg as spg
import supg.cdr.Operators2DCDR as operators
# Create example data.
mesh_file = util.unique_file(suffix=".msh")
geo_file = util.unique_file(suffix=".geo")
gmsh.write_geo_file(gmsh.unit_square(0.05), geo_file=geo_file)
gmsh.call_gmsh(geo_file=geo_file, mesh_file=mesh_file)
mesh = m.mesh_factory(mesh_file)
# compute the PODSUPG operators too.
fe_facade = spg.SUPGFacade(order=2)
ops = operators.Operators2DCDR(mesh, fe_facade, stabilization_coeff=3.0)
if mesh.interior_nodes.min() == 0:
last_boundary_node = max(mesh.boundary_nodes['land'])
else:
last_boundary_node = max(mesh.boundary_nodes['land']) - 1
first_interior_node = last_boundary_node + 1
mass = get_matrix('mass', mesh, stabilization_coeff=3.0).todense()
convection = get_matrix('convection', mesh, stabilization_coeff=3.0).todense()
stiffness = get_matrix('stiffness', mesh, stabilization_coeff=3.0).todense()
hessian = get_matrix('hessian', mesh, stabilization_coeff=3.0).todense()
from cfem import *
sys.path.append(os.path.expanduser("~/Documents/Code/ArgyrisPack"))
sys.path.append(os.path.expanduser("~/Documents/Code/PODSUPG"))
import ap.mesh.meshes as m
import supg.core.gmsh as gmsh
import supg.core.supg as spg
import supg.cdr.Operators2DCDR as operators
# Create example data.
mesh_file = util.unique_file(suffix=".msh")
geo_file = util.unique_file(suffix=".geo")
gmsh.write_geo_file(gmsh.unit_square(0.05), geo_file=geo_file)
gmsh.call_gmsh(geo_file=geo_file, mesh_file=mesh_file)
mesh = m.mesh_factory(mesh_file)
# compute the PODSUPG operators too.
fe_facade = spg.SUPGFacade(order=2)
ops = operators.Operators2DCDR(mesh, fe_facade, stabilization_coeff=3.0)
if mesh.interior_nodes.min() == 0:
last_boundary_node = max(mesh.boundary_nodes["land"])
else:
last_boundary_node = max(mesh.boundary_nodes["land"]) - 1
first_interior_node = last_boundary_node + 1
mass = get_matrix("mass", mesh, stabilization_coeff=3.0).todense()
convection = get_matrix("convection", mesh, stabilization_coeff=3.0).todense()
stiffness = get_matrix("stiffness", mesh, stabilization_coeff=3.0).todense()
hessian = get_matrix("hessian", mesh, stabilization_coeff=3.0).todense()
def stokes():
eps = sys.float_info.epsilon
# USER SET PARAMETERS
reynolds = 1e0
eps = 1e-4 / reynolds
mesh_file = 'convergence/01.mesh'
root_dir = './files/'
print "Loading and parsing the mesh..."
domain = m.mesh_factory(root_dir + mesh_file)
elements = domain.elements
nodes = np.unique(elements)
pnodes = np.unique(elements.T[:3])
interior_nodes = domain.interior_nodes
coordinates = domain.nodes
n, m = len(nodes), len(pnodes)
weight = 1 / 6.0
gauss_pts = np.array([[0.5, 0.0],
[0.0, 0.5],
[0.5, 0.5]])
A = sp.lil_matrix((n, n))
B_up = sp.lil_matrix((n, m))
B_vp = sp.lil_matrix((n, m))
F_x = np.zeros(n)
F_y = F_x.copy()
quad_basis = fn.Quadratic_Basis_Function()
lin_basis = fn.Linear_Basis_Function()
counter = 1
total = len(elements)
print "Constructing system..."
for element in elements:
#if np.mod(counter, 100) == 1:
#print "Element %d of %d..." % (counter, total)
# Precalculate some stuff
element_coords = get_coordinates(element, domain.nodes)
B = calculate_B(element_coords[:3])
detJ = 1 / np.abs(np.linalg.det(B))
weight_scaled = weight * detJ
# Allocate local matrices
local_A = sp.lil_matrix((6, 6))
#local_T = sp.lil_matrix((3, 3))
local_B_up = sp.lil_matrix((6, 3))
local_B_vp = sp.lil_matrix((6, 3))
local_F_x = np.zeros(n)
local_F_y = np.zeros(n)
for i in xrange(6):
# Assemble load vectors
for point in gauss_pts:
x_g, y_g = point
local_F_x[i] += weight_scaled * f1(x_g, y_g)
local_F_y[i] += weight_scaled * f2(x_g, y_g)
F_x[element[i] - 1] += local_F_x[i]
F_y[element[i] - 1] += local_F_y[i]
for j in xrange(6):
# Assemble S
for point in gauss_pts:
x_g, y_g = point
local_A[i, j] += (weight_scaled / reynolds) * np.dot(
np.dot(quad_basis.grad(j, x_g, y_g), B),
np.dot(B.T, quad_basis.grad(i, x_g, y_g)))
A[element[i] - 1, element[j] - 1] += local_A[i, j]
if j < 3:
# Assemble Gx and Gy
for point in gauss_pts:
x_g, y_g = point
local_B_up[i, j] += weight_scaled * (
lin_basis(j, x_g, y_g) *
np.dot(quad_basis.grad(i, x_g, y_g), B[0]))
local_B_vp[i, j] += weight_scaled * (
lin_basis(j, x_g, y_g) *
np.dot(quad_basis.grad(i, x_g, y_g), B[1]))
pnode_j = np.where(pnodes == element[j])[0][0]
B_up[element[i] - 1, pnode_j] += local_B_up[i, j]
B_vp[element[i] - 1, pnode_j] += local_B_vp[i, j]
counter += 1
A = A.tocsr()
A = A[interior_nodes - 1, :]
A = A.tocsc()
A = A[:, interior_nodes - 1]
B_up = B_up.tocsr()
B_up = B_up[interior_nodes - 1, :]
B_vp = B_vp.tocsr()
B_vp = B_vp[interior_nodes - 1, :]
F_x = F_x[interior_nodes - 1, :]
F_y = F_y[interior_nodes - 1, :]
# Update dimensions since we nuked the Dirchlet BCs, all = 0
k = len(interior_nodes)
M = sp.bmat([[A, sp.csc_matrix((k, k))],
[sp.csc_matrix((k, k)), A]]) + \
sp.bmat([[B_up.dot(B_up.T), B_up.dot(B_vp.T)],
[B_vp.dot(B_up.T), B_vp.dot(B_vp.T)]]) / eps
M = M.tocsc()
print "Solving the linear systems..."
UV = np.zeros(2 * k)
UV = spl.gmres(M, np.append(F_x, F_y))[0]
P = np.zeros(m)
P = -sp.bmat([[B_up.T, B_vp.T]]).dot(UV) / eps
U = np.zeros(n)
V = np.zeros(n)
U[interior_nodes - 1] += UV[:k]
V[interior_nodes - 1] += UV[k:2 * k]
UVP = np.zeros(2 * n + m)
UVP[:n] = U[:]
UVP[n:2 * n] = V[:]
UVP[2 * n:] = P[:]
# POST PROCESSING for system one
x, y = coordinates[pnodes - 1].T
tri = np.zeros(np.shape(elements[:, :3]))
for i, element in enumerate(elements[:, :3]):
for j, vert in enumerate(element):
tri[i, j] = np.where(pnodes == vert)[0][0]
print "Saving some data..."
p = UVP[2 * n:]
u = UVP[n:2 * n]
v = UVP[:n]
np.savetxt('./files/UVP.txt', UVP)
np.savetxt('./files/tri.txt', tri)
np.savetxt('./files/x.txt', x)
np.savetxt('./files/y.txt', y)
np.savetxt('./files/p.txt', p)
np.savetxt('./files/u.txt', u[pnodes - 1])
np.savetxt('./files/v.txt', v[pnodes - 1])
print "All done! Thank you, come again!\n\n"