def test_plot_field_iga_salt():
geometry = make_salt_dome(refine=True, )
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.analysis.MultiPatch import point_solution_mp
x = np.arange(0, 6000, 200)
y = np.arange(0, 3000, 200)
x = x[1:-1]
y = y[1:-1]
xx, yy = np.meshgrid(x,y)
tt = np.empty(xx.shape)
for i in range(len(x)):
for j in range(len(y)):
tt[i,j] = point_solution_mp(xx[i,j], yy[i,j], geometry)
#tt = point_solution_mp(xx,yy,geometry)
plt.imshow(tt, cmap="viridis", origin="lower")
plt.colorbar()
plt.show()
def test_plot_solution_salt_dome():
from pygeoiga.nurb.cad import make_salt_dome
geometry = make_salt_dome(refine=True,
knot_ins=[
np.arange(0.2, 1, 0.2),
np.arange(0.2, 1, 0.2)
]) #refine=np.arange(0.05,1,0.05))
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
T_r = None
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)
from pygeoiga.analysis.MultiPatch import map_MP_elements
geometry = map_MP_elements(geometry, D)
plot_pvista(geometry)
def test_global_stifffness_matrix():
from pygeoiga.nurb.cad import make_L_shape
from pygeoiga.analysis.MultiPatch import patch_topology
geometry = make_L_shape(refine=True,
knot_ins=([0.3, 0.5, 0.7], [0.4, 0.6]))
geometry, gDoF = patch_topology(geometry)
print(gDoF)
from pygeoiga.analysis.MultiPatch import form_k_IGA_mp
K_glob = np.zeros((gDoF, gDoF))
K_glob = form_k_IGA_mp(geometry, K_glob)
fig, ax = plt.subplots(1, 3, sharey=True, figsize=(10, 3))
for count, patch_id in enumerate(geometry):
K = geometry[patch_id].get("K")
print(K.shape)
ax[count].spy(K)
ax[0].set_xlabel("$K$ for $\Omega_1$", fontsize=15)
ax[1].set_xlabel("$K$ for $\Omega_2$", fontsize=15)
ax[2].set_xlabel("$K$ for $\Omega_3$", fontsize=15)
fig.show()
fig2, ax2 = plt.subplots()
ax2.spy(K_glob)
ax2.set_xlabel("Global $K$ for $\Omega$", fontsize=15)
fig2.show()
save = False
if save or save_all:
fig.savefig(fig_folder + "K_single_patch.pdf", **kwargs_savefig)
fig2.savefig(fig_folder + "K_multi_patch.pdf", **kwargs_savefig)
def test_plot_solution_mp_3d():
import matplotlib
matplotlib.use('Qt5Agg')
geometry = make_3_layer_patches()
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 = lambda x, m: T_t + 10 * np.sin(np.pi * x / m) # [°C]
T_l = None
T_r = None
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_knots, create_figure
fig, ax = create_figure()
for patch_id in geometry.keys():
ax = p_knots(geometry[patch_id].get("knots"), geometry[patch_id].get("B"),
color = geometry[patch_id].get("color"), ax=ax, dim=2, point=False, line=True)
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(D), vmax = np.max(D), levels=50, show=False, colorbar=True, ax=ax,
point = True, fill=True, color = "k")
plt.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 test_plot_solution_mp_fault():
geometry = make_fault_model(refine=True)
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 = 40 # [°C]
T_l = None
T_r = None
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")
fig_sol, ax_sol = create_figure("2d")#
fig_point, ax_point = 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)
#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_knots(geometry[patch_id].get("knots"), geometry[patch_id].get("B"),
# color = geometry[patch_id].get("color"), ax=ax_sol, dim=2, point=False, line=True)
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, contour=False)
ax_point = p_temperature(x, y, t, vmin=np.min(D), vmax=np.max(D), levels=100, show=False, colorbar=True, ax=ax_point,
point=True, fill=False)
ax_sol = p_surface(geometry[patch_id].get("knots"), geometry[patch_id].get("B"), ax=ax_sol, dim=2,
color="k", alpha=1, fill=False, border=True)
fig.show()
fig_sol.show()
fig_point.show()
fig_all, ax_all = create_figure("2d")
p_temperature_mp(geometry=geometry, vmin=np.min(D), vmax=np.max(D), levels=200, show=False, colorbar=True, ax=ax_all,
point=False, fill=True, contour=False)
fig_all.show()
def do_IGA(function, T_t, T_b, knot_ins):
geometry = function(refine=True, knot_ins=knot_ins)
from pygeoiga.analysis.MultiPatch import patch_topology, form_k_IGA_mp
geometry, gDoF = patch_topology(geometry)
K_glob_IGA = np.zeros((gDoF, gDoF))
F_IGA = np.zeros(gDoF)
a_IGA = np.zeros(gDoF)
K_glob_IGA = form_k_IGA_mp(geometry, K_glob_IGA)
from pygeoiga.analysis.MultiPatch import boundary_condition_mp
bc_IGA, a_IGA = boundary_condition_mp(geometry, a_IGA, T_t, T_b, None,
None)
bc_IGA["gDOF"] = gDoF
from pygeoiga.analysis.common import solve
a_IGA, F_IGA = solve(bc_IGA, K_glob_IGA, F_IGA, a_IGA)
from pygeoiga.analysis.MultiPatch import map_MP_elements
geometry = map_MP_elements(geometry, a_IGA)
return geometry, gDoF
def test_plot_solution_3_layer_mp():
from pygeoiga.nurb.cad import make_3_layer_patches
geometry = make_3_layer_patches(refine=True, )
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 = 25 # [°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)
plot_pvista(geometry)
def test_plot_solution_mp_fault():
from pygeoiga.nurb.cad import make_fault_model
geometry = make_fault_model(refine=True)
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 = 40 # [°C]
T_l = None
T_r = None
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)
from pygeoiga.analysis.MultiPatch import map_MP_elements
geometry = map_MP_elements(geometry, D)
plot_pvista(geometry)
def same_IGA_BEZIER(geometry,
T_t,
T_b,
save=False,
filename="temp",
levels=None):
from pygeoiga.analysis.MultiPatch import patch_topology, bezier_extraction_mp, form_k_IGA_mp, form_k_bezier_mp
geometry, gDoF = patch_topology(geometry)
import copy
bezier_geometry = copy.deepcopy(geometry)
bezier_geometry = bezier_extraction_mp(bezier_geometry)
K_glob_IGA = np.zeros((gDoF, gDoF))
F_IGA = np.zeros(gDoF)
a_IGA = np.zeros(gDoF)
K_glob_be = np.zeros((gDoF, gDoF))
F_be = np.zeros(gDoF)
a_be = np.zeros(gDoF)
K_glob_IGA = form_k_IGA_mp(geometry, K_glob_IGA)
K_glob_be = form_k_bezier_mp(bezier_geometry, K_glob_be)
from pygeoiga.analysis.MultiPatch import boundary_condition_mp
bc_IGA, a_IGA = boundary_condition_mp(geometry, a_IGA, T_t, T_b, None,
None)
bc_IGA["gDOF"] = gDoF
bc_be, a_be = boundary_condition_mp(bezier_geometry, a_be, T_t, T_b, None,
None)
bc_be["gDOF"] = gDoF
from pygeoiga.analysis.common import solve
a_IGA, F_IGA = solve(bc_IGA, K_glob_IGA, F_IGA, a_IGA)
a_be, F_be = solve(bc_be, K_glob_be, F_be, a_be)
from pygeoiga.analysis.MultiPatch import map_MP_elements
geometry = map_MP_elements(geometry, a_IGA)
bezier_geometry = map_MP_elements(bezier_geometry, a_be)
figsize = (6, 5)
#plot_IGA(geometry, a_IGA, gDoF, name="IGA")
plot_field(geometry,
a_IGA,
gDoF,
file_name=filename + "_IGA.pdf",
name="IGA",
figsize=figsize,
save=save,
levels=levels)
#plot_IGA(bezier_geometry, a_be, gDoF, name ="Bezier")
plot_field(bezier_geometry,
a_be,
gDoF,
file_name=filename + "_bezier.pdf",
name="Bezier",
figsize=figsize,
save=save,
levels=levels)
fig, ax = plt.subplots(figsize=figsize)
min_p = None
max_p = None
cmap = plt.get_cmap("RdBu")
xmin = 0
xmax = 0
ymin = 0
ymax = 0
cbar = True
for patch_id in geometry.keys():
err = geometry[patch_id].get("t_sol") - bezier_geometry[patch_id].get(
"t_sol")
x = geometry[patch_id].get("x_sol")
y = geometry[patch_id].get("y_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
if min_p is None or min_p > err.min():
min_p = err.min()
if max_p is None or max_p < err.max():
max_p = err.max()
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 patch_id in geometry.keys():
err = geometry[patch_id].get("t_sol") - bezier_geometry[patch_id].get(
"t_sol")
x = geometry[patch_id].get("x_sol")
y = geometry[patch_id].get("y_sol")
ax.contourf(x, y, err, vmin=min_p, vmax=max_p, cmap=cmap)
import matplotlib
from mpl_toolkits.axes_grid1 import make_axes_locatable
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad="2%")
norm = matplotlib.colors.TwoSlopeNorm(vmin=min_p, vcenter=0, vmax=max_p)
#norm = matplotlib.colors.Normalize(vmin=min_p, vmax=max_p, v)
mappeable = matplotlib.cm.ScalarMappable(norm=norm, cmap=cmap)
cbar = ax.figure.colorbar(mappeable,
cax=cax,
ax=ax,
label="Difference (IGA-Bezier)")
fig.show()
if save or save_all:
fig.savefig(fig_folder + filename + "_difference.pdf",
**kwargs_savefig)
def test_comparison_efficiency():
from time import process_time
levels = [15, 20, 30, 40, 50, 60, 70, 80, 85]
T_t = 10
T_b = 90
T_l = None
T_r = None
from pygeoiga.nurb.cad import make_salt_dome
start_model = process_time()
geometry = make_salt_dome(refine=True)
finish_model = process_time()
start_FEM = process_time()
geometry, gDoF = patch_topology(geometry)
geometry = bezier_extraction_mp(geometry)
K_glob = np.zeros((gDoF, gDoF))
s_k_FEM = process_time()
K_glob = form_k_bezier_mp(geometry, K_glob)
e_k_FEM = process_time()
D = np.zeros(gDoF)
b = np.zeros(gDoF)
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)
finish_FEM = process_time()
from pygeoiga.analysis.MultiPatch import form_k_IGA_mp
geometry = make_salt_dome(refine=True) # refine=np.arange(0.05,1,0.05))
start_IGA = process_time()
geometry, gDoF = patch_topology(geometry)
K_glob = np.zeros((gDoF, gDoF))
s_k_IGA = process_time()
K_glob = form_k_IGA_mp(geometry, K_glob)
e_k_IGA = process_time()
D = np.zeros(gDoF)
b = np.zeros(gDoF)
T_t = 10 # [°C]
T_b = 90 # [°C]
T_l = None
T_r = None
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)
finish_IGA = process_time()
time_FEM = finish_FEM - start_FEM
time_k_fem = e_k_FEM - s_k_FEM
time_IGA = finish_IGA - start_IGA
time_k_iga = e_k_IGA - s_k_IGA
time_model_refinement = finish_model - start_model
print("gDoF: ", gDoF)
print("FEM: ", time_FEM) # FEM: 241.05022452400001
print("K_FEM; ", time_k_fem) # K_FEM; 172.537146357
print("IGA: ", time_IGA) # IGA: 372.34105559899996
print("K_IGA; ", time_k_iga) # K_IGA; 316.763859975
print("Refinement: ",
time_model_refinement) # Refinement: 0.06600132199999997