def get_slip_to_traction(m, tectosaur_cfg):
import tectosaur
from tectosaur.ops.sparse_integral_op import make_integral_op
from tectosaur.constraint_builders import free_edge_constraints, continuity_constraints
from tectosaur.constraints import build_constraint_matrix
from tectosaur.ops.mass_op import MassOp
from scipy.sparse.linalg import spsolve
pts, tris = m
tectosaur.logger.setLevel(tectosaur_cfg['log_level'])
n_dofs = tris.shape[0] * 9
cs = []
# cs.extend(traction_continuity_constraints(pts, tris, np.array([])))
cs = continuity_constraints(tris, np.array([]))
# cs.extend(free_edge_constraints(tris))
cm, c_rhs = build_constraint_matrix(cs, n_dofs)
all_tri_idxs = np.arange(tris.shape[0])
hypersingular_op = make_integral_op(
pts, tris, 'elasticH3', [tectosaur_cfg['sm'], tectosaur_cfg['pr']],
tectosaur_cfg, all_tri_idxs, all_tri_idxs)
traction_mass_op = MassOp(tectosaur_cfg['quad_mass_order'], pts, tris)
constrained_traction_mass_op = cm.T.dot(traction_mass_op.mat.dot(cm))
def slip_to_traction(slip):
rhs = hypersingular_op.dot(slip.reshape(-1))
# rhs = cm.dot(cm.T.dot(hypersingular_op.dot(slip.reshape(-1))))
out = spsolve(traction_mass_op.mat, rhs)
# out = cm.dot(spsolve(constrained_traction_mass_op, cm.T.dot(rhs)))
return out
return slip_to_traction
def direct_solve(iop, constraints, rhs=None):
cm, c_rhs = build_constraint_matrix(constraints, iop.shape[0])
cm = cm.tocsr()
cmT = cm.T
iop_constrained = cmT.dot(cmT.dot(iop.mat.T).T)
if rhs is None:
rhs_constrained = cmT.dot(-iop.mat.dot(c_rhs))
else:
rhs_constrained = cmT.dot(rhs - iop.mat.dot(c_rhs))
soln_constrained = np.linalg.solve(iop_constrained, rhs_constrained)
soln = cm.dot(soln_constrained)
return soln
def setup_edge_bcs(self):
cs = free_edge_constraints(self.m.get_tris('fault'))
cm, c_rhs, _ = build_constraint_matrix(cs, self.m.n_dofs('fault'))
constrained_slip = np.ones(cm.shape[1])
self.ones_interior = cm.dot(constrained_slip)
self.field_inslipdir_interior = self.ones_interior.copy()
self.field_inslipdir = self.field_inslipdir_interior.copy()
for d in range(3):
val = self.cfg.get('slipdir', (1.0, 0.0, 0.0))[d]
self.field_inslipdir_interior.reshape(-1, 3)[:, d] *= val
self.field_inslipdir.reshape(-1, 3)[:, d] = val
self.field_inslipdir_edges = (self.field_inslipdir -
self.field_inslipdir_interior)
def iterative_solve(iop, constraints, rhs=None, tol=1e-8):
timer = Timer(output_fnc=logger.debug)
cm, c_rhs, _ = build_constraint_matrix(constraints, iop.shape[1])
timer.report('Build constraint matrix')
cm = cm.tocsr()
timer.report('constraint matrix tocsr')
cmT = cm.T
if rhs is None:
rhs_constrained = cmT.dot(-iop.dot(c_rhs))
else:
rhs_constrained = cmT.dot(rhs - iop.dot(c_rhs))
timer.report('constrain rhs')
n = rhs_constrained.shape[0]
iter = [0]
def mv(v):
iter[0] += 1
logger.debug('iteration # ' + str(iter[0]))
return cmT.dot(iop.dot(cm.dot(v)))
# P = sparse.linalg.spilu(cmT.dot(iop.nearfield_no_correction_dot(cm)))
timer.report("Build preconditioner")
def prec_f(x):
# return P.solve(x)
return x
M = sparse.linalg.LinearOperator((n, n), matvec=prec_f)
A = sparse.linalg.LinearOperator((n, n), matvec=mv)
def report_res(R):
logger.debug('residual: ' + str(R))
pass
soln = sparse.linalg.gmres(A,
rhs_constrained,
M=M,
tol=tol,
callback=report_res,
restart=200)
timer.report("GMRES")
return cm.dot(soln[0]) + c_rhs
def build_system(pts, tris, ops, slip):
trac_cs = []
trac_cs.extend(jump_constraints(np.zeros_like(slip), True))
disp_cs = []
disp_cs.extend(continuity_constraints(tris, np.array([])))
disp_cs.extend(jump_constraints(slip, False))
ND = tris.shape[0] * 9
n_total_dofs = ND * 4
cs = build_composite_constraints((trac_cs, 0), (disp_cs, 2 * ND))
cm, c_rhs = build_constraint_matrix(cs, n_total_dofs)
chunk_mat = gdbem(ops)
ops_and_starts = []
for i in range(4):
for j in range(4):
chunk = chunk_mat[i][j]
if chunk == 0:
continue
ops_and_starts.append((chunk, i * ND, j * ND))
lhs = CompositeOp(*ops_and_starts)
rhs = -lhs.dot(c_rhs)
return cm, lhs, rhs
def build_continuity(m, cfg):
cs = tct.continuity_constraints(m.pts, m.tris, m.tris.shape[0])
cs.extend(free_edge_constraints(m.get_tris('fault')))
cm, c_rhs, _ = build_constraint_matrix(cs, m.n_dofs('fault'))
return cm
import numpy as np
import scipy.sparse
import tectosaur.mesh as mesh
from tectosaur.constraints import constraints, build_constraint_matrix
from tectosaur.dense_integral_op import DenseIntegralOp
sm = 1.0
pr = 0.25
w = 4
corners = [[w, w, 0], [w, -w, 0], [-w, -w, 0], [-w, w, 0]]
m = mesh.make_rect(4, 4, corners)
cs = constraints(m[1], np.empty((0, 3)), m[0])
cm = build_constraint_matrix(cs, m[1].shape[0] * 9)
cm = cm[0].todense()
old_iop = None
for i, nq in enumerate(range(2, 20, 1)):
eps = (2.0**-np.arange(0, nq)) / (6.7)
# eps = np.linspace(1.1, 0.9, nq)
# eps = [1.0, 0.3]
# eps = np.linspace((1 + nq) / 10.0, 0.1, nq)
# if i == 0:
# eps = [0.2, 0.1]
# elif i == 1:
# eps = [0.2, 0.1, 0.05]
# elif i == 2:
# eps = [0.2, 0.1, 0.05, 0.025]
# elif i == 3:
# eps = [0.2, 0.1, 0.05, 0.025, 0.0125]
print(eps)
def regularized_tester(K, sep, continuity, mass_op_factor=0.0, which=None):
if which is None:
raise Exception('select some operators!')
n_m = 30
full_K_name = f'elastic{K}3'
full_RK_name = f'elasticR{K}3'
m, surf1_idxs, surf2_idxs = make_meshes(n_m=n_m, sep=sep)
if sep == 0.0:
surf2_idxs = surf1_idxs
near_threshold = 2.0
nq_near = 5
nq_far = 2
if any_nearfield(m[0], m[1], surf1_idxs, surf2_idxs, near_threshold):
nearfield = True
else:
nearfield = False
def sparse_unregularized(far_op, Kn):
return SparseIntegralOp(6,
nq_far,
nq_near,
near_threshold,
Kn, [1.0, 0.25],
m[0],
m[1],
np.float32,
farfield_op_type=far_op,
obs_subset=surf1_idxs,
src_subset=surf2_idxs)
def change_K_tri_tri(to):
def f(*args, to=to):
args = list(args)
args[1] = to
return TriToTriDirectFarfieldOp(*args)
return f
def add_sparse_reg(farfield_K, farfield_type):
ops.append(
SumOp([
RegularizedSparseIntegralOp(10,
10,
6,
nq_far,
nq_near,
near_threshold,
full_RK_name,
farfield_K, [1.0, 0.25],
m[0],
m[1],
np.float32,
farfield_type,
obs_subset=surf1_idxs,
src_subset=surf2_idxs),
MultOp(MassOp(3, m[0], m[1][surf1_idxs]), mass_op_factor)
]))
ops = [sparse_unregularized(PtToPtDirectFarfieldOp, full_K_name)]
if 'pt_to_pt_fmm' in which:
ops.append(
sparse_unregularized(PtToPtFMMFarfieldOp(150, 2.5, 5),
full_K_name))
if 'tri_farfield_regularized' in which:
ops.append(
sparse_unregularized(change_K_tri_tri(full_RK_name), full_K_name))
if 'dense_regularized' in which:
ops.append(
SumOp([
RegularizedDenseIntegralOp(10,
10,
6,
nq_far,
nq_near,
near_threshold,
full_RK_name,
full_RK_name, [1.0, 0.25],
m[0],
m[1],
np.float32,
obs_subset=surf1_idxs,
src_subset=surf2_idxs),
MultOp(MassOp(3, m[0], m[1][surf1_idxs]), mass_op_factor)
]))
if 'sparse_regularized' in which:
add_sparse_reg(full_RK_name, TriToTriDirectFarfieldOp)
if 'sparse_regularized_fmm' in which:
add_sparse_reg(full_K_name, PtToPtFMMFarfieldOp(150, 2.5, 5))
if 'sparse_regularized_but_unregularized_far':
add_sparse_reg(full_K_name, change_K_tri_tri(full_K_name))
print('built ops')
x = build_x_field(m, surf1_idxs, surf2_idxs)
x_flat = x.flatten()
outs = [o.dot(x_flat) for o in ops]
if continuity:
from tectosaur.constraint_builders import continuity_constraints, \
free_edge_constraints
from tectosaur.constraints import build_constraint_matrix
cs = continuity_constraints(m[1][surf1_idxs], np.array([]))
cs.extend(free_edge_constraints(m[1][surf1_idxs]))
cm, c_rhs = build_constraint_matrix(cs, outs[0].shape[0])
final_outs = [cm.T.dot(v) for v in outs]
plot_outs = [cm.dot(v) for v in final_outs]
else:
plot_outs = outs
final_outs = outs
should_plot = True
if should_plot:
plot_fnc(m, surf1_idxs, surf2_idxs, x, plot_outs)
for i in range(len(final_outs)):
for j in range(i + 1, len(final_outs)):
print(i, j, final_outs[i] / final_outs[j])
np.testing.assert_almost_equal(final_outs[i], final_outs[j], 6)