class Mumps():
A = None
ctx = None
x = None
def __init__(self, A, **kwagrs):
self.ctx = DMumpsContext()
self.A = A.tocsc()
self.ctx.set_icntl(14, 60)
self.ctx.set_centralized_sparse(A)
# print 'Factoring'
self.ctx.set_silent()
# print 'Done'
self.ctx.run(job=4) # Factorization
def solve(self,b):
# print 'Solving'
self.x = b.copy()
self.ctx.set_rhs(self.x)
self.ctx.run(job=3) # Solve
# print 'Done'
return self.x
def clean(self):
self.ctx.destroy()
def solve(self):
mesh = self.mesh
NE = mesh.number_of_edges()
NC = mesh.number_of_cells()
itype = mesh.itype
ftype = mesh.ftype
A = self.get_left_matrix()
b = self.get_right_vector()
x = np.r_[self.uh, self.ph] #把self.uh,self.ph组合在一起
b = b - A @ x
# Modify matrix
bdIdx = np.zeros((A.shape[0], ), dtype=itype)
bdIdx[NE] = 1
Tbd = spdiags(bdIdx, 0, A.shape[0], A.shape[1])
T = spdiags(1 - bdIdx, 0, A.shape[0], A.shape[1])
AD = T @ A @ T + Tbd
scipy.sparse.save_npz('AD.npz', AD)
b[NE] = self.ph[0]
with open("b.csv", "w", newline="") as datacsv:
csvwriter = csv.writer(datacsv, dialect=("excel"))
csvwriter.writerow(['b'])
csvwriter.writerows([b])
# solve
x[:] = spsolve(AD, b)
# solve
from mumps import DMumpsContext
ctx = DMumpsContext()
if ctx.myid == 0:
ctx.set_centralized_sparse(AD.tocoo())
x = b.copy()
ctx.set_rhs(x)
ctx.set_silent()
ctx.run(job=6)
self.uh[:] = x[:NE]
self.ph[:] = x[NE:]
print('ph', self.ph)
print('pI', self.pI)
return x
def solve(self):
mesh = self.mesh
NE = mesh.number_of_edges()
NC = mesh.number_of_cells()
itype = mesh.itype
ftype = mesh.ftype
A = self.get_left_matrix()
b = self.get_right_vector()
x = np.r_[self.uh, self.ph] #把self.uh,self.ph组合在一起
b = b - A @ x
# Modify matrix
bdIdx = np.zeros((A.shape[0], ), dtype=itype)
bdIdx[NE] = 1
Tbd = spdiags(bdIdx, 0, A.shape[0], A.shape[1])
T = spdiags(1 - bdIdx, 0, A.shape[0], A.shape[1])
AD = T @ A @ T + Tbd
b[NE] = self.ph[0]
K = AD.todense()
# solve
x[:] = spsolve(AD, b)
# solve
from mumps import DMumpsContext
ctx = DMumpsContext()
if ctx.myid == 0:
ctx.set_centralized_sparse(AD.tocoo())
x = b.copy()
ctx.set_rhs(x)
ctx.set_silent()
ctx.run(job=6)
self.uh[:] = x[:NE]
self.ph[:] = x[NE:]
print('ph', self.ph)
print('pI', self.pI)
return x
def picard_iteration(self, maxit=10):
GD = self.GD
e0 = 1.0
k = 0
while e0 > 1e-10:
# 构建总系统
A, F, isBdDof = self.get_total_system()
# 处理边界条件, 这里是 0 边界
gdof = len(isBdDof)
bdIdx = np.zeros(gdof, dtype=np.int_)
bdIdx[isBdDof] = 1
Tbd = diags(bdIdx)
T = diags(1 - bdIdx)
A = T @ A @ T + Tbd
F[isBdDof] = 0.0
# 求解
if False:
x = spsolve(A, F)
else:
ctx = DMumpsContext()
if ctx.myid == 0:
ctx.set_centralized_sparse(A)
x = F.copy()
ctx.set_rhs(x) # Modified in place
ctx.run(job=6) # Analysis + Factorization + Solve
ctx.destroy() # Cleanup
vgdof = self.vspace.number_of_global_dofs()
pgdof = self.pspace.number_of_global_dofs()
cgdof = self.cspace.number_of_global_dofs()
e0 = 0.0
start = 0
end = vgdof
self.cv[:] = x[start:end]
start = end
end += pgdof
e0 += np.sum((self.cp - x[start:end])**2)
self.cp[:] = x[start:end]
start = end
end += pgdof
e0 += np.sum((self.cs - x[start:end])**2)
self.cs[:] = x[start:end]
e0 = np.sqrt(e0) # 误差的 l2 norm
k += 1
for i in range(GD):
start = end
end += cgdof
self.cu[:, i] = x[start:end]
print(e0)
if k >= maxit:
print('picard iteration arrive max iteration with error:', e0)
break
A = space.linear_elasticity_matrix(lam, mu)
#A = space.recovery_linear_elasticity_matrix(lam, mu)
F = space.source_vector(pde.source, dim=2)
bc = NeumannBC(space, pde.neumann, threshold=pde.is_neumann_boundary)
F = bc.apply(F)
bc = DirichletBC(space, pde.dirichlet, threshold=pde.is_dirichlet_boundary)
A, F = bc.apply(A, F, uh)
ctx = DMumpsContext()
ctx.set_silent()
if ctx.myid == 0:
ctx.set_centralized_sparse(A)
x = F.copy()
ctx.set_rhs(x) # Modified in place
ctx.run(job=6) # Analysis + Factorization + Solve
ctx.destroy() # Cleanup
uh.T.flat[:] = x
# uh.T.flat[:] = spsolve(A, F) # (2, gdof ).flat
uI = space.interpolation(pde.displacement, dim=2)
e = uh - uI
#error = np.sqrt(np.mean(e**2))
error = sum(np.sqrt(np.sum(e**2, axis=-1))) / sum(
np.sqrt(np.sum(uI**2, axis=-1)))
print('error:\n', error)
bc = mesh.entity_barycenter('edge')