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example_1.py
115 lines (82 loc) · 3.2 KB
/
example_1.py
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import numpy as np
import scipy.sparse as sps
from porepy.grids.grid import Grid
from porepy.fracs import mortars
import example_1_data
import solvers
# ------------------------------------------------------------------------------#
def reference_solution():
# Compute the reference solution with the RT0
cells_2d = 100000
solver = "rt0"
gb_ref = example_1_data.create_gb(cells_2d)
example_1_data.add_data(gb_ref, solver)
folder = "example_1_reference"
solvers.solve_rt0(gb_ref, folder)
return gb_ref
# ------------------------------------------------------------------------------#
def convergence_test(N, gb_ref, solver, solver_fct):
f = open(solver + "_error.txt", "w")
for i in np.arange(N):
cells_2d = 200 * 4 ** i
alpha_1d = None
alpha_mortar = 0.75
gb = example_1_data.create_gb(cells_2d, alpha_1d, alpha_mortar)
example_1_data.add_data(gb, solver)
folder = "example_1_" + solver + "_" + str(i)
solver_fct(gb, folder)
error_0d = 0
ref_0d = 0
error_1d = 0
ref_1d = 0
for e_ref, d_ref in gb_ref.edges():
for e, d in gb.edges():
if d_ref["edge_number"] == d["edge_number"]:
break
mg_ref = d_ref["mortar_grid"]
mg = d["mortar_grid"]
m_ref = d_ref["mortar_solution"]
m = d["mortar_solution"]
num_cells = int(mg.num_cells / 2)
m_switched = np.hstack((m[num_cells:], m[:num_cells]))
if mg_ref.dim == 0:
error_0d += np.power(m - m_ref, 2)[0]
ref_0d += np.power(m_ref, 2)[0]
if mg_ref.dim == 1:
Pi_ref = np.empty((mg.num_sides(), mg.num_sides()), dtype=np.object)
for idx, (side, g_ref) in enumerate(mg_ref.side_grids.items()):
g = mg.side_grids[side]
Pi_ref[idx, idx] = mortars.split_matrix_1d(
g, g_ref, example_1_data.tol()
)
Pi_ref = sps.bmat(Pi_ref, format="csc")
inv_k = 1.0 / (2.0 * d_ref["kn"])
M = sps.diags(inv_k / mg_ref.cell_volumes)
delta = m_ref - Pi_ref * m
delta_switched = m_ref - Pi_ref * m_switched
error_1d_loc = np.dot(delta, M * delta)
error_1d_loc_switched = np.dot(delta_switched, M * delta_switched)
error_1d += min(error_1d_loc, error_1d_loc_switched)
ref_1d += np.dot(m_ref, M * m_ref)
error_0d = "%1.2e" % np.sqrt(error_0d / ref_0d)
error_1d = "%1.2e" % np.sqrt(error_1d / ref_1d)
def cond(g):
return not (isinstance(g, Grid))
diam_mg = "%1.2e" % gb.diameter(cond)
def cond(g):
return isinstance(g, Grid)
diam_g = "%1.2e" % gb.diameter(cond)
f.write(
str(i)
+ " \t"
+ diam_g
+ " \t"
+ diam_mg
+ " \t"
+ error_0d
+ " \t"
+ error_1d
+ "\n"
)
f.close()
# ------------------------------------------------------------------------------#