# -*- coding: utf-8 -*-
"""
Test all terms in terms_dg. Performs numerical test on simple mesh.
"""
import numpy as nm
import numpy.testing as nmts
import scipy.sparse as sp
import pytest
from sfepy.base.base import Struct
from sfepy.discrete import DGFieldVariable, Material, Integral
from sfepy.discrete import Variables
from sfepy.discrete.common.dof_info import EquationMap
from sfepy.terms.terms_dg import AdvectionDGFluxTerm, \
NonlinearHyperbolicDGFluxTerm, NonlinearScalarDotGradTerm, \
DiffusionDGFluxTerm, DiffusionInteriorPenaltyTerm
from sfepy.tests.test_dg_field import prepare_dgfield_1D, prepare_field_2D
[docs]class DGTermTestEnvornment:
"""
Class for easy creation of all the data needed for testing terms.
"""
[docs] def burg_fun(self, u):
vu = self.burg_velo * u[..., None] ** 2
return vu
[docs] def burg_fun_d(self, u):
v1 = 2 * self.burg_velo * u[..., None]
return v1
def __init__(self, dim, approx_order, **kwargs):
"""
Creates Struct object with all the data necessary to test terms
:param dim: dimension
:param approx_order: approximation order
:param kwargs: velo, diffusion or penalty for prepare_materials
:return: term test scope
"""
if dim == 1:
(field, regions), mesh = prepare_dgfield_1D(approx_order)
elif dim == 2:
(field, regions), mesh = prepare_field_2D(approx_order)
self.field = field
self.regions = regions
self.mesh = mesh
self.n_cell = field.n_cell
self.n_nod = field.n_nod
self.n_el_nod = field.n_el_nod
self.u, self.v = self.prepare_variables(field)
self.u.data = [(nm.zeros(self.n_nod))]
self.variables = Variables([ self.u, self.v])
self.integral = Integral('i', order=approx_order * 2)
self.a, self.D, self.Cw = self.prepare_materials(field, **kwargs)
if dim == 1:
velo = nm.array(1.0)
elif dim == 2:
velo = nm.array([1.0, 0])
self.burg_velo = velo.T / nm.linalg.norm(velo)
self.nonlin = Material('nonlin',
values={'.fun': self.burg_fun,
'.dfun': self.burg_fun_d})
self.out = nm.zeros((self.n_cell, 1, self.n_el_nod, 1))
[docs] def prepare_variables(self, field):
"""
Prepares state and test variables, adds empty
eq_map to state variable
:param field:
:return: state, test
"""
n_nod = field.n_nod
u = DGFieldVariable('u', 'unknown', field, history=1)
v = DGFieldVariable('v', 'test', field, primary_var_name='u')
var_di = Struct(
details=Struct(dpn=1, n_nod=n_nod,
name="field_var_dof_details"),
indx=slice(0, n_nod, None), n_dof=n_nod, name='u_dof_info',
var_name="u")
u.eq_map = EquationMap("eq_map", ["u.0"], var_di)
u.eq_map._init_empty(field)
return u, v
[docs] def prepare_materials(self, field, velo=1.0, diffusion=0.1, penalty=100):
"""
Crates material objects with data attribute, containing properly shaped
data to pass to terms
:param field: DGField
:param velo: optional values for velocity a
:param diffusion: optional value for diffusion tensor D
:param penalty: optional value for diffusion penalty Cw
:return: a, D, Cw
"""
a = Material('a', val=[velo])
a.data = nm.ones((field.n_cell, 1)) * velo
D = Material('D', val=[diffusion])
D.data = nm.ones((field.n_cell, 1, 1)) * diffusion
Cw = Material("Cw", values={".val": penalty})
Cw.data = penalty
return a, D, Cw
[docs]@pytest.fixture(scope='module', params=[{'dim': 1, 'approx_order': 3}])
def dg_test_env(request):
return DGTermTestEnvornment(**request.param)
[docs]class TestAdvectDGFluxTerm:
[docs] def test_function_explicit_1D(self, dg_test_env):
te = dg_test_env
term = AdvectionDGFluxTerm("adv_stiff(a.val, u, v)",
"a.val, u[-1], v",
te.integral, te.regions["omega"],
u=te.u, v=te.v, a=te.a)
# te.u.data[0][::te.n_el_nod] = 1
result = nm.zeros(te.out.shape)
out, _ = term.function(te.out,
te.u,
None, # diff_var
te.field,
te.regions["omega"],
te.a.data
)
nmts.assert_almost_equal(out, result)
[docs] def test_function_implicit_1D(self, dg_test_env):
te = dg_test_env
term = AdvectionDGFluxTerm("adv_stiff(a.val, u, v)",
"a.val, u, v",
te.integral, te.regions["omega"],
u=te.u, v=te.v, a=te.a)
# te.u.data[0][::ts.n_el_nod] = 1
expected = nm.zeros(((te.n_cell * te.n_el_nod),) * 2)
(out, iel1, iel2, _, _), _ = term.function(
te.out, # out, note that for implicit mode the out
# argument is ignored
te.u, # state
"u", # diff_var
te.field,
te.regions["omega"],
te.a.data, # advelo
)
out = sp.csr_matrix((out, (iel1, iel2)),
shape=((te.n_cell * te.n_el_nod),) * 2).toarray()
assert expected.shape == out.shape
[docs]class TestNonlinearHyperDGFluxTerm:
[docs] def test_function_explicit_1D(self, dg_test_env):
te = dg_test_env
term = NonlinearHyperbolicDGFluxTerm("adv_stiff(f, df u, v)",
"nonlin.f, nonlin.df, u[-1], v",
te.integral, te.regions["omega"],
u=te.u, v=te.v, nonlin=te.nonlin)
# te.u.data[0][::ts.n_el_nod] = 1
result = nm.zeros(te.out.shape)
out, _ = term.function(te.out,
te.u,
te.field,
te.regions["omega"],
te.burg_fun,
te.burg_fun_d
)
nmts.assert_almost_equal(out, result)
[docs]class TestDiffusionDGFluxTerm:
[docs] def test_function_explicit_right_1D(self, dg_test_env):
te = dg_test_env
term = DiffusionDGFluxTerm("diff_lf_flux(D.val, v, u)",
"D.val, v, u[-1]",
te.integral, te.regions["omega"],
u=te.u, v=te.v, D=te.D)
term.mode = "avg_state"
result = nm.zeros(te.out.shape)
out, _ = term.function(te.out, # out
te.u, # state
None, # diff_var, explicit
te.field,
te.regions["omega"],
te.D.data, # advelo
)
nmts.assert_almost_equal(out, result)
[docs] def test_function_explicit_left_1D(self, dg_test_env):
te = dg_test_env
term = DiffusionDGFluxTerm("diff_lf_flux(D.val, u, v)",
"D.val, u[-1], v",
te.integral, te.regions["omega"],
u=te.u, v=te.v, D=te.D)
term.mode = "avg_virtual"
result = nm.zeros(te.out.shape)
out, _ = term.function(te.out, # out
te.u, # state
None, # diff_var, explicit
te.field,
te.regions["omega"],
te.D.data, # advelo
)
nmts.assert_almost_equal(out, result)
[docs] def test_function_implicit_right_1D(self, dg_test_env):
te = dg_test_env
term = DiffusionDGFluxTerm("diff_lf_flux(D.val, v, u)",
"D.val, v, u",
te.integral, te.regions["omega"],
u=te.u, v=te.v, D=te.D)
term.mode = "avg_state"
expected = nm.zeros(((te.n_cell * te.n_el_nod),) * 2)
(out, iel1, iel2, _, _), _ = term.function(
te.out, # out
te.u, # state
"u", # diff_var, explicit
te.field,
te.regions["omega"],
te.D.data, # advelo
)
out = sp.csr_matrix((out, (iel1, iel2)),
shape=((te.n_cell * te.n_el_nod),) * 2).toarray()
assert expected.shape == out.shape
[docs] def test_function_implicit_left_1D(self, dg_test_env):
te = dg_test_env
term = DiffusionDGFluxTerm("diff_lf_flux(D.val, u, v)",
"D.val, u[-1], v",
te.integral, te.regions["omega"],
u=te.u, v=te.v, D=te.D)
term.mode = "avg_virtual"
expected = nm.zeros(((te.n_cell * te.n_el_nod),) * 2)
(out, iel1, iel2, _, _), _ = term.function(
te.out, # out
te.u, # state
"u", # diff_var, explicit
te.field,
te.regions["omega"],
te.D.data, # advelo
)
out = sp.csr_matrix((out, (iel1, iel2)),
shape=((te.n_cell * te.n_el_nod),) * 2).toarray()
assert expected.shape == out.shape
[docs]class TestDiffusionInteriorPenaltyTerm:
[docs] def test_function_explicit_1D(self, dg_test_env):
te = dg_test_env
term = DiffusionInteriorPenaltyTerm("adv_stiff(Cw.val, u, v)",
"Cw.val, u[-1], v",
te.integral, te.regions["omega"],
u=te.u, v=te.v, Cw=te.Cw)
# te.u.data[0][::ts.n_el_nod] = 1
result = nm.zeros(te.out.shape)
out, _ = term.function(te.out,
te.u,
None, # diff_var
te.field,
te.regions["omega"],
te.Cw.data,
te.D.data
)
nmts.assert_almost_equal(out, result)
[docs] def test_function_implicit_1D(self, dg_test_env):
te = dg_test_env
term = DiffusionInteriorPenaltyTerm("adv_stiff(D.val, a.val, u, v)",
"Cw.val, u, v",
te.integral, te.regions["omega"],
u=te.u, v=te.v, a=te.Cw)
# te.u.data[0][::ts.n_el_nod] = 1
expected = nm.zeros(((te.n_cell * te.n_el_nod),) * 2)
(out, iel1, iel2, _, _), _ = term.function(
te.out, # out, note that for implicit mode the out
# argument is ignored
te.u, # state
"u", # diff_var
te.field,
te.regions["omega"],
te.Cw.data,
te.D.data,
)
out = sp.csr_matrix((out, (iel1, iel2)),
shape=((te.n_cell * te.n_el_nod),) * 2).toarray()
assert expected.shape == out.shape
[docs]class TestNonlinScalarDotGradTerm:
[docs] def test_function_explicit_1D(self, dg_test_env):
te = dg_test_env
term = NonlinearScalarDotGradTerm("adv_stiff(f, df u, v)",
"nonlin.f, nonlin.df, u[-1], v",
te.integral, te.regions["omega"],
u=te.u, v=te.v, nonlin=te.nonlin)
term.setup()
# te.u.data[0][::ts.n_el_nod] = 1
expected = nm.zeros(te.out.shape)
out = nm.zeros(te.out.shape)
fargs = term.get_fargs(
te.burg_fun,
te.burg_fun_d,
te.u,
te.v
)
fargs = (out,) + fargs
out = term.function(*fargs)
nmts.assert_almost_equal(out, expected)