def run(geo, AllDirichlet=True, f=None):
with context():
from pigasus.gallery.poisson import poisson
import numpy as np
import matplotlib.pyplot as plt
PDE = poisson(geo, AllDirichlet=True)
if f is None:
sin = np.sin ; pi = np.pi ; kx = 2. * pi ; ky = 2. * pi
f = lambda x,y : [( kx**2 + ky**2 ) * sin ( kx * x ) * sin ( ky * y )]
PDE.assembly(f=f)
PDE.solve()
PDE.plot()
plt.colorbar(); plt.show()
PDE.free()
except:
px = 2
try:
py = int(sys.argv[4])
except:
py = 2
geo = circle(radius=1. / sqrt(2), n=[nx, ny], p=[px, py])
#-----------------------------------
# ...
u_exact = lambda x, y: [-2.0 * log(x**2 + y**2 + 0.5)]
# ...
with context():
PDE = poisson_picard( geometry=geo \
, AllDirichlet=AllDirichlet )
# ...
print(">>> Solving using Picard <<<")
# ...
if PDE.Dirichlet:
U = PDE.unknown_dirichlet
else:
U = PDE.unknown
# ...
from pigasus.fem.utils import function
def run(patch, method, nx, px, alpha, nsteps, ub=None, ue=None):
with context():
import numpy as np
if ub is None:
ub = patch.knots[0][0]
if ue is None:
ue = patch.knots[0][-1]
u = np.linspace(ub, ue, nsteps)
P = patch.evaluate(u)
x = P[:, 0]
y = P[:, 1]
z = P[:, 2]
#-----------------------------------
def MakeConstraint(cond, face=None, value=None):
if cond.lower() == "closed":
constraint = {}
constraint['patch_id_m'] = 0
constraint['face_m'] = 0
constraint['patch_id_s'] = 0
constraint['face_s'] = 1
if cond.lower() == "c0":
constraint = {}
constraint['patch_id_m'] = 0
constraint['face_m'] = face
constraint['type'] = "C0"
constraint['values'] = [value]
if cond.lower() == "c1":
constraint = {}
constraint['patch_id_m'] = 0
constraint['face_m'] = face
constraint['type'] = "C1"
constraint['values'] = [value]
return constraint
#-----------------------------------
from pigasus.fit.curfit import curfit
from pigasus.fit.curfit import compute_uk
#-----------------------------------
print(("Approximation using " + method + " knots"))
print(("n " + str(nx) + " p ", str(px)))
#-----------------------------------
#-----------------------------------
# ...
list_x = list(x)
list_y = list(y)
# ...
# ...
list_Q = list(zip(list_x, list_y))
uk = compute_uk(list_Q, method=method)
U1 = []
U1 += list(uk)
list_xk = []
list_yk = []
list_xk += list_x
list_yk += list_y
lists_uk = [U1]
lists_xk = [list_xk]
lists_yk = [list_yk]
# ...
#-----------------------------------
#-----------------------------------
constraints = []
# ... C0_COND
constraint = MakeConstraint("C0", 0, [x[0], y[0]])
constraints.append(constraint)
constraint = MakeConstraint("C0", 1, [x[-1], y[-1]])
constraints.append(constraint)
#-----------------------------------
#-----------------------------------
from igakit.cad_geometry import line
geo = line(n=[nx], p=[px])
#-----------------------------------
#-----------------------------------
fit = curfit(geometry=geo, constraints=constraints, alpha=alpha)
#-----------------------------------
#-----------------------------------
patch_id = 0
xk = lists_xk[patch_id]
yk = lists_yk[patch_id]
geo = fit.construct([xk, yk], uk=lists_uk)
#-----------------------------------
fit.PDE.free()
return geo
def run(patch, method, nx, px, alpha, nsteps, ub=None, ue=None):
with context():
import numpy as np
if ub is None:
ub = patch.knots[0][0]
if ue is None:
ue = patch.knots[0][-1]
u = np.linspace(ub,ue,nsteps)
P = patch.evaluate(u)
x = P[:,0] ; y = P[:,1] ; z = P[:,2]
#-----------------------------------
def MakeConstraint(cond, face=None, value=None):
if cond.lower() == "closed":
constraint = {}
constraint['patch_id_m'] = 0
constraint['face_m'] = 0
constraint['patch_id_s'] = 0
constraint['face_s'] = 1
if cond.lower() == "c0":
constraint = {}
constraint['patch_id_m'] = 0
constraint['face_m'] = face
constraint['type'] = "C0"
constraint['values'] = [value]
if cond.lower() == "c1":
constraint = {}
constraint['patch_id_m'] = 0
constraint['face_m'] = face
constraint['type'] = "C1"
constraint['values'] = [value]
return constraint
#-----------------------------------
from pigasus.fit.curfit import curfit
from pigasus.fit.curfit import compute_uk
#-----------------------------------
print(("Approximation using " + method + " knots"))
print(("n " + str(nx) + " p ", str(px)))
#-----------------------------------
#-----------------------------------
# ...
list_x = list(x) ; list_y = list(y)
# ...
# ...
list_Q = list(zip(list_x, list_y))
uk = compute_uk(list_Q, method=method)
U1 = []
U1 += list(uk)
list_xk = [] ; list_yk = []
list_xk += list_x ; list_yk += list_y
lists_uk = [U1]
lists_xk = [list_xk]
lists_yk = [list_yk]
# ...
#-----------------------------------
#-----------------------------------
constraints = []
# ... C0_COND
constraint = MakeConstraint("C0", 0, [x[0], y[0]])
constraints.append(constraint)
constraint = MakeConstraint("C0", 1, [x[-1], y[-1]])
constraints.append(constraint)
#-----------------------------------
#-----------------------------------
from igakit.cad_geometry import line
geo = line(n=[nx], p=[px])
#-----------------------------------
#-----------------------------------
fit = curfit(geometry=geo, constraints=constraints, alpha=alpha)
#-----------------------------------
#-----------------------------------
patch_id = 0
xk = lists_xk[patch_id]
yk = lists_yk[patch_id]
geo = fit.construct([xk, yk], uk=lists_uk)
#-----------------------------------
fit.PDE.free()
return geo
