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 main(id_problem, is_coarse=False, tol=1e-5, if_export=False):
gb = example_1_create_grid.create(0.5 / float(id_problem), tol)
if is_coarse:
co.coarsen(gb, 'by_tpfa')
folder_export = "example_1_vem_coarse/"
else:
folder_export = "example_1_vem/"
file_name_error = folder_export + "vem_error.txt"
if if_export:
save = Exporter(gb, "vem", folder_export)
example_1_data.assign_frac_id(gb)
# Assign parameters
example_1_data.add_data(gb, tol)
# Choose and define the solvers and coupler
solver_flow = vem_dual.DualVEMDFN(gb.dim_max(), 'flow')
A_flow, b_flow = solver_flow.matrix_rhs(gb)
solver_source = vem_source.DualSourceDFN(gb.dim_max(), 'flow')
A_source, b_source = solver_source.matrix_rhs(gb)
up = sps.linalg.spsolve(A_flow + A_source, b_flow + b_source)
solver_flow.split(gb, "up", up)
gb.add_node_props(["discharge", 'pressure', "P0u", "err"])
solver_flow.extract_u(gb, "up", "discharge")
solver_flow.extract_p(gb, "up", 'pressure')
solver_flow.project_u(gb, "discharge", "P0u")
only_max_dim = lambda g: g.dim == gb.dim_max()
diam = gb.diameter(only_max_dim)
error_pressure = example_1_data.error_pressure(gb, "p")
error_discharge = example_1_data.error_discharge(gb, "P0u")
print("h=", diam, "- err(p)=", error_pressure, "- err(P0u)=",
error_discharge)
error_pressure = example_1_data.error_pressure(gb, 'pressure')
with open(file_name_error, 'a') as f:
info = str(gb.num_cells(only_max_dim)) + " " +\
str(gb.num_cells(only_max_dim)) + " " +\
str(error_pressure) + " " +\
str(error_discharge) + " " +\
str(gb.num_faces(only_max_dim)) + "\n"
f.write(info)
if if_export:
save.write_vtk(['pressure', "err", "P0u"])
def main(id_problem, tol=1e-5, if_export=False):
folder_export = "example_1_tpfa/"
file_name_error = folder_export + "tpfa_error.txt"
gb = example_1_create_grid.create(0.5 / float(id_problem), tol)
if if_export:
save = Exporter(gb, "tpfa", folder_export)
example_1_data.assign_frac_id(gb)
# Assign parameters
example_1_data.add_data(gb, tol)
# Choose and define the solvers and coupler
solver_flow = tpfa.TpfaDFN(gb.dim_max(), "flow")
A_flow, b_flow = solver_flow.matrix_rhs(gb)
solver_source = source.IntegralDFN(gb.dim_max(), "flow")
A_source, b_source = solver_source.matrix_rhs(gb)
p = sps.linalg.spsolve(A_flow + A_source, b_flow + b_source)
solver_flow.split(gb, "pressure", p)
def only_max_dim(g):
return g.dim == gb.dim_max()
diam = gb.diameter(only_max_dim)
error_pressure = example_1_data.error_pressure(gb, "pressure")
print("h=", diam, "- err(p)=", error_pressure)
with open(file_name_error, "a") as f:
info = (str(gb.num_cells(only_max_dim)) + " " +
str(gb.num_cells(only_max_dim)) + " " + str(error_pressure) +
"\n")
f.write(info)
if if_export:
save.write_vtk(["pressure", "err"])
data = {"kf_high": 1e2, "kf_low": 1e-2}
tol = 1e-8
# Compute the reference solution with the RT0
cells_2d = 100000
data["solver"] = "rt0"
gb_ref = example_1_data.create_gb(domain, cells_2d, tol=tol)
# only when solving for the vem case
internal_flag = FaceTag.FRACTURE
[
g.remove_face_tag_if_tag(FaceTag.BOUNDARY, internal_flag)
for g, _ in gb_ref
]
example_1_data.add_data(gb_ref, domain, data, tol)
folder = "example_1_reference"
solve_rt0(gb_ref, folder)
N = 5
data["solver"] = "tpfa"
f = open(data["solver"] + "_error.txt", "w")
for i in np.arange(N):
cells_2d = 200 * 4**i
alpha_1d = None
alpha_mortar = 0.5
gb = example_1_data.create_gb(domain, cells_2d, alpha_1d, alpha_mortar,
tol)
example_1_data.add_data(gb, domain, data, tol)
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. / (2. * 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()
