def test_plot_local_solution_salt():
from pygeoiga.nurb.cad import make_salt_dome
from pygeoiga.nurb.nrb_to_gmsh import convert_geometry_mp_to_gmsh
geometry = make_salt_dome(refine=False)
mesh, script, physical_tag_id = convert_geometry_mp_to_gmsh(
geometry,
size=100,
save_geo=datapath + "salt_dome_model.geo",
save_msh=datapath + "salt_dome_model.msh")
from pygeoiga.FE_solvers.run_fenics import convert_msh_to_xdmf, run_simulation, p_temperature_fenics
input = datapath + "salt_dome_model.msh"
convert_msh_to_xdmf(input)
nodal_coordinates, temperature_nodes = run_simulation(
input,
topology_info=physical_tag_id,
top_bc=10,
bot_bc=40,
geometry=geometry,
show=False)
from pygeoiga.plot.solution_mpl import p_temperature
fig, ax = plt.subplots()
ax.set_aspect("equal")
ax = p_temperature(nodal_coordinates[:, 0],
nodal_coordinates[:, 1],
temperature_nodes,
vmin=temperature_nodes.min(),
vmax=temperature_nodes.max(),
ax=ax,
point=False,
fill=True,
contour=False,
colorbar=True,
levels=100)
ax = p_temperature(nodal_coordinates[:, 0],
nodal_coordinates[:, 1],
temperature_nodes,
vmin=temperature_nodes.min(),
vmax=temperature_nodes.max(),
ax=ax,
point=False,
fill=False,
contour=True,
colorbar=False,
levels=10)
fig.show()
print(len(temperature_nodes))
#695 200
#2381 100
fig.savefig(datapath + "salt_dome_model_100.png")
def test_plot_local_solution_unconformity():
from pygeoiga.nurb.cad import make_unconformity_model
from pygeoiga.nurb.nrb_to_gmsh import convert_geometry_mp_to_gmsh
geometry = make_unconformity_model(refine=False)
mesh, script, physical_tag_id = convert_geometry_mp_to_gmsh(
geometry,
size=50,
save_geo=datapath + "unconformity_model.geo",
save_msh=datapath + "unconformity_model.msh")
from pygeoiga.FE_solvers.run_fenics import convert_msh_to_xdmf, run_simulation
input = datapath + "unconformity_model.msh"
convert_msh_to_xdmf(input)
nodal_coordinates, temperature_nodes = run_simulation(
input,
topology_info=physical_tag_id,
top_bc=10,
bot_bc=40,
geometry=geometry,
show=False)
from pygeoiga.plot.solution_mpl import p_temperature
fig, ax = plt.subplots()
ax.set_aspect("equal")
ax = p_temperature(nodal_coordinates[:, 0],
nodal_coordinates[:, 1],
temperature_nodes,
vmin=temperature_nodes.min(),
vmax=temperature_nodes.max(),
ax=ax,
point=True,
fill=False)
fig.show()
def test_plot_solution_salt_dome():
from pygeoiga.nurb.cad import make_salt_dome
from pygeoiga.analysis.MultiPatch import patch_topology, form_k_IGA_mp, boundary_condition_mp
from pygeoiga.analysis.common import solve
from pygeoiga.plot.solution_mpl import p_temperature, p_temperature_mp
from pygeoiga.analysis.MultiPatch import map_MP_elements
geometry = make_salt_dome(refine=True, knot_ins= [np.arange(0.2,1,0.2), np.arange(0.2,1,0.2)])
geometry, gDoF = patch_topology(geometry)
K_glob = np.zeros((gDoF, gDoF))
K_glob = form_k_IGA_mp(geometry, K_glob)
D = np.zeros(gDoF)
b = np.zeros(gDoF)
T_t = 10 # [°C]
T_b = 90 # [°C]
T_l = None#10
T_r = None#40
bc, D = boundary_condition_mp(geometry, D, T_t, T_b, T_l, T_r)
bc["gDOF"] = gDoF
D, b = solve(bc, K_glob, b, D)
geometry = map_MP_elements(geometry, D)
from pygeoiga.plot.nrbplotting_mpl import p_surface, p_cpoints, p_knots, create_figure
fig, ax = create_figure("2d")
#ax.view_init(azim=270, elev=90)
fig_sol, ax_sol = create_figure("2d")
geometrypatch = make_salt_dome(refine=False)
figpatch, axpatch = create_figure("2d")
for patch_id in geometry.keys():
ax = p_surface(geometry[patch_id].get("knots"), geometry[patch_id].get("B"), ax=ax, dim=2,
color=geometry[patch_id].get("color"), alpha=0.5)
#ax = p_cpoints(geometry[patch_id].get("B"), ax=ax, dim=2, color="black", marker=".", point=True, line=False)
ax = p_knots(geometry[patch_id].get("knots"), geometry[patch_id].get("B"), ax=ax, dim=2, point=False,
line=True)
axpatch = p_surface(geometrypatch[patch_id].get("knots"), geometrypatch[patch_id].get("B"), ax=axpatch, dim=2,
color=geometrypatch[patch_id].get("color"), alpha=0.5)
#axpatch = p_cpoints(geometry[patch_id].get("B"), ax=axpatch, dim=2, color="black", marker=".", point=True, line=False)
axpatch = p_knots(geometrypatch[patch_id].get("knots"), geometrypatch[patch_id].get("B"), ax=axpatch, dim=2, point=False,
line=True)
#ax_sol = p_cpoints(geometry[patch_id].get("B"), ax=ax_sol, dim=2, color=geometry[patch_id].get("color"), marker=".", point=True, line=False)
ax_sol = p_surface(geometry[patch_id].get("knots"), geometry[patch_id].get("B"), ax=ax_sol, dim=2,
color="k", fill=False)
x = geometry[patch_id].get("x_sol")
y = geometry[patch_id].get("y_sol")
t = geometry[patch_id].get("t_sol")
ax_sol = p_temperature(x,y,t, vmin = np.min(D), vmax = np.max(D), levels=50, show=False, colorbar=True, ax=ax_sol,
point = False, fill=True)#, color = "k")
fig.show()
fig_sol.show()
figpatch.show()
fig_all, ax_all = create_figure("2d")
p_temperature_mp(geometry=geometry, vmin=np.min(D), vmax=np.max(D), levels=50, show=False, colorbar=True,
ax=ax_all, point=False, fill=True, contour=False)
plt.show()
def p_temperature_fenics(coordinates,
temperature,
typ="2d",
ax=None,
inter_points=100,
**kwargs):
from pygeoiga.plot.solution_mpl import p_temperature
# if ax is None:
# if typ=="2d":
# fig, ax = plt.subplots()
# ax.set_aspect("equal")
# elif typ=="3d":
# fig = plt.figure()
# ax = fig.add_subplot(111, projection='3d')
x_temp = coordinates[:, 0]
y_temp = coordinates[:, 1]
t_temp = temperature
# Set up a regular grid of interpolation points
xi = np.linspace(x_temp.min(), x_temp.max(), inter_points)
yi = np.linspace(y_temp.min(), y_temp.max(), inter_points)
xi, yi = np.meshgrid(xi, yi)
import scipy.interpolate
ti = scipy.interpolate.griddata((x_temp, y_temp),
t_temp, (xi, yi),
method='linear')
p_temperature(
x_pos=None,
y_pos=None,
temperature=ti,
extent=[x_temp.min(),
x_temp.max(),
y_temp.min(),
y_temp.max()],
**kwargs)
def plot_solution(self, ax=None, **kwargs_temperature):
if ax is None:
fig, ax = create_figure("2d", figsize=(10, 20))
tmin = 200
tmax = -200
for patch_name in self.geometry.keys():
t = self.geometry[patch_name].get("t_sol")
tmin = t.min() if t.min() < tmin else tmin
tmax = t.max() if t.max() > tmax else tmax
for patch_name in tqdm(self.geometry.keys(),
desc="Plotting solutions"):
x = self.geometry[patch_name].get("x_sol")
y = self.geometry[patch_name].get("y_sol")
t = self.geometry[patch_name].get("t_sol")
ax = p_temperature(x,
y,
t,
vmin=tmin,
vmax=tmax,
ax=ax,
**kwargs_temperature)
return ax
def plot_field(geometry,
a,
gDoF,
figsize=(5, 5),
file_name="temp.pdf",
save=False,
levels=None,
name="_"):
from pygeoiga.plot.nrbplotting_mpl import p_surface, p_cpoints, p_knots
from pygeoiga.plot.solution_mpl import p_temperature, p_triangular_mesh, p_temperature_mp
fig_sol, ax = plt.subplots(figsize=figsize)
xmin = 0
xmax = 0
ymin = 0
ymax = 0
cbar = True
for patch_id in geometry.keys():
x = geometry[patch_id].get("x_sol")
y = geometry[patch_id].get("y_sol")
t = geometry[patch_id].get("t_sol")
xmin = x.min() if x.min() < xmin else xmin
xmax = x.max() if x.max() > xmax else xmax
ymin = y.min() if y.min() < ymin else ymin
ymax = y.max() if y.max() > ymax else ymax
ax = p_temperature(x,
y,
t,
vmin=np.min(a),
vmax=np.max(a),
levels=200,
show=False,
colorbar=cbar,
ax=ax,
point=False,
fill=True,
contour=False)
cbar = False
ax.set_title("%s DoF %s" % (gDoF, name))
ax.set_aspect("equal")
ax.set_ylabel(r"$y$")
ax.set_xlabel(r"$x$")
ax.set_xlim(xmin, xmax)
ax.set_ylim(ymin, ymax)
for c in ax.collections:
c.set_edgecolor("face")
for patch_id in geometry.keys():
x = geometry[patch_id].get("x_sol")
y = geometry[patch_id].get("y_sol")
t = geometry[patch_id].get("t_sol")
ax = p_temperature(x,
y,
t,
vmin=np.min(a),
vmax=np.max(a),
levels=levels,
show=False,
colorbar=False,
colors=["black"],
ax=ax,
point=False,
fill=False,
contour=True,
cmap=None,
linewidths=0.5)
plt.tight_layout()
fig_sol.show()
if save or save_all:
fig_sol.savefig(fig_folder + file_name, **kwargs_savefig)
def plot_IGA(geometry,
a,
gDoF,
figsize=(5, 5),
file_name="temp.pdf",
save=False,
levels=None,
name="_"):
from pygeoiga.plot.nrbplotting_mpl import p_surface, p_cpoints, p_knots
from pygeoiga.plot.solution_mpl import p_temperature, p_triangular_mesh, p_temperature_mp
figsize = (figsize[0] * 2, figsize[1])
fig_sol, [ax2, ax3] = plt.subplots(1, 2, figsize=figsize, sharey=True)
xmin = 0
xmax = 0
ymin = 0
ymax = 0
cbar = True
for patch_id in geometry.keys():
x = geometry[patch_id].get("x_sol")
y = geometry[patch_id].get("y_sol")
t = geometry[patch_id].get("t_sol")
xmin = x.min() if x.min() < xmin else xmin
xmax = x.max() if x.max() > xmax else xmax
ymin = y.min() if y.min() < ymin else ymin
ymax = y.max() if y.max() > ymax else ymax
ax2 = p_temperature(x,
y,
t,
vmin=np.min(a),
vmax=np.max(a),
show=False,
colorbar=False,
ax=ax2,
point=True,
fill=False,
markersize=25)
ax2 = p_knots(geometry[patch_id].get("knots"),
geometry[patch_id].get("B"),
ax=ax2,
color='k',
dim=2,
point=False,
line=True,
linestyle="--",
linewidth=0.2)
ax3 = p_temperature(x,
y,
t,
vmin=np.min(a),
vmax=np.max(a),
levels=200,
show=False,
colorbar=cbar,
ax=ax3,
point=False,
fill=True,
contour=False)
cbar = False
ax2.set_title("%s DoF_%s" % (gDoF, name))
for ax in ax2, ax3:
ax.set_aspect("equal")
ax.set_ylabel(r"$y$")
ax.set_xlabel(r"$x$")
ax.set_xlim(xmin, xmax)
ax.set_ylim(ymin, ymax)
for c in ax3.collections:
c.set_edgecolor("face")
for patch_id in geometry.keys():
x = geometry[patch_id].get("x_sol")
y = geometry[patch_id].get("y_sol")
t = geometry[patch_id].get("t_sol")
ax3 = p_temperature(x,
y,
t,
vmin=np.min(a),
vmax=np.max(a),
levels=levels,
show=False,
colorbar=False,
colors=["black"],
ax=ax3,
point=False,
fill=False,
contour=True,
cmap=None,
linewidths=0.5)
#ax3 = p_temperature_mp(geometry, vmin=np.min(a), vmax=np.max(a), levels=levels,
# show=False, colorbar=False, colors=["black"], ax=ax3,
# point=False, fill=False, contour=True, cmap=None,
# linewidths=0.5)
plt.tight_layout()
fig_sol.show()
if save or save_all:
fig_sol.savefig(fig_folder + file_name, **kwargs_savefig)
def plot_mp_FEM(geometry, a, gDoF, levels=None):
fig_sol, [ax2, ax3] = plt.subplots(1, 2, figsize=(10, 5), sharey=True)
xmin = 0
xmax = 0
ymin = 0
ymax = 0
cbar = True
for patch_id in geometry.keys():
x = geometry[patch_id].get("x_sol")
y = geometry[patch_id].get("y_sol")
t = geometry[patch_id].get("t_sol")
xmin = x.min() if x.min() < xmin else xmin
xmax = x.max() if x.max() > xmax else xmax
ymin = y.min() if y.min() < ymin else ymin
ymax = y.max() if y.max() > ymax else ymax
ax2 = p_temperature(x,
y,
t,
vmin=np.min(a),
vmax=np.max(a),
show=False,
colorbar=False,
ax=ax2,
point=True,
fill=False,
markersize=25)
ax2 = p_knots(geometry[patch_id].get("knots"),
geometry[patch_id].get("B"),
ax=ax2,
color='k',
dim=2,
point=False,
line=True,
linestyle="--",
linewidth=0.2)
ax3 = p_temperature(x,
y,
t,
vmin=np.min(a),
vmax=np.max(a),
levels=200,
show=False,
colorbar=cbar,
ax=ax3,
point=False,
fill=True,
contour=False)
cbar = False
ax2.set_title("%s DoF" % gDoF)
for ax in ax2, ax3:
ax.set_aspect("equal")
ax.set_ylabel(r"$y$")
ax.set_xlabel(r"$x$")
ax.set_xlim(xmin, xmax)
ax.set_ylim(ymin, ymax)
for c in ax3.collections:
c.set_edgecolor("face")
for patch_id in geometry.keys():
x = geometry[patch_id].get("x_sol")
y = geometry[patch_id].get("y_sol")
t = geometry[patch_id].get("t_sol")
ax3 = p_temperature(x,
y,
t,
vmin=np.min(a),
vmax=np.max(a),
levels=levels,
show=False,
colorbar=False,
colors=["black"],
ax=ax3,
point=False,
fill=False,
contour=True,
cmap=None,
linewidths=0.5)
plt.tight_layout()
fig_sol.show()
def test_listings():
import numpy as np
from collections import OrderedDict
def create_three_layer_model():
# Lower layer control points
bottom_c = np.array([[[0., 0., 1.], [0., 50., 1.], [0., 100., 1.]],
[[250., 0., 1.], [250., 180., 1.], [250., 250., 1.]],
[[500., 0., 1.], [500., 50., 1.], [500., 100., 1.]]])
knot_b = ([0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1]) # knot vector (U, V)
# Middle layer control points
middle_c = np.array([[[0., 100., 1.], [0., 200., 1.], [0., 300., 1.]],
[[250., 250., 1.], [250., 380., 1.], [250., 400., 1.]],
[[500., 100., 1.], [500., 200., 1.], [500., 300., 1.]]])
knot_m = ([0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1]) # knot vector (U, V)
# Upper layer control points
upper_c = np.array([[[0., 300., 1.], [0., 400., 1.], [0., 500., 1.]],
[[250., 400., 1.], [250., 450., 1.], [250., 500., 1.]],
[[500., 300., 1.], [500., 400., 1.], [500., 500., 1.]]])
knot_u = ([0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1]) # knot vector (U, V)
cpoints = [bottom_c, middle_c, upper_c]
knots = [knot_b, knot_m, knot_u]
geometry = OrderedDict({})
name = ["Granite", "Mudstone", "Sandstone"] # type of litholgy
for i, lith in enumerate(name):
geometry[lith] = {"B": cpoints[i], "knots": knots[i]}
return geometry
def assign_properties(geometry: dict):
color = ["red", "blue", "green"] # Assign a fixed color to the NURBS. Useful for visualization
kappa = [3.1, 0.9, 3] # Thermal conductivity of the layer [W/mK]
position = [(1, 1), (2, 1), (3, 1)] # Position of the patch in a global grid (Row and colum)
for i, patch_name in enumerate(geometry.keys()):
geometry[patch_name]["kappa"] = kappa[i]
geometry[patch_name]["color"] = color[i]
geometry[patch_name]["position"] = position[i]
# Topology of patches -BOUNDARIES - faces of the patch in contact
# 0: down; 1: right; 2: up; 3: left
# Granite is in contact to mudstone in the "up" face
geometry["Granite"]["patch_faces"] = {2: "Mudstone"}
# Mudstone is in contact to granite in the "down" face and to sandstone in the "up" face
geometry["Mudstone"]["patch_faces"] = {0: "Granite", 2: "Sandstone"}
# Sandstone is in contact to mudstone in the "down" face
geometry["Sandstone"]["patch_faces"] = {0: "Mudstone"}
# Specify the face that have a boundary condition
#geometry["granite"]["BC"] = {0: "bot_bc"}
#geometry["sandstone"]["BC"] = {2: "top_bc"}
return geometry
def refinement(geometry: dict):
# Knot insertion following the computational procedure of Piegl and Tille (1997)
from pygeoiga.nurb.refinement import knot_insertion
knot_ins_0 = np.arange(0.1, 1, 0.1)
knot_ins_1 = np.arange(0.1, 1, 0.1)
for count, patch_name in enumerate(geometry.keys()):
B = geometry[patch_name].get("B")
knots = geometry[patch_name].get("knots")
B, knots = knot_insertion(B, degree=(2, 2), knots=knots,
knots_ins=knot_ins_0, direction=0) # U refinement
B, knots = knot_insertion(B, degree=(2, 2), knots=knots,
knots_ins=knot_ins_1, direction=1) # V refinement
geometry[patch_name]["B"] = B
geometry[patch_name]["knots"] = knots
return geometry
def form_k_IGA(K_glb: np.ndarray,
IEN: np.ndarray,
P: list,
kappa: float,
nx: int,
ny: int,
degree: int,
knots: float):
"""
Function to form the stiffness matrix
Args:
K_glb: empty stiffness matrix
IEN: element topology = numbering of control points
P: coordinates of NURBS control points x, y, z in single matrix (:,3)
kappa: Thermal conductivity
nx: number of elements in u direction
ny: number of elments in v direction
degree: polynomial order
knots: knot vector (U, V)
Returns:
K -> Stiffness matrix
"""
from pygeoiga.analysis.common import gauss_points
from pygeoiga.analysis.iga import nurb_basis_IGA, jacobian_IGA
# Gauss quadrature for performing numerical integration. Gauss points and weights
G, W = gauss_points(degree)
# Assign a value of thermal conductivity to each control point and calculate the element thermal conductivity
#kappa_element = kappa_domain(kappa, IEN)
# Knot vector from each parametric direction
U = knots[0][degree:-degree]
V = knots[1][degree:-degree]
e = 0
for i in range(ny):
for j in range(nx):
IEN_e = IEN[e] # Element topology of current element
eDOF = IEN_e # Element degrees of freedom
#kappa_e = kappa_element[e] #
k = 0
for g in range(len(G)):
# Obtain gauss points from reference element
xi = G[g, 0] # Gauss point in xi direction
eta = G[g, 1] # Gauss point in eta direction
w = W[g] # weight of Gauss point
# Map Gauss points to parameter space
u = U[j] + (xi + 1) * (U[j + 1] - U[j]) / 2
v = V[i] + (eta + 1) * (V[i + 1] - V[i]) / 2
# Evaluate basis functions and derivatives
N_u, dN_u, N_v, dN_v = nurb_basis_IGA(u, v, knots=knots, degree=degree)
# Map of derivatives from parameter space to reference element
dN_xi = dN_u / 2
dN_eta = dN_v / 2
# Collect the basis functions and derivatives which support the element
N_u = N_u[j:j + degree + 1]
dN_xi = dN_xi[j:j + degree + 1]
N_v = N_v[i:i + degree + 1]
dN_eta = dN_eta[i:i + degree + 1]
# Calculate the Jacobian to map from the reference element to physical space
J, dxy = jacobian_IGA(N_u, dN_xi, N_v, dN_eta, P, IEN_e, degree)
# add contributions to local stiffness matrix
k = k + (dxy.T @ dxy) * np.linalg.det(J) * w * kappa#kappa_e
# Add local stiffness matrix to global stiffness matrix
K_glb[np.ix_(eDOF, eDOF)] = K_glb[np.ix_(eDOF, eDOF)] + k
e += 1
return K_glb
geometry = create_three_layer_model()
geometry = assign_properties(geometry)
geometry = refinement(geometry)
from pygeoiga.analysis.MultiPatch import patch_topology
# Extract the information from each patch and create a global numbering of the multi-patch geometry.
# The total amount of non-repeated control points will be global degrees of freedom
geometry, gDoF = patch_topology(geometry)
print(gDoF)
#from pygeoiga.analysis.iga import form_k_IGA
def assemble_stiffness_matrix(geometry: dict, gDoF: int):
"""
Args:
geometry: NURBS multipatch
gDoF: Global degrees of freedom
Return:
K_glob: Global stiffnes matrix
"""
# Set empty the stiffness matrix according to the global degrees of freedom
K_glob = np.zeros((gDoF, gDoF))
# iterate over the patches
for patch_id in geometry.keys():
pDof = geometry[patch_id].get("patch_DOF") # Degrees of freedom per patch
K = np.zeros((pDof, pDof)) # Initialize empty patch stiffness matrix
nx, ny = geometry[patch_id].get("n_element") # number of elements in u and v parametric coordinates
U, V = geometry[patch_id].get("knots") # knot vectors
degree = geometry[patch_id].get("degree") # degree of NURBS patch
# Currently support only the same degree for both parametric directions
assert degree[0] == degree[1]
degree = degree[0]
P = geometry[patch_id].get("list_cp") # Get list with location of control points
IEN = geometry[patch_id].get("IEN") # connectivity array (element topology)
kappa = geometry[patch_id].get("kappa") # Patch thermal conductivity
# create patch stiffness matrix
K = form_k_IGA(K, IEN, P, kappa, nx, ny, degree, knots=(U, V))
# Assemble global stiffness matrix according to global indexing
patch_glob_num = geometry[patch_id].get("glob_num")
K_glob[np.ix_(patch_glob_num,
patch_glob_num)] = K_glob[np.ix_(patch_glob_num,
patch_glob_num)] + K
return K_glob
K_glob = assemble_stiffness_matrix(geometry, gDoF)
fig, ax = plt.subplots(constrained_layout=True)
ax.spy(K_glob)
ax.set_xlabel("Global $K$ of Anticline multi-patch geometry")
fig.show()
save = False
if save or save_all:
fig.savefig(fig_folder+"stiffnes_matrix.pdf", **kwargs_savefig)
from pygeoiga.analysis.MultiPatch import boundary_condition_mp
a = np.zeros(gDoF)
T_top = 10; T_bottom = 25; T_left = None; T_right = None
# Also possible to pass a function as
#T_bottom = lambda x, m: 10 * np.sin(np.pi * x / m)
# with x the position of the node and m the total number of nodes
bc, a = boundary_condition_mp(geometry, a, T_top, T_bottom, T_left, T_right)
bc["gDOF"] = gDoF
from scipy.sparse.linalg import cg
# Empty Force vector
F = np.zeros(gDoF)
def solve(bc: dict, K: np.ndarray, F: np.ndarray, a: np.ndarray):
prDOF = bc.get("prDOF") # list of indexes for control points with boundary condition
gDOF = bc.get("gDOF") # Degrees of freedom for the system
# Find the active control points
acDOF = np.setxor1d(np.arange(0, gDOF), prDOF).astype('int')
# Reduced stiffness matrix using only active control points
Kfs = K[np.ix_(acDOF, prDOF)]
f = F[acDOF]
bf_n = f - Kfs @ a[prDOF]
# Solve for the system of equations for displacement vector
a[acDOF], _ = cg(A=K[np.ix_(acDOF, acDOF)], b=bf_n)
# Calculate Force vector
F = K @ a
return a, F
a, F = solve(bc, K_glob, F, a)
from pygeoiga.analysis.iga import map_solution_elements
def map_MP_elements(geometry, a):
for patch_id in geometry.keys():
degree, _ = geometry[patch_id].get("degree") # Degree of NURBS patch
P = geometry[patch_id].get("list_cp") # List of control points associated to the patch
nx, ny = geometry[patch_id].get("n_element") # number of elements in u and v diection
n, m = geometry[patch_id].get("n_basis") # number of basis functions in u and v direction
ncp = n * m # Total amount of control points
W = geometry[patch_id].get("list_weight") # List of weights
knots = geometry[patch_id].get("knots") # knot vectors in u and v
glob_num = geometry[patch_id].get("glob_num") # global index numbering
a_patch = a[glob_num] # Extract from the displacement vector the values corresponding to the patch control points
IEN = geometry[patch_id].get("IEN") # Connectivity array (element topology)
# Procedure to obtain the coordinate x and y of the temperature value t
x_temp, y_temp, t_temp = map_solution_elements(a_patch, degree, P, nx, ny, n, m, ncp, IEN, W, knots)
geometry[patch_id]["x_sol"] = x_temp
geometry[patch_id]["y_sol"] = y_temp
geometry[patch_id]["t_sol"] = t_temp
return geometry
geometry = map_MP_elements(geometry, a)
fig_sol, [ax1, ax2, ax3] = plt.subplots(1, 3, figsize=(15,5), sharey=True)
from pygeoiga.plot.nrbplotting_mpl import p_surface, p_cpoints, p_knots, np
from pygeoiga.plot.solution_mpl import p_temperature
for patch_id in geometry.keys():
ax1 = p_surface(geometry[patch_id].get("knots"),
geometry[patch_id].get("B"),
color=geometry[patch_id].get("color"),
dim=2,
fill=True,
border=False,
ax=ax1)
x = geometry[patch_id].get("x_sol")
y = geometry[patch_id].get("y_sol")
t = geometry[patch_id].get("t_sol")
ax2 = p_temperature(x, y, t, vmin=np.min(a), vmax=np.max(a), levels=100, show=False, colorbar=False,
ax=ax2, point=True, fill=False, markersize=50)
ax2 = p_knots(geometry[patch_id].get("knots"),
geometry[patch_id].get("B"),
ax=ax2,
color='k',
dim=2,
point=False,
line=True,
linestyle="--",
linewidth=0.2)
#ax2 = p_cpoints(geometry[patch_id].get("B"), dim=2, ax=ax2, point=True, line=False)
ax3 = p_temperature(x, y, t, vmin=np.min(a), vmax=np.max(a), levels=200, show=False, colorbar=True, ax=ax3,
point=False, fill=True, contour=False)
ax1.legend(labels=list(geometry.keys()),
handles=ax1.patches,
loc='upper left',
bbox_to_anchor=(0.05, .9),
borderaxespad=0)
ax1.set_ylabel(r"$y$")
for ax in ax1, ax2, ax3:
ax.set_aspect("equal")
ax.set_xlabel(r"$x$")
ax.set_xlim(0,500)
ax.set_ylim(0,500)
for c in ax3.collections:
c.set_edgecolor("face")
plt.tight_layout()
fig_sol.show()
save = False
if save or save_all:
fig_sol.savefig(fig_folder + "solution_anticline.pdf", **kwargs_savefig)