def __init__(self,
Z_dict,
B_dict,
f_dict,
tol=1.0e-3,
dtype=np.float,
dual_interface_algorithm='PCPG'):
#f_dict = manager.vector2localdict(f,manager.global2local_primal_dofs)
#self.feti_obj = SerialFETIsolver(Z_dict,B_dict,f_dict,tolerance=tol,dtype=np.complex)
#self.mapdict = manager.local2global_primal_dofs
self.Z_dict = Z_dict
self.B_dict = B_dict
self.tol = tol
self.feti_obj = SerialFETIsolver(
self.Z_dict,
self.B_dict,
f_dict,
tolerance=self.tol,
dtype=dtype,
max_int=100,
dual_interface_algorithm=dual_interface_algorithm,
pseudoinverse_kargs={
'method': 'splusps',
'tolerance': 1.0E-12
})
self.dtype = dtype
def test_elimination_matrix(self):
self.setUp()
L_target = self.L
Lexp_target = self.Lexp
solver_obj = SerialFETIsolver(self.K_dict, self.B_dict, self.f_dict)
sol_obj = solver_obj.solve()
u_dual = np.array([])
u_dict = sol_obj.u_dict
lambda_dict = sol_obj.lambda_dict
alpha_dict = sol_obj.alpha_dict
for domain_id in self.domain_list:
u_dual = np.append(u_dual, u_dict[domain_id])
L_calc = solver_obj.manager.assemble_global_L()
Lexp_calc = solver_obj.manager.assemble_global_L_exp()
n = L_target.shape[0]
#testing orthogonality
np.testing.assert_array_almost_equal(L_calc.dot(Lexp_calc), np.eye(n))
# testing L matrix asseblying method
np.testing.assert_array_almost_equal(np.sort(L_calc.dot(u_dual)),
np.sort(self.u_global))
def system(u, tol=1.0e-8):
global counts
f = P.T.dot(M.dot(P.dot(u)))
f_dict = manager.vector2localdict(f, manager.global2local_primal_dofs)
feti_obj = SerialFETIsolver(K_dict, B_dict, f_dict, tolerance=tol)
solution_obj = feti_obj.solve()
u_dict = solution_obj.u_dict
counts += 1
return solution_obj.displacement
def system_without_projection(u, tol=1.0e-8):
global countswp
f = M.dot(u)
f_dict = manager.vector2localdict(f, manager.global2local_primal_dofs)
feti_obj = SerialFETIsolver(K_dict, B_dict, f_dict, tolerance=tol)
solution_obj = feti_obj.solve()
u_dict = solution_obj.u_dict
countswp += 1
return solution_obj.displacement
def system(u, tol=1.0e-8):
f = P.T.dot(M.dot(P.dot(u)))
f_dict = manager.vector2localdict(f, manager.global2local_primal_dofs)
feti_obj = SerialFETIsolver(K_dict,
B_dict,
f_dict,
tolerance=tol,
pseudoinverse_kargs={
'method': 'splusps',
'tolerance': 1.0E-8
})
solution_obj = feti_obj.solve()
u_dict = solution_obj.u_dict
return P.dot(solution_obj.displacement)
def test_compare_serial_and_parallel_solver(self,
pseudoinverse_kargs={
'method': 'svd',
'tolerance': 1.0E-8
}):
print(
'Starting Comparison between Serial and Parallel FETI solver ..........'
)
case_id, nx, ny = 1, 2, 1
print('Critial Case Selected %i ' % case_id)
print('Number of Domain in the X-direction %i ' % nx)
print('Number of Domain in the Y-direction %i ' % ny)
K_dict, B_dict, f_dict = create_FETI_case(case_id, nx, ny)
solver_obj = SerialFETIsolver(K_dict,
B_dict,
f_dict,
pseudoinverse_kargs=pseudoinverse_kargs)
start_time = time.time()
print('Starting Serial FETI solver ..........')
sol_obj = solver_obj.solve()
elapsed_time = time.time() - start_time
print('Serial Solver : Elapsed time : %f ' % elapsed_time)
u_dual_serial, lambda_serial, alpha_serial = self.obj_to_array(sol_obj)
print('\n\n Starting Parallel FETI solver ..........')
solver_obj = ParallelFETIsolver(
K_dict, B_dict, f_dict, pseudoinverse_kargs=pseudoinverse_kargs)
start_time = time.time()
sol_obj = solver_obj.solve()
elapsed_time = time.time() - start_time
print('Parallel Solver : Elapsed time : %f ' % elapsed_time)
u_dual_parallel, lambda_parallel, alpha_parallel = self.obj_to_array(
sol_obj)
np.testing.assert_almost_equal(u_dual_serial,
u_dual_parallel,
decimal=10)
np.testing.assert_almost_equal(
lambda_serial / np.linalg.norm(lambda_serial),
lambda_parallel / np.linalg.norm(lambda_parallel),
decimal=10)
np.testing.assert_almost_equal(alpha_serial,
alpha_parallel,
decimal=10)
print('End Comparison Serial and Parallel FETI solver ..........\n\n')
def test_total_FETI_approach(self):
''' This test incorporate Dirichlet constraint in the Boolean matrix
The constraint are considered the 0-th Neighbor
F->
|>0 0-----0-----0 0-----0-----0
Dir D1 D2
'''
print('Test Total FETI solver ..........')
K1 = np.array([[1, -1], [-1, 1]])
K2 = np.array([[1, -1], [-1, 1]])
B0 = np.array([[-1, 0]])
B1 = np.array([[0, 1]])
B2 = np.array([[-1, 0]])
f1 = np.array([0., 0.])
f2 = np.array([0., 1.])
# Using PyFETI to solve the probrem described above
K_dict = {1: K1, 2: K2}
B_dict = {1: {(1, 2): B1, (1, 1): B0}, 2: {(2, 1): B2}}
f_dict = {1: f1, 2: f2}
solver_obj = SerialFETIsolver(K_dict, B_dict, f_dict)
solution_obj = solver_obj.solve()
u_dual = solution_obj.displacement
lambda_ = solution_obj.interface_lambda
alpha = solution_obj.alpha
solver_obj = ParallelFETIsolver(K_dict, B_dict, f_dict)
solution_obj = solver_obj.solve()
solver_obj.manager.delete()
u_dual_par = solution_obj.displacement
lambda_par = solution_obj.interface_lambda
alpha_par = solution_obj.alpha
np.testing.assert_almost_equal(u_dual, u_dual_par, decimal=10)
np.testing.assert_almost_equal(lambda_, lambda_par, decimal=10)
np.testing.assert_almost_equal(alpha, alpha_par, decimal=10)
print('End Total FETI solver ..........')
def test_simple_bar_problem(self):
K1 = np.array([[2., -1.], [-1., 1.]])
K2 = np.array([[1., -1.], [-1., 2.]])
B1 = np.array([[0., 1]])
B2 = np.array([[-1, 0]])
f1 = np.array([0., 0.])
f2 = np.array([0., 1.])
K_dict = {1: K1, 2: K2}
B_dict = {1: {(1, 2): B1}, 2: {(2, 1): B2}}
f_dict = {1: f1, 2: f2}
solver_obj = SerialFETIsolver(K_dict, B_dict, f_dict)
solution_obj = solver_obj.solve()
u_dual = solution_obj.displacement
lambda_ = solution_obj.interface_lambda
alpha = solution_obj.alpha
u_target = np.array([0.25, 0.5, 0.5, 0.75])
np.testing.assert_almost_equal(u_dual, u_target, decimal=10)
def case2():
Ks_dict = {}
Ks_dict[1] = K_dict[1]
Ks_dict[2] = K_dict[6]
Ms_dict = {}
Ms_dict[1] = M_dict[1]
Ms_dict[2] = M_dict[6]
Bs_dict = {}
Bs_dict[1] = {(1,1) : B_dict[1][1,1], (1,2) : B_dict[1][1,6] }
Bs_dict[2] = {(2,1) : B_dict[6][6,1]}
fs_dict = {1 : np.zeros(K_dict[1].shape[0]),
2 : np.zeros(K_dict[6].shape[0])}
K_feti_obj = SerialFETIsolver(Ks_dict,Bs_dict,fs_dict)
M_feti_obj = SerialFETIsolver(Ms_dict,Bs_dict,fs_dict)
Ks, _ = K_feti_obj.manager.assemble_global_K_and_f()
Ms, _ = M_feti_obj.manager.assemble_global_K_and_f()
B = K_feti_obj.manager.assemble_global_B()
from scipy.sparse import linalg
BBT_inv = linalg.inv(B.dot(B.T))
Ps = np.eye(B.shape[1]) - B.T.dot(BBT_inv.dot(B))
obj = ProjLinearSys(Ks.A,Ms.A,Ps.A)
Dp = obj.getLinearOperator()
v0 = np.random.rand(Ks.shape[0])
nmodes= 9
eigval_, Vp = sparse.linalg.eigsh(Dp,k=nmodes,v0=Ps.A.dot(v0))
val_wp_ = np.sort(1/eigval_)
freq_wp_ = np.sqrt(val_wp_)/(2.0*np.pi)
freq_wp_
ansys_freq = np.array([4.5495,39.845,59.994,72.253,131.34,148.82,169.8,197.68,231.13])
def test_simple_bar_with_redundante_contraints(self):
'''
A simple example with Reduntant Constraints Positive Define Domains
'''
K1 = np.array([[2, -1], [-1, 1]])
K2 = np.array([[1, -1], [-1, 2]])
B1 = np.array([[0, 1], [0, 1], [0, 1]])
B2 = np.array([[-1, 0], [-1, 0], [-1, 0]])
f1 = np.array([0., 0.])
f2 = np.array([0., 1.])
K_dict = {1: K1, 2: K2}
B_dict = {1: {(1, 2): B1}, 2: {(2, 1): B2}}
f_dict = {1: f1, 2: f2}
solver_obj = SerialFETIsolver(K_dict, B_dict, f_dict)
solution_obj = solver_obj.solve()
u_dual = solution_obj.displacement
lambda_ = solution_obj.interface_lambda
alpha = solution_obj.alpha
u_target = np.array([0.25, 0.5, 0.5, 0.75])
np.testing.assert_almost_equal(u_dual, u_target, decimal=10)
def test_serial_solver(self, precond_type=None):
print('Testing Serial FETI solver ..........\n\n')
solver_obj = SerialFETIsolver(self.K_dict,
self.B_dict,
self.f_dict,
precond_type=precond_type,
tolerance=1E-11)
sol_obj = solver_obj.solve()
self.postproc(sol_obj)
K_dual = sparse.block_diag((self.K_dict[1], self.K_dict[2]))
f_dual = np.concatenate((self.f_dict[1].data, self.f_dict[2].data))
u_dual = sol_obj.displacement
np.testing.assert_almost_equal(self.f_global.data,
self.L @ f_dual,
decimal=10)
u_primal = self.dual2primal(K_dual, u_dual, f_dual, self.L, self.Lexp)
np.testing.assert_almost_equal(self.u_global, u_primal, decimal=10)
print('end Serial FETI solver ..........\n\n')
return u_dual, sol_obj
class FETI_system():
def __init__(self,
Z_dict,
B_dict,
f_dict,
tol=1.0e-3,
dtype=np.float,
dual_interface_algorithm='PCPG'):
#f_dict = manager.vector2localdict(f,manager.global2local_primal_dofs)
#self.feti_obj = SerialFETIsolver(Z_dict,B_dict,f_dict,tolerance=tol,dtype=np.complex)
#self.mapdict = manager.local2global_primal_dofs
self.Z_dict = Z_dict
self.B_dict = B_dict
self.tol = tol
self.feti_obj = SerialFETIsolver(
self.Z_dict,
self.B_dict,
f_dict,
tolerance=self.tol,
dtype=dtype,
max_int=100,
dual_interface_algorithm=dual_interface_algorithm,
pseudoinverse_kargs={
'method': 'splusps',
'tolerance': 1.0E-12
})
self.dtype = dtype
def apply(self, f):
f_dict = self.array2dict(f)
self.feti_obj.f_dict = f_dict
solution_obj = self.feti_obj.solve()
u_dict = solution_obj.u_dict
return solution_obj.displacement
def array2dict(self, v):
v_dict = {}
for key, posid in mapdict.items():
if v.ndim < 2:
v_dict[key] = v[posid]
else:
v_dict[key] = v[posid, :]
return v_dict
def dict2array(self, v_dict):
v = np.zeros(self.shape[0], dtype=self.dtype)
for key, posid in self.mapdict.items():
v[posid] = v_dict[key]
return v
def solve_eig(K_dict, M_dict, B_dict, nmodes=10):
f_dict = {}
for i, K in K_dict.items():
f_dict[i] = np.zeros(K.shape[0])
K_feti_obj = SerialFETIsolver(K_dict, B_dict, f_dict)
M_feti_obj = SerialFETIsolver(M_dict, B_dict, f_dict)
K, _ = K_feti_obj.manager.assemble_global_K_and_f()
M, _ = M_feti_obj.manager.assemble_global_K_and_f()
B = K_feti_obj.manager.assemble_global_B()
from scipy.sparse import linalg
#BBT_inv = linalg.inv(B.dot(B.T))
P = sparse.eye(B.shape[1]) - 0.5 * (B.T.dot(B))
obj = ProjLinearSys(K, M, P)
Dp = obj.getLinearOperator()
v0 = np.random.rand(K.shape[0])
eigval_, Vp = sparse.linalg.eigsh(Dp, k=nmodes, v0=P.dot(v0))
print(eigval_)
val_wp_ = np.sort(1 / eigval_)
freq_wp_ = np.sqrt(val_wp_) / (2.0 * np.pi)
return freq_wp_, Vp, B.shape[0]
def test_compare_svd_splusps(self):
print('Starting Comparison between Serial SVD and SPLUSPS ..........')
case_id, nx, ny = 4, 4, 4
print('Critical Case Selected %i ' % case_id)
print('Number of Domain in the X-direction %i ' % nx)
print('Number of Domain in the Y-direction %i ' % ny)
K_dict, B_dict, f_dict = create_FETI_case(case_id, nx, ny)
solver_obj = SerialFETIsolver(K_dict,
B_dict,
f_dict,
pseudoinverse_kargs={
'method': 'svd',
'tolerance': 1.0E-8
})
start_time = time.time()
print('....................................')
print('Starting SVD FETI solver ..........')
sol_obj = solver_obj.solve()
elapsed_time = time.time() - start_time
print('SVD Solver : Elapsed time : %f ' % elapsed_time)
u_dual_svd, lambda_svd, alpha_svd = self.obj_to_array(sol_obj)
print('\n\n Starting SPLUSPS FETI solver ..........')
solver_obj = SerialFETIsolver(K_dict,
B_dict,
f_dict,
pseudoinverse_kargs={
'method': 'splusps',
'tolerance': 1.0E-8
})
start_time = time.time()
sol_obj_slu = solver_obj.solve()
elapsed_time = time.time() - start_time
print('SPLUSPS Solver : Elapsed time : %f ' % elapsed_time)
print('....................................')
# check gap using SPLUSPS local solver
self.check_interface_gap(sol_obj_slu.u_dict, solver_obj.B_dict)
# assembling dual vectors
u_dual_slu, lambda_slu, alpha_slu = self.obj_to_array(sol_obj_slu)
# compare results
norm = np.linalg.norm(u_dual_svd)
norm_lambda = np.linalg.norm(lambda_svd)
norm_alpha = np.linalg.norm(alpha_svd)
np.testing.assert_almost_equal(u_dual_svd / norm,
u_dual_slu / norm,
decimal=10)
np.testing.assert_almost_equal(lambda_svd / norm_lambda,
lambda_slu / norm_lambda,
decimal=10)
print('End Comparison SVD and SPLUSPS FETI solver ..........\n\n')
def test_verify_F_operator(self):
K_dict = {1: K1, 2: K2, 3: K3, 4: K4}
B_dict = {
1: {
(1, 2): B12,
(1, 3): B13,
(1, 4): B14
},
2: {
(2, 1): B21,
(2, 4): B24,
(2, 3): B23
},
3: {
(3, 1): B31,
(3, 4): B34,
(3, 2): B32
},
4: {
(4, 2): B42,
(4, 3): B43,
(4, 1): B41
}
}
q_dict = {1: q1, 2: q2, 3: q3, 4: q4}
solver_obj = SerialFETIsolver(K_dict, B_dict, q_dict)
L = solver_obj.manager.assemble_global_L()
Lexp = solver_obj.manager.assemble_global_L_exp()
B = solver_obj.manager.assemble_global_B()
K, f = solver_obj.manager.assemble_global_K_and_f()
R = solver_obj.manager.assemble_global_kernel()
e = solver_obj.manager.assemble_e()
F_feti = solver_obj.manager.assemble_global_F()
K_inv = np.linalg.pinv(K.A)
F = B @ K_inv @ B.T
d = B @ K_inv @ f
x = np.ones(F.shape[0])
np.testing.assert_almost_equal(F.dot(x), F_feti.dot(x), decimal=10)
if i - 1 < 0:
minus = +23
sign_plus = np.sign(plus)
sign_minus = np.sign(plus)
B_dict[local_index] = {
(local_index, local_index + plus):
sign_plus * B_local_dict[cyclic_left_label],
(local_index, local_index + minus):
sign_minus * B_local_dict[cyclic_right_label]
}
f_dict[local_index] = np.zeros(K1.shape[0])
feti_obj1 = SerialFETIsolver(K_dict, B_dict, f_dict, tolerance=1.0e-12)
feti_obj2 = SerialFETIsolver(M_dict, B_dict, f_dict, tolerance=1.0e-12)
manager = feti_obj1.manager
managerM = feti_obj2.manager
print('Assembling Matrix')
date_str = datetime.now().strftime('%Y_%m_%d_%H_%M_%S')
print(date_str)
B = manager.assemble_global_B()
M_, _ = managerM.assemble_global_K_and_f()
K, _ = manager.assemble_global_K_and_f()
M = M_
save_object(B, 'B.pkl')
save_object(M, 'M.pkl')
def create(case_id):
case_folder = 'case_' + str(case_id)
try:
os.mkdir(case_folder)
except:
pass
m1 = load_pkl('3D_simple_bladed_disk_24_sectors_' + str(case_id) +
'_nodes.pkl')
m1.change_tag_in_eldf('phys_group', 'RIGHT_ELSET', cyclic_right_label)
m1.change_tag_in_eldf('phys_group', 'LEFT_ELSET', cyclic_left_label)
m1.change_tag_in_eldf('phys_group', 'BODY_1_1_SOLID_ELSET', domain_label)
m1.change_tag_in_eldf('phys_group', 'BODY_1_1_ELSET', 5)
m1.change_tag_in_eldf('phys_group', 'DIRICHLET_ELSET', dirichlet_label)
# creating material
my_material = amfe.KirchhoffMaterial(E=210.0E9,
nu=0.3,
rho=7.86E3,
plane_stress=True,
thickness=1.0)
my_system1 = amfe.MechanicalSystem()
my_system1.set_mesh_obj(m1)
my_system1.set_domain(4, my_material)
K1, _ = my_system1.assembly_class.assemble_k_and_f()
M1 = my_system1.assembly_class.assemble_m()
el_df = copy.deepcopy(m1.el_df)
try:
connectivity = []
for _, item in el_df.iloc[:, m1.node_idx:].iterrows():
connectivity.append(list(item.dropna().astype(dtype='int64')))
el_df['connectivity'] = connectivity
except:
pass
sector_angle = 360 / Nsectors
id_matrix = my_system1.assembly_class.id_matrix
id_map_df = dict2dfmap(id_matrix)
nodes_coord = m1.nodes
cyc_obj = Cyclic_Constraint(id_map_df,
el_df,
nodes_coord,
dirichlet_label,
cyclic_left_label,
cyclic_right_label,
sector_angle,
unit=unit,
tol_radius=tol_radius,
dimension=dimension)
translate_dict = {}
translate_dict['d'] = dirichlet_label
translate_dict['r'] = cyclic_right_label
translate_dict['l'] = cyclic_left_label
s = cyc_obj.s
B_local_dict = {}
for key, value in translate_dict.items():
B_local_dict[value] = s.build_B(key)
mesh_list = [m1.rot_z(i * 360 / Nsectors) for i in range(Nsectors)]
#plot_mesh_list(mesh_list)
system_list = []
K_dict = {}
M_dict = {}
B_dict = {}
f_dict = {}
for i, mi in enumerate(mesh_list):
sysi = amfe.MechanicalSystem()
sysi.set_mesh_obj(mi)
sysi.set_domain(domain_label, my_material)
system_list.append(sysi)
K1, _ = sysi.assembly_class.assemble_k_and_f()
M1 = sysi.assembly_class.assemble_m()
K_dict[i + 1] = Matrix(
K1, key_dict=s.selection_dict).eliminate_by_identity('d')
M_dict[i + 1] = Matrix(
M1,
key_dict=s.selection_dict).eliminate_by_identity('d',
multiplier=0.0)
plus = +1
minus = -1
local_index = i + 1
if i + 2 > Nsectors:
plus = -23
if i - 1 < 0:
minus = +23
sign_plus = np.sign(plus)
sign_minus = np.sign(plus)
B_dict[local_index] = {
(local_index, local_index + plus):
sign_plus * B_local_dict[cyclic_left_label],
(local_index, local_index + minus):
sign_minus * B_local_dict[cyclic_right_label]
}
f_dict[local_index] = np.zeros(K1.shape[0])
feti_obj1 = SerialFETIsolver(K_dict,
B_dict,
f_dict,
tolerance=1.0e-12,
pseudoinverse_kargs={
'method': 'splusps',
'tolerance': 1.0E-8
})
feti_obj2 = SerialFETIsolver(M_dict,
B_dict,
f_dict,
tolerance=1.0e-12,
pseudoinverse_kargs={
'method': 'splusps',
'tolerance': 1.0E-8
})
manager = feti_obj1.manager
managerM = feti_obj2.manager
manager.build_local_to_global_mapping()
print('Assembling Matrix')
date_str = datetime.now().strftime('%Y_%m_%d_%H_%M_%S')
print(date_str)
B = manager.assemble_global_B()
M_, _ = managerM.assemble_global_K_and_f()
K, _ = manager.assemble_global_K_and_f()
M = M_
L = manager.assemble_global_L()
Lexp = manager.assemble_global_L_exp()
save_object(B, os.path.join(case_folder, 'B.pkl'))
save_object(M, os.path.join(case_folder, 'M.pkl'))
save_object(K, os.path.join(case_folder, 'K.pkl'))
save_object(L, os.path.join(case_folder, 'L.pkl'))
save_object(Lexp, os.path.join(case_folder, 'Lexp.pkl'))
save_object(K_dict, os.path.join(case_folder, 'K_dict.pkl'))
save_object(M_dict, os.path.join(case_folder, 'M_dict.pkl'))
save_object(B_dict, os.path.join(case_folder, 'B_dict.pkl'))
save_object(f_dict, os.path.join(case_folder, 'f_dict.pkl'))
print('End')
date_str = datetime.now().strftime('%Y_%m_%d_%H_%M_%S')
print(date_str)
def _test_2d_thermal_problem(self):
# Using PyFETI to solve the probrem described above
num_domain = 3
if num_domain == 4:
K_dict = {1: K1, 2: K2, 3: K3, 4: K4}
B_dict = {
1: {
(1, 2): B12,
(1, 3): B13,
(1, 4): B14
},
2: {
(2, 1): B21,
(2, 4): B24,
(2, 3): B23
},
3: {
(3, 1): B31,
(3, 4): B34,
(3, 2): B32
},
4: {
(4, 2): B42,
(4, 3): B43,
(4, 1): B41
}
}
q_dict = {1: q1, 2: q2, 3: q3, 4: q4}
elif num_domain == 2:
K_dict = {1: K1, 2: K2}
B_dict = {1: {(1, 2): B12}, 2: {(2, 1): B21}}
q_dict = {1: q1, 2: q4}
elif num_domain == 3:
K_dict = {1: K1, 2: K2, 3: K3}
B_dict = {
1: {
(1, 2): B12
},
2: {
(2, 1): B21,
(2, 3): B12
},
3: {
(3, 2): B21
}
}
q_dict = {1: q1, 2: q2, 3: q4}
solver_obj = SerialFETIsolver(K_dict, B_dict, q_dict)
L = solver_obj.manager.assemble_global_L()
Lexp = solver_obj.manager.assemble_global_L_exp()
B = solver_obj.manager.assemble_global_B()
K, f = solver_obj.manager.assemble_global_K_and_f()
R = solver_obj.manager.assemble_global_kernel()
e = solver_obj.manager.assemble_e()
G = solver_obj.manager.assemble_G()
GGT_inv = np.linalg.inv(G.dot(G.T))
P = np.eye(B.shape[0]) - (G.T.dot(GGT_inv)).dot(G)
F_feti = solver_obj.manager.assemble_global_F()
f_primal = L.dot(f)
K_primal = L.dot(K.dot(Lexp))
T_primal = np.linalg.solve(K_primal, f_primal)
T_dual = Lexp.dot(T_primal)
interface_gap = B.dot(T_dual)
np.testing.assert_almost_equal(interface_gap,
0 * interface_gap,
decimal=10)
K_inv = np.linalg.pinv(K.A)
F = B @ K_inv @ B.T
d = B @ K_inv @ f
lambda_im = G.T.dot(GGT_inv).dot(e)
r0 = d - F.dot(lambda_im)
Fp = P.T.dot(F.dot(P))
dp = P.T.dot(d)
lambda_ker, info = sparse.linalg.cg(Fp, dp, M=P)
#lambda_ker, info = sparse.linalg.minres(Fp,dp,M=P)
F_action = lambda x: F.dot(x)
Projection_action = lambda x: P.dot(x)
lampda_ker, rk, proj_r_hist, lambda_hist = PCPG(F_action,
r0,
Projection_action,
tolerance=1.e-16,
max_int=1000)
lambda_cg = lambda_im + lambda_ker
r = d - F.dot(lambda_cg)
alpha = GGT_inv.dot(G.dot(r))
T_cg = K_inv @ (f - B.T @ lambda_cg) + R.dot(alpha)
np.testing.assert_almost_equal(T_cg, T_dual, decimal=10)
# In[5]:
zeros = np.zeros(K1.shape[0])
case = FETIcase_builder(domains_X,
domains_Y,
K1,
zeros,
B_local_dict,
s,
BC_type='G',
force_scaling=1.0)
K_dict, B_dict, f_dict = case.build_subdomain_matrices()
# In[6]:
feti_obj = SerialFETIsolver(K_dict, B_dict, f_dict, tolerance=1.0e-6)
solution_obj = feti_obj.solve()
u_dict = solution_obj.u_dict
for i, sysi in enumerate(system_list):
sysi.u_output = [u_dict[i + 1]]
# In[7]:
p0 = 1
fig, ax2 = plt.subplots(1, 1, figsize=(10, 3))
for i, sysi in enumerate(system_list):
amfe.plot_2D_system_solution(sysi, u_id=0, ax=ax2, factor=p0)
delta_ = 1.5
ax2.set_xlim([-delta_, (2.0 + delta_) * width])
Ks_dict = {}
Ks_dict[1] = K_dict[1]
Ks_dict[2] = K_dict[6]
Ms_dict = {}
Ms_dict[1] = M_dict[1]
Ms_dict[2] = M_dict[6]
Bs_dict = {}
Bs_dict[1] = {(1, 1): B_dict[1][1, 1], (1, 2): B_dict[1][1, 6]}
Bs_dict[2] = {(2, 1): B_dict[6][6, 1]}
fs_dict = {1: np.zeros(K_dict[1].shape[0]), 2: np.zeros(K_dict[6].shape[0])}
K_feti_obj = SerialFETIsolver(Ks_dict, Bs_dict, fs_dict)
M_feti_obj = SerialFETIsolver(Ms_dict, Bs_dict, fs_dict)
Ks, _ = K_feti_obj.manager.assemble_global_K_and_f()
Ms, _ = M_feti_obj.manager.assemble_global_K_and_f()
B = K_feti_obj.manager.assemble_global_B()
from scipy.sparse import linalg
BBT_inv = linalg.inv(B.dot(B.T))
Ps = np.eye(B.shape[1]) - B.T.dot(BBT_inv.dot(B))
# In[45]:
obj = ProjLinearSys(Ks.A, Ms.A, Ps.A)
Dp = obj.getLinearOperator()
v0 = np.random.rand(Ks.shape[0])
def run_case(tol_factor=6):
Nsectors = 24
domain_label = 4
cyclic_left_label = 3
cyclic_right_label = 2
dirichlet_label = 1
unit = 'deg'
tol_radius = 1.0e-5
dimension = 3
FETI_tolerance = 10.0**-tol_factor
feti_obj = SerialFETIsolver(K_dict,
B_dict,
f_dict,
tolerance=FETI_tolerance,
pseudoinverse_kargs={
'method': 'splusps',
'tolerance': 1.0E-8
})
manager = feti_obj.manager
manager.build_local_to_global_mapping()
scaling = manager.assemble_global_scaling()
S = sparse.diags(1. / scaling)
B = manager.assemble_global_B()
B_ = B
P = sparse.eye(K.shape[0]) - S.dot(B_.T.dot(B_))
print_date('Loading Matrix')
def system_without_projection(u, tol=1.0e-8):
f = M.dot(u)
f_dict = manager.vector2localdict(f, manager.global2local_primal_dofs)
feti_obj = SerialFETIsolver(K_dict,
B_dict,
f_dict,
tolerance=tol,
pseudoinverse_kargs={
'method': 'splusps',
'tolerance': 1.0E-8
})
solution_obj = feti_obj.solve()
u_dict = solution_obj.u_dict
return solution_obj.displacement
D_wp = sparse.linalg.LinearOperator(
shape=M.shape,
matvec=lambda x: system_without_projection(x, tol=FETI_tolerance))
nmodes = 30
np.random.seed(1)
u0 = np.random.rand(D_wp.shape[0])
u0 /= np.linalg.norm(u0)
print_date('Solving Classical Dual Eigenproblem')
eigval_without_projection_, V_wp_ = sparse.linalg.eigsh(D_wp,
k=nmodes,
v0=u0)
freq_dual_wp_, V_wp_ = eig2freq(eigval_without_projection_, V_wp_)
save_pkl(V_wp_, '%i_cyclic_V_wp_.pkl' % tol_factor)
save_pkl(freq_dual_wp_, '%i_cyclic_freq_dual_wp_.pkl' % tol_factor)
def system(u, tol=1.0e-8):
f = P.T.dot(M.dot(P.dot(u)))
f_dict = manager.vector2localdict(f, manager.global2local_primal_dofs)
feti_obj = SerialFETIsolver(K_dict,
B_dict,
f_dict,
tolerance=tol,
pseudoinverse_kargs={
'method': 'splusps',
'tolerance': 1.0E-8
})
solution_obj = feti_obj.solve()
u_dict = solution_obj.u_dict
return P.dot(solution_obj.displacement)
D = sparse.linalg.LinearOperator(
shape=M.shape, matvec=lambda x: system(x, tol=FETI_tolerance))
print_date('Solving Projected Dual Eigenproblem')
eigval, V = sparse.linalg.eigsh(D, k=nmodes, v0=P.dot(u0))
freq_dual, V = eig2freq(eigval, V)
save_pkl(V, '%i_cyclic_V.pkl' % tol_factor)
save_pkl(freq_dual, '%i_cyclic_freq_dual.pkl' % tol_factor)
freq_list = [freq_dual, freq_dual_wp_]
V_list = [V, V_wp_]
return freq_list, V_list