def HighOrderMeshTet_SEMISTABLE(C,
mesh,
Decimals=10,
equally_spaced=False,
check_duplicates=True,
parallelise=False,
nCPU=1,
compute_boundary_info=True):
from Florence.FunctionSpace import Tet
from Florence.QuadratureRules.FeketePointsTet import FeketePointsTet
from Florence.MeshGeneration.NodeArrangement import NodeArrangementTet
# SWITCH OFF MULTI-PROCESSING FOR SMALLER PROBLEMS WITHOUT GIVING A MESSAGE
Parallel = parallelise
if (mesh.elements.shape[0] < 500) and (C < 5):
Parallel = False
nCPU = 1
if not equally_spaced:
eps = FeketePointsTet(C)
# COMPUTE BASES FUNCTIONS AT ALL NODAL POINTS
Neval = np.zeros((4, eps.shape[0]), dtype=np.float64)
hpBases = Tet.hpNodal.hpBases
for i in range(4, eps.shape[0]):
Neval[:, i] = hpBases(0,
eps[i, 0],
eps[i, 1],
eps[i, 2],
Transform=1,
EvalOpt=1)[0]
else:
from Florence.QuadratureRules.EquallySpacedPoints import EquallySpacedPointsTet
eps = EquallySpacedPointsTet(C)
# COMPUTE BASES FUNCTIONS AT ALL NODAL POINTS
hpBases = Tet.hpNodal.hpBases
Neval = np.zeros((4, eps.shape[0]), dtype=np.float64)
for i in range(4, eps.shape[0]):
Neval[:, i] = hpBases(0,
eps[i, 0],
eps[i, 1],
eps[i, 2],
Transform=1,
EvalOpt=1,
equally_spaced=True)[0]
# THIS IS NECESSARY FOR REMOVING DUPLICATES
makezero(Neval, tol=1e-12)
nodeperelem = mesh.elements.shape[1]
renodeperelem = int((C + 2.) * (C + 3.) * (C + 4.) / 6.)
left_over_nodes = renodeperelem - nodeperelem
reelements = -1 * np.ones(
(mesh.elements.shape[0], renodeperelem), dtype=np.int64)
reelements[:, :4] = mesh.elements
# TOTAL NUMBER OF (INTERIOR+EDGE+FACE) NODES
iesize = np.int64(C * (C - 1) * (C - 2) / 6. + 6. * C + 2 * C * (C - 1))
repoints = np.zeros(
(mesh.points.shape[0] + iesize * mesh.elements.shape[0], 3),
dtype=np.float64)
repoints[:mesh.points.shape[0], :] = mesh.points
telements = time()
xycoord_higher = []
ParallelTuple1 = []
if Parallel:
# GET HIGHER ORDER COORDINATES - PARALLEL
ParallelTuple1 = parmap.map(ElementLoopTet,
np.arange(0, mesh.elements.shape[0]),
mesh.elements,
mesh.points,
'tet',
eps,
Neval,
pool=MP.Pool(processes=nCPU))
maxNode = np.max(reelements)
for elem in range(0, mesh.elements.shape[0]):
# maxNode = np.max(reelements) # BIG BOTTLENECK
if Parallel:
xycoord_higher = ParallelTuple1[elem]
else:
xycoord = mesh.points[mesh.elements[elem, :], :]
# GET HIGHER ORDER COORDINATES
xycoord_higher = GetInteriorNodesCoordinates(
xycoord, 'tet', elem, eps, Neval)
# EXPAND THE ELEMENT CONNECTIVITY
newElements = np.arange(maxNode + 1, maxNode + 1 + left_over_nodes)
reelements[elem, 4:] = newElements
# INSTEAD COMPUTE maxNode BY INDEXING
maxNode = newElements[-1]
repoints[mesh.points.shape[0] + elem * iesize:mesh.points.shape[0] +
(elem + 1) * iesize] = xycoord_higher[4:, :]
if Parallel:
del ParallelTuple1
telements = time() - telements
#--------------------------------------------------------------------------------------
# NOW REMOVE DUPLICATED POINTS
tnodes = time()
nnode_linear = mesh.points.shape[0]
# KEEP ZEROFY ON, OTHERWISE YOU GET STRANGE BEHVAIOUR
# rounded_repoints = makezero(repoints[nnode_linear:,:].copy())
rounded_repoints = repoints[nnode_linear:, :].copy()
makezero(rounded_repoints)
rounded_repoints = np.round(rounded_repoints, decimals=Decimals)
_, idx_repoints, inv_repoints = unique2d(rounded_repoints,
order=False,
consider_sort=False,
return_index=True,
return_inverse=True)
# idx_repoints.sort()
del rounded_repoints
idx_repoints = np.concatenate(
(np.arange(nnode_linear), idx_repoints + nnode_linear))
repoints = repoints[idx_repoints, :]
unique_reelements, inv_reelements = np.unique(reelements[:, 4:],
return_inverse=True)
unique_reelements = unique_reelements[inv_repoints]
reelements = unique_reelements[inv_reelements]
reelements = reelements.reshape(mesh.elements.shape[0], renodeperelem - 4)
reelements = np.concatenate((mesh.elements, reelements), axis=1)
# SANITY CHECK fOR DUPLICATES
#---------------------------------------------------------------------#
# NOTE THAT THIS REMAPS THE ELEMENT CONNECTIVITY FOR THE WHOLE MESH
# AND AS A RESULT THE FIRST FEW COLUMNS WOULD NO LONGER CORRESPOND TO
# LINEAR CONNECTIVITY
if check_duplicates:
last_shape = repoints.shape[0]
deci = int(Decimals) - 2
if Decimals < 6:
deci = Decimals
repoints, idx_repoints, inv_repoints = remove_duplicates_2D(
repoints, decimals=deci)
unique_reelements, inv_reelements = np.unique(reelements,
return_inverse=True)
unique_reelements = unique_reelements[inv_repoints]
reelements = unique_reelements[inv_reelements]
reelements = reelements.reshape(mesh.elements.shape[0], renodeperelem)
if last_shape != repoints.shape[0]:
warn(
'Duplicated points generated in high order mesh. Lower the "Decimals". I have fixed it for now'
)
#---------------------------------------------------------------------#
tnodes = time() - tnodes
#------------------------------------------------------------------------------------------
#------------------------------------------------------------------------------------------
if compute_boundary_info:
# BUILD FACES NOW
tfaces = time()
# GET MESH EDGES AND FACES
fsize = int((C + 2.) * (C + 3.) / 2.)
refaces = np.zeros((mesh.faces.shape[0], fsize),
dtype=mesh.faces.dtype)
refaces = np.zeros((mesh.faces.shape[0], fsize))
# DO NOT CHANGE THE FACES, BY RECOMPUTING THEM, AS THE LINEAR FACES CAN COME FROM
# AN EXTERNAL MESH GENERATOR, WHOSE ORDERING MAY NOT BE THE SAME, SO JUST FIND WHICH
# ELEMENTS CONTAIN THESE FACES
face_to_elements = mesh.GetElementsWithBoundaryFacesTet()
node_arranger = NodeArrangementTet(C)[0]
refaces = reelements[face_to_elements[:, 0][:, None],
node_arranger[face_to_elements[:, 1], :]].astype(
mesh.faces.dtype)
tfaces = time() - tfaces
#------------------------------------------------------------------------------------------
#------------------------------------------------------------------------------------------
# BUILD EDGES NOW
tedges = time()
# BUILD A 2D MESH
from Florence import Mesh
tmesh = Mesh()
tmesh.element_type = "tri"
tmesh.elements = refaces
tmesh.nelem = tmesh.elements.shape[0]
# GET BOUNDARY EDGES
reedges = tmesh.GetEdgesTri()
del tmesh
tedges = time() - tedges
#------------------------------------------------------------------------------------------
class nmesh(object):
# """Construct pMesh"""
points = repoints
elements = reelements
edges = np.array([[], []])
faces = np.array([[], []])
nnode = repoints.shape[0]
nelem = reelements.shape[0]
info = 'tet'
if compute_boundary_info:
nmesh.edges = reedges
nmesh.faces = refaces
gc.collect()
# print '\nHigh order meshing timing:\n\t\tElement loop:\t '+str(telements)+' seconds\n\t\tNode loop:\t\t '+str(tnodes)+\
# ' seconds'+'\n\t\tEdge loop:\t\t '+str(tedges)+' seconds'+\
# '\n\t\tFace loop:\t\t '+str(tfaces)+' seconds\n'
return nmesh
def test_BEM():
"""Unnecessary test for the ugly and non-working and legacy BEM
for the sake of coverage
"""
from Florence.BoundaryElements import GetBasesBEM2D
from Florence.BoundaryElements import GenerateCoordinates
from Florence.BoundaryElements import CoordsJacobianRadiusatGaussPoints, CoordsJacobianRadiusatGaussPoints_LM
from Florence.BoundaryElements import AssemblyBEM2D
from Florence.BoundaryElements.Assembly import AssemblyBEM2D_Sparse
from Florence.BoundaryElements import Sort_BEM
from Florence import QuadratureRule, FunctionSpace, Mesh
# Unnecessary loop
for i in range(10):
mesh = Mesh()
mesh.element_type = "line"
mesh.points = np.array([
[0.,0.],
[1.,0.],
[1.,1.],
[0.,1.],
])
mesh.elements = np.array([
[0,1],
[1,2],
[2,3],
[3,0],
])
mesh.nelem = 4
q = QuadratureRule(mesh_type="line")
for C in range(10):
N, dN = GetBasesBEM2D(C,q.points)
N, dN = GetBasesBEM2D(2,q.points)
global_coord = np.zeros((mesh.points.shape[0],3))
global_coord[:,:2] = mesh.points
Jacobian = 2*np.ones((q.weights.shape[0],mesh.nelem))
nx = 4*np.ones((q.weights.shape[0],mesh.nelem))
ny = 3*np.ones((q.weights.shape[0],mesh.nelem))
XCO = 2*np.ones((q.weights.shape[0],mesh.nelem))
YCO = np.ones((q.weights.shape[0],mesh.nelem))
N = np.ones((mesh.elements.shape[1],q.weights.shape[0]))
dN = 0.5*np.ones((mesh.elements.shape[1],q.weights.shape[0]))
GenerateCoordinates(mesh.elements,mesh.points,0,q.points)
CoordsJacobianRadiusatGaussPoints(mesh.elements,global_coord,0,N,dN,q.weights)
# Not working
# CoordsJacobianRadiusatGaussPoints_LM(mesh.elements,global_coord[:,:3],0,N,dN,q.weights,mesh.elements)
class GeoArgs(object):
Lagrange_Multipliers = "activated"
def __init__(self):
Lagrange_Multipliers = "activated"
geo_args = GeoArgs()
K1, K2 = AssemblyBEM2D(0,global_coord,mesh.elements,mesh.elements,dN,N,
q.weights,q.points,Jacobian, nx, ny, XCO, YCO, geo_args)
AssemblyBEM2D_Sparse(0,global_coord,mesh.elements,mesh.elements,dN,N,
q.weights,q.points,Jacobian, nx, ny, XCO, YCO, geo_args)
bdata = np.zeros((2*mesh.points.shape[0],2))
bdata[:4,1] = -1
bdata[4:,0] = -1
Sort_BEM(bdata,K1, K2)
def QuadBallSphericalArc(center=(0., 0., 0.),
inner_radius=9.,
outer_radius=10.,
n=10,
nthick=1,
element_type="hex",
cut_threshold=None,
portion=1. / 8.):
"""Similar to QuadBall but hollow and creates only 1/8th or 1/4th or 1/2th of the sphere.
Starting and ending angles are not supported. Radial division (nthick: to be consistent
with SphericalArc method of Mesh class) is supported
input:
cut_threshold [float] cutting threshold for element removal since this function is based
QuadBall. Ideal value is zero, so prescribe a value as close to zero
as possible, however that might not always be possible as the cut
might take remove some wanted elements [default = -0.01]
portion [float] portion of the sphere to take. Can only be 1/8., 1/4., 1/2.
"""
assert inner_radius < outer_radius
mm = QuadBallSurface(n=n, element_type=element_type)
offset = outer_radius * 2.
if cut_threshold is None:
cut_threshold = -0.01
if portion == 1. / 8.:
mm.RemoveElements(
np.array([[cut_threshold, cut_threshold, cut_threshold],
[offset, offset, offset]]))
elif portion == 1. / 4.:
mm.RemoveElements(
np.array([[cut_threshold, cut_threshold, -offset],
[offset, offset, offset]]))
elif portion == 1. / 2.:
mm.RemoveElements(
np.array([[cut_threshold, -offset, -offset],
[offset, offset, offset]]))
else:
raise ValueError("The value of portion can only be 1/8., 1/4. or 1/2.")
radii = np.linspace(inner_radius, outer_radius, nthick + 1)
mesh = Mesh()
mesh.element_type = "hex"
mesh.nelem = 0
mesh.nnode = 0
for i in range(nthick):
mm1, mm2 = deepcopy(mm), deepcopy(mm)
if not np.isclose(radii[i], 1):
mm1.points *= radii[i]
if not np.isclose(radii[i + 1], 1):
mm2.points *= radii[i + 1]
if i == 0:
elements = np.hstack(
(mm1.elements, mm1.nnode + mm2.elements)).astype(np.int64)
mesh.elements = np.copy(elements)
mesh.points = np.vstack((mm1.points, mm2.points))
else:
elements = np.hstack(
(mesh.elements[(i - 1) * mm2.nelem:i * mm2.nelem, 4:],
mesh.nnode + mm2.elements)).astype(np.int64)
mesh.elements = np.vstack((mesh.elements, elements))
mesh.points = np.vstack((mesh.points, mm2.points))
mesh.nelem = mesh.elements.shape[0]
mesh.nnode = mesh.points.shape[0]
mesh.elements = np.ascontiguousarray(mesh.elements, dtype=np.int64)
mesh.nelem = mesh.elements.shape[0]
mesh.nnode = mesh.points.shape[0]
mesh.GetBoundaryFaces()
mesh.GetBoundaryEdges()
mesh.points[:, 0] += center[0]
mesh.points[:, 1] += center[1]
mesh.points[:, 2] += center[2]
return mesh
print("The problem requires 2D analyses. Solving", number_of_planar_surfaces, "2D problems")
for niter in range(number_of_planar_surfaces):
pmesh = Mesh()
if mesh.element_type == "tet":
pmesh.element_type = "tri"
no_face_vertices = 3
elif mesh.element_type == "hex":
pmesh.element_type = "quad"
no_face_vertices = 4
else:
raise ValueError("Curvilinear mesher for element type {} not yet implemented".format(mesh.element_type))
pmesh.elements = mesh.faces[planar_mesh_faces[planar_mesh_faces[:,1]==surface_flags[niter,0],0],:]
pmesh.nelem = np.int64(surface_flags[niter,1])
pmesh.GetBoundaryEdges()
unique_edges = np.unique(pmesh.edges).astype(nodesDBC.dtype)
# Dirichlet2D = np.zeros((unique_edges.shape[0],3))
# nodesDBC2D = np.zeros(unique_edges.shape[0]).astype(np.int64)
unique_elements, inv = np.unique(pmesh.elements, return_inverse=True)
unique_elements = unique_elements.astype(nodesDBC.dtype)
aranger = np.arange(unique_elements.shape[0],dtype=np.uint64)
pmesh.elements = aranger[inv].reshape(pmesh.elements.shape)
# counter = 0
# for i in unique_edges:
# nodesDBC2D[counter] = np.where(nodesDBC==i)[0][0]
# Dirichlet2D[counter,:] = Dirichlet[nodesDBC2D[counter],:]
# counter += 1