def Fraction(x):
buff = Fra(x).limit_denominator(100000)
n, d = buff.numerator, buff.denominator
if n > 1e2:
return fractObj(round(x, 8), 1)
else:
return fractObj(n, d)
def test_gen(self):
l_xi = sympy.symbols('xi_1')
l_syms, l_basis = Line.gen(0)
self.assertEqual(l_syms, [l_xi])
self.assertEqual(l_basis, [1])
l_syms, l_basis = Line.gen(1)
self.assertEqual(l_syms, [l_xi])
self.assertEqual(l_basis, [sympy.sympify(1), 2 * l_xi - 1])
l_syms, l_basis = Line.gen(2)
self.assertEqual(l_syms, [l_xi])
self.assertEqual(l_basis, [
sympy.sympify(1), 2 * l_xi - 1,
Fra(3, 2) * (2 * l_xi - 1)**2 - Fra(1, 2)
])
l_syms, l_basis = Line.gen(3)
self.assertEqual(l_syms, [l_xi])
self.assertEqual(l_basis, [
sympy.sympify(1), 2 * l_xi - 1,
Fra(3, 2) * (2 * l_xi - 1)**2 - Fra(1, 2), -3 * l_xi + Fra(5, 2) *
(2 * l_xi - 1)**3 + Fra(3, 2)
])
def intSfDg(i_deg, i_symsS, i_symsV):
assert (len(i_symsV) == 3)
assert (len(i_symsS) == 2)
# tet type
l_ty = edge_pre.types.Tet.Tet(i_deg)
# substitutes for the volume coordinates
l_subs = (
((i_symsV[0], i_symsS[1]), (i_symsV[1], i_symsS[0]), (i_symsV[2], 0)),
((i_symsV[0], i_symsS[0]), (i_symsV[1], 0), (i_symsV[2], i_symsS[1])),
((i_symsV[0], 0), (i_symsV[1], i_symsS[1]), (i_symsV[2], i_symsS[0])),
((i_symsV[0], 1 - i_symsS[0] - i_symsS[1]), (i_symsV[1], i_symsS[0]),
(i_symsV[2], i_symsS[1])),
)
# sub-face intgration intervals
l_intSf = []
# inc from one vertex to the next
l_inc = l_ty.ves[1][0] - l_ty.ves[0][0]
assert (l_inc == l_ty.ves[2][1] - l_ty.ves[0][1])
assert (l_inc == l_ty.ves[3][2] - l_ty.ves[0][2])
l_inc = Fra(l_inc, l_ty.n_ses)
# set intervals
for l_e2 in range(l_ty.n_ses):
for l_e1 in range(l_ty.n_ses - l_e2):
l_intSf = l_intSf + [[(i_symsS[0], l_e1 * l_inc,
(l_e1 + 1) * l_inc -
(i_symsS[1] - l_e2 * l_inc)),
(i_symsS[1], l_e2 * l_inc,
(l_e2 + 1) * l_inc)]]
# add second triangle only if not the last quad
if (l_e1 != l_ty.n_ses - l_e2 - 1):
l_intSf = l_intSf + [[(i_symsS[0], (l_e1 + 1) * l_inc -
(i_symsS[1] - l_e2 * l_inc),
(l_e1 + 1) * l_inc),
(i_symsS[1], l_e2 * l_inc,
(l_e2 + 1) * l_inc)]]
# check that we got all sub-triangles
assert (len(l_intSf) == l_ty.n_sfs)
return l_subs, [l_intSf, l_intSf, l_intSf, l_intSf]
def svs(i_deg):
l_ty = edge_pre.types.Tet.Tet(i_deg)
# inc from one vertex to the next
l_inc = l_ty.ves[1][0] - l_ty.ves[0][0]
assert (l_inc == l_ty.ves[2][1] - l_ty.ves[0][1])
assert (l_inc == l_ty.ves[3][2] - l_ty.ves[0][2])
l_inc = Fra(l_inc, l_ty.n_ses)
# vertices
l_svs = []
for l_e3 in range(l_ty.n_ses + 1):
for l_e2 in range(l_ty.n_ses + 1 - l_e3):
for l_e1 in range(l_ty.n_ses + 1 - l_e3 - l_e2):
l_svs = l_svs + [[
l_ty.ves[0][0] + l_e1 * l_inc, l_ty.ves[0][1] +
l_e2 * l_inc, l_ty.ves[0][2] + l_e3 * l_inc
]]
return l_svs
def test_intSc( self ):
# first order
l_intIn, l_intSend, l_intSurf = Hex.intSc( 0, ['xi0', 'xi1', 'xi2'] )
self.assertEqual( l_intIn, [] )
self.assertEqual( l_intSend, [ [ ( 'xi0', 0, 1 ),
( 'xi1', 0, 1 ),
( 'xi2', 0, 1 ) ] ] )
self.assertEqual( l_intSurf, [ [ [ ( 'xi0', 0, 1 ),
( 'xi1', 0, 1 ),
( 'xi2', 0, 1 ) ] ] for l_sf in range(6) ] )
# second order
l_intIn, l_intSend, l_intSurf = Hex.intSc( 1, ['xi0', 'xi1', 'xi2'] )
self.assertEqual( l_intIn, [ [ ( 'xi0', Fra(1,3), Fra(2,3) ),
( 'xi1', Fra(1,3), Fra(2,3) ),
( 'xi2', Fra(1,3), Fra(2,3) ) ] ] )
self.assertEqual( l_intSend, [ [ ( 'xi0', Fra(0,3), Fra(1,3) ),
( 'xi1', Fra(0,3), Fra(1,3) ),
( 'xi2', Fra(0,3), Fra(1,3) ) ],
[ ( 'xi0', Fra(1,3), Fra(2,3) ),
( 'xi1', Fra(0,3), Fra(1,3) ),
( 'xi2', Fra(0,3), Fra(1,3) ) ],
[ ( 'xi0', Fra(2,3), Fra(3,3) ),
( 'xi1', Fra(0,3), Fra(1,3) ),
( 'xi2', Fra(0,3), Fra(1,3) ) ],
[ ( 'xi0', Fra(0,3), Fra(1,3) ),
( 'xi1', Fra(1,3), Fra(2,3) ),
( 'xi2', Fra(0,3), Fra(1,3) ) ],
[ ( 'xi0', Fra(1,3), Fra(2,3) ),
( 'xi1', Fra(1,3), Fra(2,3) ),
( 'xi2', Fra(0,3), Fra(1,3) ) ],
[ ( 'xi0', Fra(2,3), Fra(3,3) ),
( 'xi1', Fra(1,3), Fra(2,3) ),
( 'xi2', Fra(0,3), Fra(1,3) ) ],
[ ( 'xi0', Fra(0,3), Fra(1,3) ),
( 'xi1', Fra(2,3), Fra(3,3) ),
( 'xi2', Fra(0,3), Fra(1,3) ) ],
[ ( 'xi0', Fra(1,3), Fra(2,3) ),
( 'xi1', Fra(2,3), Fra(3,3) ),
( 'xi2', Fra(0,3), Fra(1,3) ) ],
[ ( 'xi0', Fra(2,3), Fra(3,3) ),
( 'xi1', Fra(2,3), Fra(3,3) ),
( 'xi2', Fra(0,3), Fra(1,3) ) ],
[ ( 'xi0', Fra(0,3), Fra(1,3) ),
( 'xi1', Fra(0,3), Fra(1,3) ),
( 'xi2', Fra(1,3), Fra(2,3) ) ],
[ ( 'xi0', Fra(1,3), Fra(2,3) ),
( 'xi1', Fra(0,3), Fra(1,3) ),
( 'xi2', Fra(1,3), Fra(2,3) ) ],
[ ( 'xi0', Fra(2,3), Fra(3,3) ),
( 'xi1', Fra(0,3), Fra(1,3) ),
( 'xi2', Fra(1,3), Fra(2,3) ) ],
[ ( 'xi0', Fra(0,3), Fra(1,3) ),
( 'xi1', Fra(0,3), Fra(1,3) ),
( 'xi2', Fra(2,3), Fra(3,3) ) ],
[ ( 'xi0', Fra(1,3), Fra(2,3) ),
( 'xi1', Fra(0,3), Fra(1,3) ),
( 'xi2', Fra(2,3), Fra(3,3) ) ],
[ ( 'xi0', Fra(2,3), Fra(3,3) ),
( 'xi1', Fra(0,3), Fra(1,3) ),
( 'xi2', Fra(2,3), Fra(3,3) ) ],
[ ( 'xi0', Fra(2,3), Fra(3,3) ),
( 'xi1', Fra(1,3), Fra(2,3) ),
( 'xi2', Fra(1,3), Fra(2,3) ) ],
[ ( 'xi0', Fra(2,3), Fra(3,3) ),
( 'xi1', Fra(2,3), Fra(3,3) ),
( 'xi2', Fra(1,3), Fra(2,3) ) ],
[ ( 'xi0', Fra(2,3), Fra(3,3) ),
( 'xi1', Fra(1,3), Fra(2,3) ),
( 'xi2', Fra(2,3), Fra(3,3) ) ],
[ ( 'xi0', Fra(2,3), Fra(3,3) ),
( 'xi1', Fra(2,3), Fra(3,3) ),
( 'xi2', Fra(2,3), Fra(3,3) ) ],
[ ( 'xi0', Fra(0,3), Fra(1,3) ),
( 'xi1', Fra(2,3), Fra(3,3) ),
( 'xi2', Fra(1,3), Fra(2,3) ) ],
[ ( 'xi0', Fra(1,3), Fra(2,3) ),
( 'xi1', Fra(2,3), Fra(3,3) ),
( 'xi2', Fra(1,3), Fra(2,3) ) ],
[ ( 'xi0', Fra(0,3), Fra(1,3) ),
( 'xi1', Fra(2,3), Fra(3,3) ),
( 'xi2', Fra(2,3), Fra(3,3) ) ],
[ ( 'xi0', Fra(1,3), Fra(2,3) ),
( 'xi1', Fra(2,3), Fra(3,3) ),
( 'xi2', Fra(2,3), Fra(3,3) ) ],
[ ( 'xi0', Fra(0,3), Fra(1,3) ),
( 'xi1', Fra(1,3), Fra(2,3) ),
( 'xi2', Fra(1,3), Fra(2,3) ) ],
[ ( 'xi0', Fra(0,3), Fra(1,3) ),
( 'xi1', Fra(1,3), Fra(2,3) ),
( 'xi2', Fra(2,3), Fra(3,3) ) ],
[ ( 'xi0', Fra(1,3), Fra(2,3) ),
( 'xi1', Fra(1,3), Fra(2,3) ),
( 'xi2', Fra(2,3), Fra(3,3) ) ] ] )
self.assertEqual( l_intSurf[0:2], [ [ [ ( 'xi0', Fra(0,3), Fra(1,3) ),
( 'xi1', Fra(0,3), Fra(1,3) ),
( 'xi2', Fra(0,3), Fra(1,3) ) ],
[ ( 'xi0', Fra(1,3), Fra(2,3) ),
( 'xi1', Fra(0,3), Fra(1,3) ),
( 'xi2', Fra(0,3), Fra(1,3) ) ],
[ ( 'xi0', Fra(2,3), Fra(3,3) ),
( 'xi1', Fra(0,3), Fra(1,3) ),
( 'xi2', Fra(0,3), Fra(1,3) ) ],
[ ( 'xi0', Fra(0,3), Fra(1,3) ),
( 'xi1', Fra(1,3), Fra(2,3) ),
( 'xi2', Fra(0,3), Fra(1,3) ) ],
[ ( 'xi0', Fra(1,3), Fra(2,3) ),
( 'xi1', Fra(1,3), Fra(2,3) ),
( 'xi2', Fra(0,3), Fra(1,3) ) ],
[ ( 'xi0', Fra(2,3), Fra(3,3) ),
( 'xi1', Fra(1,3), Fra(2,3) ),
( 'xi2', Fra(0,3), Fra(1,3) ) ],
[ ( 'xi0', Fra(0,3), Fra(1,3) ),
( 'xi1', Fra(2,3), Fra(3,3) ),
( 'xi2', Fra(0,3), Fra(1,3) ) ],
[ ( 'xi0', Fra(1,3), Fra(2,3) ),
( 'xi1', Fra(2,3), Fra(3,3) ),
( 'xi2', Fra(0,3), Fra(1,3) ) ],
[ ( 'xi0', Fra(2,3), Fra(3,3) ),
( 'xi1', Fra(2,3), Fra(3,3) ),
( 'xi2', Fra(0,3), Fra(1,3) ) ] ],
[ [ ( 'xi0', Fra(0,3), Fra(1,3) ),
( 'xi1', Fra(0,3), Fra(1,3) ),
( 'xi2', Fra(0,3), Fra(1,3) ) ],
[ ( 'xi0', Fra(1,3), Fra(2,3) ),
( 'xi1', Fra(0,3), Fra(1,3) ),
( 'xi2', Fra(0,3), Fra(1,3) ) ],
[ ( 'xi0', Fra(2,3), Fra(3,3) ),
( 'xi1', Fra(0,3), Fra(1,3) ),
( 'xi2', Fra(0,3), Fra(1,3) ) ],
[ ( 'xi0', Fra(0,3), Fra(1,3) ),
( 'xi1', Fra(0,3), Fra(1,3) ),
( 'xi2', Fra(1,3), Fra(2,3) ) ],
[ ( 'xi0', Fra(1,3), Fra(2,3) ),
( 'xi1', Fra(0,3), Fra(1,3) ),
( 'xi2', Fra(1,3), Fra(2,3) ) ],
[ ( 'xi0', Fra(2,3), Fra(3,3) ),
( 'xi1', Fra(0,3), Fra(1,3) ),
( 'xi2', Fra(1,3), Fra(2,3) ) ],
[ ( 'xi0', Fra(0,3), Fra(1,3) ),
( 'xi1', Fra(0,3), Fra(1,3) ),
( 'xi2', Fra(2,3), Fra(3,3) ) ],
[ ( 'xi0', Fra(1,3), Fra(2,3) ),
( 'xi1', Fra(0,3), Fra(1,3) ),
( 'xi2', Fra(2,3), Fra(3,3) ) ],
[ ( 'xi0', Fra(2,3), Fra(3,3) ),
( 'xi1', Fra(0,3), Fra(1,3) ),
( 'xi2', Fra(2,3), Fra(3,3) ) ] ] ] )
def test_gatherLine(self):
#
# 2nd order
#
l_syms, l_basis = edge_pre.dg.basis.Line.gen(1)
l_int = [(l_syms[0], 0, 1)]
l_mapsSc, l_detsSc = edge_pre.sc.grid.Line.intSc(1, l_syms)
l_gather = Project.gather(l_syms, l_basis, l_int,
l_mapsSc[0] + l_mapsSc[1],
l_detsSc[0] + l_detsSc[1])
l_gatherUt = sympy.Matrix([[Fra(1, 3), 0], [Fra(1, 3), -Fra(3, 4)],
[Fra(1, 3), Fra(3, 4)]])
self.assertEqual(l_gather, l_gatherUt)
#
# 3rd order
#
l_syms, l_basis = edge_pre.dg.basis.Line.gen(2)
l_int = [(l_syms[0], 0, 1)]
l_mapsSc, l_detsSc = edge_pre.sc.grid.Line.intSc(2, l_syms)
l_gather = Project.gather(l_syms, l_basis, l_int,
l_mapsSc[0] + l_mapsSc[1],
l_detsSc[0] + l_detsSc[1])
l_gatherUt = sympy.Matrix([[Fra(1, 5), -Fra(1, 4), -Fra(25, 84)],
[Fra(1, 5), 0, -Fra(25, 42)],
[Fra(1, 5),
Fra(1, 4), -Fra(25, 84)],
[Fra(1, 5), -Fra(1, 2),
Fra(25, 42)],
[Fra(1, 5),
Fra(1, 2),
Fra(25, 42)]])
self.assertEqual(l_gather, l_gatherUt)
def test_intSfDg(self):
l_xi0 = sympy.symbols('xi_0')
l_xi1 = sympy.symbols('xi_1')
l_xi2 = sympy.symbols('xi_2')
l_chi0 = sympy.symbols('chi_0')
l_chi1 = sympy.symbols('chi_1')
# 1st order
l_subs, l_intSfDg = Hex.intSfDg(0, [l_chi0, l_chi1],
[l_xi0, l_xi1, l_xi2])
self.assertEqual(l_subs,
(((l_xi0, l_chi1), (l_xi1, l_chi0), (l_xi2, 0)),
((l_xi0, l_chi0), (l_xi1, 0), (l_xi2, l_chi1)),
((l_xi0, 1), (l_xi1, l_chi0), (l_xi2, l_chi1)),
((l_xi0, l_chi1), (l_xi1, 1), (l_xi2, l_chi0)),
((l_xi0, 0), (l_xi1, l_chi1), (l_xi2, l_chi0)),
((l_xi0, l_chi0), (l_xi1, l_chi1), (l_xi2, 1))))
self.assertEqual(
l_intSfDg,
[
[ # DG face 0
[(l_chi0, 0, 1), (l_chi1, 0, 1)]
],
[ # DG face 1
[(l_chi0, 0, 1), (l_chi1, 0, 1)]
],
[ # DG face 2
[(l_chi0, 0, 1), (l_chi1, 0, 1)]
],
[ # DG face 3
[(l_chi0, 0, 1), (l_chi1, 0, 1)]
],
[ # DG face 4
[(l_chi0, 0, 1), (l_chi1, 0, 1)]
],
[ # DG face 5
[(l_chi0, 0, 1), (l_chi1, 0, 1)]
]
])
# 2nd order
l_subs, l_intSfDg = Hex.intSfDg(1, [l_chi0, l_chi1],
[l_xi0, l_xi1, l_xi2])
self.assertEqual(l_subs,
(((l_xi0, l_chi1), (l_xi1, l_chi0), (l_xi2, 0)),
((l_xi0, l_chi0), (l_xi1, 0), (l_xi2, l_chi1)),
((l_xi0, 1), (l_xi1, l_chi0), (l_xi2, l_chi1)),
((l_xi0, l_chi1), (l_xi1, 1), (l_xi2, l_chi0)),
((l_xi0, 0), (l_xi1, l_chi1), (l_xi2, l_chi0)),
((l_xi0, l_chi0), (l_xi1, l_chi1), (l_xi2, 1))))
self.assertEqual(
l_intSfDg,
[
[ # DG face 0
[(l_chi0, Fra(0, 3), Fra(1, 3)),
(l_chi1, Fra(0, 3), Fra(1, 3))],
[(l_chi0, Fra(1, 3), Fra(2, 3)),
(l_chi1, Fra(0, 3), Fra(1, 3))],
[(l_chi0, Fra(2, 3), Fra(3, 3)),
(l_chi1, Fra(0, 3), Fra(1, 3))],
[(l_chi0, Fra(0, 3), Fra(1, 3)),
(l_chi1, Fra(1, 3), Fra(2, 3))],
[(l_chi0, Fra(1, 3), Fra(2, 3)),
(l_chi1, Fra(1, 3), Fra(2, 3))],
[(l_chi0, Fra(2, 3), Fra(3, 3)),
(l_chi1, Fra(1, 3), Fra(2, 3))],
[(l_chi0, Fra(0, 3), Fra(1, 3)),
(l_chi1, Fra(2, 3), Fra(3, 3))],
[(l_chi0, Fra(1, 3), Fra(2, 3)),
(l_chi1, Fra(2, 3), Fra(3, 3))],
[(l_chi0, Fra(2, 3), Fra(3, 3)),
(l_chi1, Fra(2, 3), Fra(3, 3))]
],
[ # DG face 1
[(l_chi0, Fra(0, 3), Fra(1, 3)),
(l_chi1, Fra(0, 3), Fra(1, 3))],
[(l_chi0, Fra(1, 3), Fra(2, 3)),
(l_chi1, Fra(0, 3), Fra(1, 3))],
[(l_chi0, Fra(2, 3), Fra(3, 3)),
(l_chi1, Fra(0, 3), Fra(1, 3))],
[(l_chi0, Fra(0, 3), Fra(1, 3)),
(l_chi1, Fra(1, 3), Fra(2, 3))],
[(l_chi0, Fra(1, 3), Fra(2, 3)),
(l_chi1, Fra(1, 3), Fra(2, 3))],
[(l_chi0, Fra(2, 3), Fra(3, 3)),
(l_chi1, Fra(1, 3), Fra(2, 3))],
[(l_chi0, Fra(0, 3), Fra(1, 3)),
(l_chi1, Fra(2, 3), Fra(3, 3))],
[(l_chi0, Fra(1, 3), Fra(2, 3)),
(l_chi1, Fra(2, 3), Fra(3, 3))],
[(l_chi0, Fra(2, 3), Fra(3, 3)),
(l_chi1, Fra(2, 3), Fra(3, 3))]
],
[ # DG face 2
[(l_chi0, Fra(0, 3), Fra(1, 3)),
(l_chi1, Fra(0, 3), Fra(1, 3))],
[(l_chi0, Fra(1, 3), Fra(2, 3)),
(l_chi1, Fra(0, 3), Fra(1, 3))],
[(l_chi0, Fra(2, 3), Fra(3, 3)),
(l_chi1, Fra(0, 3), Fra(1, 3))],
[(l_chi0, Fra(0, 3), Fra(1, 3)),
(l_chi1, Fra(1, 3), Fra(2, 3))],
[(l_chi0, Fra(1, 3), Fra(2, 3)),
(l_chi1, Fra(1, 3), Fra(2, 3))],
[(l_chi0, Fra(2, 3), Fra(3, 3)),
(l_chi1, Fra(1, 3), Fra(2, 3))],
[(l_chi0, Fra(0, 3), Fra(1, 3)),
(l_chi1, Fra(2, 3), Fra(3, 3))],
[(l_chi0, Fra(1, 3), Fra(2, 3)),
(l_chi1, Fra(2, 3), Fra(3, 3))],
[(l_chi0, Fra(2, 3), Fra(3, 3)),
(l_chi1, Fra(2, 3), Fra(3, 3))]
],
[ # DG face 3
[(l_chi0, Fra(0, 3), Fra(1, 3)),
(l_chi1, Fra(0, 3), Fra(1, 3))],
[(l_chi0, Fra(1, 3), Fra(2, 3)),
(l_chi1, Fra(0, 3), Fra(1, 3))],
[(l_chi0, Fra(2, 3), Fra(3, 3)),
(l_chi1, Fra(0, 3), Fra(1, 3))],
[(l_chi0, Fra(0, 3), Fra(1, 3)),
(l_chi1, Fra(1, 3), Fra(2, 3))],
[(l_chi0, Fra(1, 3), Fra(2, 3)),
(l_chi1, Fra(1, 3), Fra(2, 3))],
[(l_chi0, Fra(2, 3), Fra(3, 3)),
(l_chi1, Fra(1, 3), Fra(2, 3))],
[(l_chi0, Fra(0, 3), Fra(1, 3)),
(l_chi1, Fra(2, 3), Fra(3, 3))],
[(l_chi0, Fra(1, 3), Fra(2, 3)),
(l_chi1, Fra(2, 3), Fra(3, 3))],
[(l_chi0, Fra(2, 3), Fra(3, 3)),
(l_chi1, Fra(2, 3), Fra(3, 3))]
],
[ # DG face 4
[(l_chi0, Fra(0, 3), Fra(1, 3)),
(l_chi1, Fra(0, 3), Fra(1, 3))],
[(l_chi0, Fra(1, 3), Fra(2, 3)),
(l_chi1, Fra(0, 3), Fra(1, 3))],
[(l_chi0, Fra(2, 3), Fra(3, 3)),
(l_chi1, Fra(0, 3), Fra(1, 3))],
[(l_chi0, Fra(0, 3), Fra(1, 3)),
(l_chi1, Fra(1, 3), Fra(2, 3))],
[(l_chi0, Fra(1, 3), Fra(2, 3)),
(l_chi1, Fra(1, 3), Fra(2, 3))],
[(l_chi0, Fra(2, 3), Fra(3, 3)),
(l_chi1, Fra(1, 3), Fra(2, 3))],
[(l_chi0, Fra(0, 3), Fra(1, 3)),
(l_chi1, Fra(2, 3), Fra(3, 3))],
[(l_chi0, Fra(1, 3), Fra(2, 3)),
(l_chi1, Fra(2, 3), Fra(3, 3))],
[(l_chi0, Fra(2, 3), Fra(3, 3)),
(l_chi1, Fra(2, 3), Fra(3, 3))]
],
[ # DG face 5
[(l_chi0, Fra(0, 3), Fra(1, 3)),
(l_chi1, Fra(0, 3), Fra(1, 3))],
[(l_chi0, Fra(1, 3), Fra(2, 3)),
(l_chi1, Fra(0, 3), Fra(1, 3))],
[(l_chi0, Fra(2, 3), Fra(3, 3)),
(l_chi1, Fra(0, 3), Fra(1, 3))],
[(l_chi0, Fra(0, 3), Fra(1, 3)),
(l_chi1, Fra(1, 3), Fra(2, 3))],
[(l_chi0, Fra(1, 3), Fra(2, 3)),
(l_chi1, Fra(1, 3), Fra(2, 3))],
[(l_chi0, Fra(2, 3), Fra(3, 3)),
(l_chi1, Fra(1, 3), Fra(2, 3))],
[(l_chi0, Fra(0, 3), Fra(1, 3)),
(l_chi1, Fra(2, 3), Fra(3, 3))],
[(l_chi0, Fra(1, 3), Fra(2, 3)),
(l_chi1, Fra(2, 3), Fra(3, 3))],
[(l_chi0, Fra(2, 3), Fra(3, 3)),
(l_chi1, Fra(2, 3), Fra(3, 3))]
]
])
def test_scatterLine(self):
#
# 2nd order
#
l_syms, l_basis = edge_pre.dg.basis.Line.gen( 1 )
l_intIn, l_intSend, l_intSurf = edge_pre.sc.grid.Line.intSc( 1, l_syms )
# inner sub-cells
l_scatter = Project.scatter( l_basis, l_intIn )
l_scatterUt = sympy.Matrix([[1], [0]])
self.assertEqual( l_scatter, l_scatterUt )
# send sub-cells
l_scatter = Project.scatter( l_basis, l_intSend )
l_scatterUt = sympy.Matrix( [ [1, 1 ],
[-Fra(2, 3), Fra(2, 3)]
])
self.assertEqual( l_scatter, l_scatterUt )
# surf sub-cells, face 1
l_scatter = Project.scatter( l_basis, l_intSurf[0] )
l_scatterUt = sympy.Matrix( [ [1, ],
[-Fra(2, 3) ]
])
self.assertEqual( l_scatter, l_scatterUt )
# surf sub-cells, face2
l_scatter = Project.scatter( l_basis, l_intSurf[1] )
l_scatterUt = sympy.Matrix( [ [1, ],
[Fra(2, 3) ]
])
self.assertEqual( l_scatter, l_scatterUt )
#
# 3rd order
#
l_syms, l_basis = edge_pre.dg.basis.Line.gen( 2 )
l_intIn, l_intSend, l_intSurf = edge_pre.sc.grid.Line.intSc( 2, l_syms )
# inner sub-cells
l_scatter = Project.scatter( l_basis, l_intIn )
l_scatterUt = sympy.Matrix( [ [ 1, 1, 1 ],
[ -Fra(2, 5), 0, Fra(2, 5) ],
[ -Fra(6, 25), -Fra(12,25), -Fra(6,25) ]
])
self.assertEqual( l_scatter, l_scatterUt )
# send sub-cells
l_scatter = Project.scatter( l_basis, l_intSend )
l_scatterUt = sympy.Matrix( [ [ 1, 1 ],
[ -Fra(4, 5), Fra(4, 5) ],
[ Fra(12, 25), Fra(12,25) ]
])
self.assertEqual( l_scatter, l_scatterUt )
# surf sub-cells, face 1
l_scatter = Project.scatter( l_basis, l_intSurf[0] )
l_scatterUt = sympy.Matrix( [ [ 1 ],
[ -Fra(4, 5) ],
[ Fra(12, 25) ]
])
self.assertEqual( l_scatter, l_scatterUt )
# surf sub-cells, face 2
l_scatter = Project.scatter( l_basis, l_intSurf[0] )
l_scatterUt = sympy.Matrix( [ [ 1 ],
[ -Fra(4, 5) ],
[ Fra(12, 25) ]
])
self.assertEqual( l_scatter, l_scatterUt )
def test_intSfDg(self):
l_subs, l_intSfDg = Quad.intSfDg(1, ['chi0'], ['xi0', 'xi1'])
# check substitutions
self.assertEqual(l_subs, ((('xi0', 'chi0'),
('xi1', 0)), (('xi0', 1), ('xi1', 'chi0')),
(('xi0', 'chi0'),
('xi1', 1)), (('xi0', 0), ('xi1', 'chi0'))))
# check intervals
self.assertEqual(
l_intSfDg,
[
[ # DG face0
[('chi0', Fra(0, 3), Fra(1, 3))],
[('chi0', Fra(1, 3), Fra(2, 3))],
[('chi0', Fra(2, 3), Fra(3, 3))]
],
[ # DG face1
[('chi0', Fra(0, 3), Fra(1, 3))],
[('chi0', Fra(1, 3), Fra(2, 3))],
[('chi0', Fra(2, 3), Fra(3, 3))]
],
[ # DG face2
[('chi0', Fra(2, 3), Fra(3, 3))],
[('chi0', Fra(1, 3), Fra(2, 3))],
[('chi0', Fra(0, 3), Fra(1, 3))]
],
[ # DG face3
[('chi0', Fra(2, 3), Fra(3, 3))],
[('chi0', Fra(1, 3), Fra(2, 3))],
[('chi0', Fra(0, 3), Fra(1, 3))]
]
])
def test_intSc(self):
# second order
l_intIn, l_intSend, l_intSurf = Quad.intSc(1, ['xi0', 'xi1'])
self.assertEqual(l_intIn, [[('xi0', Fra(1, 3), Fra(2, 3)),
('xi1', Fra(1, 3), Fra(2, 3))]])
self.assertEqual(l_intSend, [[('xi0', Fra(0, 3), Fra(1, 3)),
('xi1', Fra(0, 3), Fra(1, 3))],
[('xi0', Fra(1, 3), Fra(2, 3)),
('xi1', Fra(0, 3), Fra(1, 3))],
[('xi0', Fra(2, 3), Fra(3, 3)),
('xi1', Fra(0, 3), Fra(1, 3))],
[('xi0', Fra(2, 3), Fra(3, 3)),
('xi1', Fra(1, 3), Fra(2, 3))],
[('xi0', Fra(2, 3), Fra(3, 3)),
('xi1', Fra(2, 3), Fra(3, 3))],
[('xi0', Fra(1, 3), Fra(2, 3)),
('xi1', Fra(2, 3), Fra(3, 3))],
[('xi0', Fra(0, 3), Fra(1, 3)),
('xi1', Fra(2, 3), Fra(3, 3))],
[('xi0', Fra(0, 3), Fra(1, 3)),
('xi1', Fra(1, 3), Fra(2, 3))]])
self.assertEqual(l_intSurf[0], [[('xi0', Fra(0, 3), Fra(1, 3)),
('xi1', Fra(0, 3), Fra(1, 3))],
[('xi0', Fra(1, 3), Fra(2, 3)),
('xi1', Fra(0, 3), Fra(1, 3))],
[('xi0', Fra(2, 3), Fra(3, 3)),
('xi1', Fra(0, 3), Fra(1, 3))]])
self.assertEqual(l_intSurf[1], [[('xi0', Fra(2, 3), Fra(3, 3)),
('xi1', Fra(0, 3), Fra(1, 3))],
[('xi0', Fra(2, 3), Fra(3, 3)),
('xi1', Fra(1, 3), Fra(2, 3))],
[('xi0', Fra(2, 3), Fra(3, 3)),
('xi1', Fra(2, 3), Fra(3, 3))]])
self.assertEqual(l_intSurf[2], [[('xi0', Fra(2, 3), Fra(3, 3)),
('xi1', Fra(2, 3), Fra(3, 3))],
[('xi0', Fra(1, 3), Fra(2, 3)),
('xi1', Fra(2, 3), Fra(3, 3))],
[('xi0', Fra(0, 3), Fra(1, 3)),
('xi1', Fra(2, 3), Fra(3, 3))]])
self.assertEqual(l_intSurf[3], [[('xi0', Fra(0, 3), Fra(1, 3)),
('xi1', Fra(2, 3), Fra(3, 3))],
[('xi0', Fra(0, 3), Fra(1, 3)),
('xi1', Fra(1, 3), Fra(2, 3))],
[('xi0', Fra(0, 3), Fra(1, 3)),
('xi1', Fra(0, 3), Fra(1, 3))]])
def test_intSfDg(self):
l_xi0 = sympy.symbols('xi_0')
l_xi1 = sympy.symbols('xi_1')
l_xi2 = sympy.symbols('xi_2')
l_chi0 = sympy.symbols('chi_0')
l_chi1 = sympy.symbols('chi_1')
# second order
l_subs, l_intSfDg = Tet.intSfDg( 1, [l_chi0, l_chi1], [l_xi0, l_xi1, l_xi2] )
# check substitutions
self.assertEqual( l_subs, ( ( ( l_xi0, l_chi1 ),
( l_xi1, l_chi0 ),
( l_xi2, 0 ) ),
( ( l_xi0, l_chi0 ),
( l_xi1, 0 ),
( l_xi2, l_chi1 ) ),
( ( l_xi0, 0 ),
( l_xi1, l_chi1 ),
( l_xi2, l_chi0 ) ),
( ( l_xi0, 1-l_chi0-l_chi1 ),
( l_xi1, l_chi0 ),
( l_xi2, l_chi1 ) ) ) )
for l_fa in l_intSfDg:
self.assertEqual( l_fa, [ # first quad
[ ( l_chi0, Fra(0,3), Fra(1,3)-l_chi1 ),
( l_chi1, Fra(0,3), Fra(1,3) ) ],
[ ( l_chi0, Fra(1,3)-l_chi1, Fra(1,3) ),
( l_chi1, Fra(0,3), Fra(1,3) ) ],
# second quad
[ ( l_chi0, Fra(1,3), Fra(2,3)-l_chi1 ),
( l_chi1, Fra(0,3), Fra(1,3) ) ],
[ ( l_chi0, Fra(2,3)-l_chi1, Fra(2,3) ),
( l_chi1, Fra(0,3), Fra(1,3) ) ],
# third quad
[ ( l_chi0, Fra(2,3), Fra(3,3)-l_chi1 ),
( l_chi1, Fra(0,3), Fra(1,3) ) ],
# fourth quad
[ ( l_chi0, Fra(0,3), Fra(1,3)-(l_chi1-Fra(1,3)) ),
( l_chi1, Fra(1,3), Fra(2,3) ) ],
[ ( l_chi0, Fra(1,3)-(l_chi1-Fra(1,3)), Fra(1,3) ),
( l_chi1, Fra(1,3), Fra(2,3) ) ],
# fifth quad
[ ( l_chi0, Fra(1,3), Fra(2,3)-(l_chi1-Fra(1,3)) ),
( l_chi1, Fra(1,3), Fra(2,3) ) ],
# sixth quad
[ ( l_chi0, Fra(0,3), Fra(1,3)-(l_chi1-Fra(2,3)) ),
( l_chi1, Fra(2,3), Fra(3,3) ) ],
] )
def test_svs(self):
# FV
l_svs = Tet.svs( 0 )
self.assertEqual( l_svs, [ [0,0,0], [1,0,0], [0,1,0], [0,0,1] ] )
# 2nd order
l_svs = Tet.svs( 1 )
self.assertEqual( l_svs, [ [ 0, 0, 0 ],
[ Fra(1,3), 0, 0 ],
[ Fra(2,3), 0, 0 ],
[ Fra(3,3), 0, 0 ],
[ 0, Fra(1,3), 0 ],
[ Fra(1,3), Fra(1,3), 0 ],
[ Fra(2,3), Fra(1,3), 0 ],
[ 0, Fra(2,3), 0 ],
[ Fra(1,3), Fra(2,3), 0 ],
[ 0, Fra(3,3), 0 ],
[ 0, Fra(0,3), Fra(1,3) ],
[ Fra(1,3), Fra(0,3), Fra(1,3) ],
[ Fra(2,3), Fra(0,3), Fra(1,3) ],
[ 0, Fra(1,3), Fra(1,3) ],
[ Fra(1,3), Fra(1,3), Fra(1,3) ],
[ 0, Fra(2,3), Fra(1,3) ],
[ 0, Fra(0,3), Fra(2,3) ],
[ Fra(1,3), Fra(0,3), Fra(2,3) ],
[ Fra(0,3), Fra(1,3), Fra(2,3) ],
[ Fra(0,3), Fra(0,3), Fra(3,3) ] ] )
def test_intSc(self):
l_xi0 = sympy.symbols('xi_0')
l_xi1 = sympy.symbols('xi_1')
# second order
l_intIn, l_intSend, l_intSurf = Tria.intSc(1, [l_xi0, l_xi1])
# inner intervals
self.assertEqual(l_intIn,
[[(l_xi0, Fra(1, 3) - l_xi1, Fra(1, 3)),
(l_xi1, Fra(0, 3), Fra(1, 3))],
[(l_xi0, Fra(2, 3) - l_xi1, Fra(2, 3)),
(l_xi1, Fra(0, 3), Fra(1, 3))],
[(l_xi0, Fra(1, 3) - (l_xi1 - Fra(1, 3)), Fra(1, 3)),
(l_xi1, Fra(1, 3), Fra(2, 3))]])
# send intervals
self.assertEqual(l_intSend,
[[(l_xi0, Fra(0, 3), Fra(1, 3) - l_xi1),
(l_xi1, Fra(0, 3), Fra(1, 3))],
[(l_xi0, Fra(1, 3), Fra(2, 3) - l_xi1),
(l_xi1, Fra(0, 3), Fra(1, 3))],
[(l_xi0, Fra(2, 3), Fra(3, 3) - l_xi1),
(l_xi1, Fra(0, 3), Fra(1, 3))],
[(l_xi0, Fra(1, 3), Fra(2, 3) - (l_xi1 - Fra(1, 3))),
(l_xi1, Fra(1, 3), Fra(2, 3))],
[(l_xi0, Fra(0, 3), Fra(1, 3) - (l_xi1 - Fra(2, 3))),
(l_xi1, Fra(2, 3), Fra(3, 3))],
[(l_xi0, Fra(0, 3), Fra(1, 3) - (l_xi1 - Fra(1, 3))),
(l_xi1, Fra(1, 3), Fra(2, 3))]])
# DG intervals
self.assertEqual(l_intSurf[0], [[(l_xi0, Fra(0, 3), Fra(1, 3) - l_xi1),
(l_xi1, Fra(0, 3), Fra(1, 3))],
[(l_xi0, Fra(1, 3), Fra(2, 3) - l_xi1),
(l_xi1, Fra(0, 3), Fra(1, 3))],
[(l_xi0, Fra(2, 3), Fra(3, 3) - l_xi1),
(l_xi1, Fra(0, 3), Fra(1, 3))]])
self.assertEqual(l_intSurf[1],
[[(l_xi0, Fra(2, 3), Fra(3, 3) - l_xi1),
(l_xi1, Fra(0, 3), Fra(1, 3))],
[(l_xi0, Fra(1, 3), Fra(2, 3) - (l_xi1 - Fra(1, 3))),
(l_xi1, Fra(1, 3), Fra(2, 3))],
[(l_xi0, Fra(0, 3), Fra(1, 3) - (l_xi1 - Fra(2, 3))),
(l_xi1, Fra(2, 3), Fra(3, 3))]])
self.assertEqual(l_intSurf[2],
[[(l_xi0, Fra(0, 3), Fra(1, 3) - (l_xi1 - Fra(2, 3))),
(l_xi1, Fra(2, 3), Fra(3, 3))],
[(l_xi0, Fra(0, 3), Fra(1, 3) - (l_xi1 - Fra(1, 3))),
(l_xi1, Fra(1, 3), Fra(2, 3))],
[(l_xi0, Fra(0, 3), Fra(1, 3) - l_xi1),
(l_xi1, Fra(0, 3), Fra(1, 3))]])
def scTySf(i_deg):
# special handling for degree 0 elements
if (i_deg == 0):
return [], [[0, 1, 2, 3]]
# get sub-vertices
l_svs = svs(i_deg)
# get sub-faces
l_scSfSvIn, l_scSfSvSend, l_scSfSvRecv = scSfSv(i_deg)
# define normals
l_normals = []
l_normals = l_normals + [sympy.Matrix([0, 0, 1])]
l_normals = l_normals + [sympy.Matrix([0, 1, 0])]
l_normals = l_normals + [sympy.Matrix([1, 0, 0])]
l_normals = l_normals + [
sympy.Matrix([
-sympy.sqrt(Fra(1, 3)), -sympy.sqrt(Fra(1, 3)),
-sympy.sqrt(Fra(1, 3))
])
]
l_normals = l_normals + [
sympy.Matrix([-sympy.sqrt(Fra(1, 2)), -sympy.sqrt(Fra(1, 2)), 0])
]
l_normals = l_normals + [
sympy.Matrix([-sympy.sqrt(Fra(1, 2)), 0, -sympy.sqrt(Fra(1, 2))])
]
# define empty sub-cell types
l_scTySf = [[], []]
# iterate over sub-faces
for l_ty in range(2):
for l_sc in [l_scSfSvIn, l_scSfSvSend][l_ty]:
# add empty list
l_scTySf[l_ty] = l_scTySf[l_ty] + [[]]
for l_sf in l_sc:
# assemble three points
l_or = sympy.Matrix(l_svs[l_sf[0]])
l_p0 = sympy.Matrix(l_svs[l_sf[1]])
l_p1 = sympy.Matrix(l_svs[l_sf[2]])
# assemble edges
l_e0 = l_p0 - l_or
l_e1 = l_p1 - l_or
# compute normalized cross product
l_cr = l_e0.cross(l_e1).normalized()
# determine type of normal
for l_no in range(len(l_normals)):
if l_cr == l_normals[l_no]:
l_ri = 1
break
elif l_cr == -l_normals[l_no]:
l_ri = 0
break
# make sure we found the correct normal
assert (l_no != len(l_normals) - 1)
# determine if this a partial DG face
l_pd = 0
if l_ty == 1:
# bottom
if (l_or[2] == 0 and l_p0[2] == 0 and l_p1[2] == 0):
assert (l_no == 0)
l_pd = 1
elif (l_or[1] == 0 and l_p0[1] == 0 and l_p1[1] == 0):
assert (l_no == 1)
l_pd = 1
elif (l_or[0] == 0 and l_p0[0] == 0 and l_p1[0] == 0):
assert (l_no == 2)
l_pd = 1
elif (l_or[0] == sympy.sympify(1) - l_or[1] - l_or[2]
and l_p0[0] == sympy.sympify(1) - l_p0[1] - l_p0[2]
and l_p1[0] == sympy.sympify(1) - l_p1[1] - l_p1[2]):
assert (l_no == 3)
l_pd = 1
# add sub-cell type
if l_pd == 0:
l_scTySf[l_ty][-1] = l_scTySf[l_ty][-1] + [
8 + l_ri * 6 + l_no
]
else:
assert (l_no < 4)
l_scTySf[l_ty][-1] = l_scTySf[l_ty][-1] + [
0 + l_ri * 4 + l_no
]
return l_scTySf[0], l_scTySf[1]
def test_intSfDg(self):
# 1st order
l_subs, l_intSfDg = Hex.intSfDg( 0, ['chi0', 'chi1'], ['xi0', 'xi1', 'xi2'] )
self.assertEqual( l_subs, ( ( ( 'xi0', 'chi0' ),
( 'xi1', 'chi1' ),
( 'xi2', 0 ) ),
( ( 'xi0', 'chi0' ),
( 'xi1', 0 ),
( 'xi2', 'chi1' ) ),
( ( 'xi0', 1 ),
( 'xi1', 'chi0' ),
( 'xi2', 'chi1' ) ),
( ( 'xi0', 'chi0' ),
( 'xi1', 1 ),
( 'xi2', 'chi1' ) ),
( ( 'xi0', 0 ),
( 'xi1', 'chi0' ),
( 'xi2', 'chi1' ) ),
( ( 'xi0', 'chi0' ),
( 'xi1', 'chi1' ),
( 'xi2', 1 ) ) ) )
self.assertEqual( l_intSfDg, [ [ # DG face 0
[ ( 'chi0', 0, 1 ),
( 'chi1', 0, 1 ) ]
],
[ # DG face 1
[ ( 'chi0', 0, 1 ),
( 'chi1', 0, 1 ) ]
],
[ # DG face 2
[ ( 'chi0', 0, 1 ),
( 'chi1', 0, 1 ) ]
],
[ # DG face 3
[ ( 'chi0', 0, 1 ),
( 'chi1', 0, 1 ) ]
],
[ # DG face 4
[ ( 'chi0', 0, 1 ),
( 'chi1', 0, 1 ) ]
],
[ # DG face 5
[ ( 'chi0', 0, 1 ),
( 'chi1', 0, 1 ) ]
] ] )
# 2nd order
l_subs, l_intSfDg = Hex.intSfDg( 1, ['chi0', 'chi1'], ['xi0', 'xi1', 'xi2'] )
self.assertEqual( l_subs, ( ( ( 'xi0', 'chi0' ),
( 'xi1', 'chi1' ),
( 'xi2', 0 ) ),
( ( 'xi0', 'chi0' ),
( 'xi1', 0 ),
( 'xi2', 'chi1' ) ),
( ( 'xi0', 1 ),
( 'xi1', 'chi0' ),
( 'xi2', 'chi1' ) ),
( ( 'xi0', 'chi0' ),
( 'xi1', 1 ),
( 'xi2', 'chi1' ) ),
( ( 'xi0', 0 ),
( 'xi1', 'chi0' ),
( 'xi2', 'chi1' ) ),
( ( 'xi0', 'chi0' ),
( 'xi1', 'chi1' ),
( 'xi2', 1 ) ) ) )
self.assertEqual( l_intSfDg, [ [ # DG face 0
[ ( 'chi0', Fra(0,3), Fra(1,3) ),
( 'chi1', Fra(0,3), Fra(1,3) ) ],
[ ( 'chi0', Fra(1,3), Fra(2,3) ),
( 'chi1', Fra(0,3), Fra(1,3) ) ],
[ ( 'chi0', Fra(2,3), Fra(3,3) ),
( 'chi1', Fra(0,3), Fra(1,3) ) ],
[ ( 'chi0', Fra(0,3), Fra(1,3) ),
( 'chi1', Fra(1,3), Fra(2,3) ) ],
[ ( 'chi0', Fra(1,3), Fra(2,3) ),
( 'chi1', Fra(1,3), Fra(2,3) ) ],
[ ( 'chi0', Fra(2,3), Fra(3,3) ),
( 'chi1', Fra(1,3), Fra(2,3) ) ],
[ ( 'chi0', Fra(0,3), Fra(1,3) ),
( 'chi1', Fra(2,3), Fra(3,3) ) ],
[ ( 'chi0', Fra(1,3), Fra(2,3) ),
( 'chi1', Fra(2,3), Fra(3,3) ) ],
[ ( 'chi0', Fra(2,3), Fra(3,3) ),
( 'chi1', Fra(2,3), Fra(3,3) ) ]
],
[ # DG face 1
[ ( 'chi0', Fra(0,3), Fra(1,3) ),
( 'chi1', Fra(0,3), Fra(1,3) ) ],
[ ( 'chi0', Fra(1,3), Fra(2,3) ),
( 'chi1', Fra(0,3), Fra(1,3) ) ],
[ ( 'chi0', Fra(2,3), Fra(3,3) ),
( 'chi1', Fra(0,3), Fra(1,3) ) ],
[ ( 'chi0', Fra(0,3), Fra(1,3) ),
( 'chi1', Fra(1,3), Fra(2,3) ) ],
[ ( 'chi0', Fra(1,3), Fra(2,3) ),
( 'chi1', Fra(1,3), Fra(2,3) ) ],
[ ( 'chi0', Fra(2,3), Fra(3,3) ),
( 'chi1', Fra(1,3), Fra(2,3) ) ],
[ ( 'chi0', Fra(0,3), Fra(1,3) ),
( 'chi1', Fra(2,3), Fra(3,3) ) ],
[ ( 'chi0', Fra(1,3), Fra(2,3) ),
( 'chi1', Fra(2,3), Fra(3,3) ) ],
[ ( 'chi0', Fra(2,3), Fra(3,3) ),
( 'chi1', Fra(2,3), Fra(3,3) ) ]
],
[ # DG face 2
[ ( 'chi0', Fra(0,3), Fra(1,3) ),
( 'chi1', Fra(0,3), Fra(1,3) ) ],
[ ( 'chi0', Fra(1,3), Fra(2,3) ),
( 'chi1', Fra(0,3), Fra(1,3) ) ],
[ ( 'chi0', Fra(2,3), Fra(3,3) ),
( 'chi1', Fra(0,3), Fra(1,3) ) ],
[ ( 'chi0', Fra(0,3), Fra(1,3) ),
( 'chi1', Fra(1,3), Fra(2,3) ) ],
[ ( 'chi0', Fra(1,3), Fra(2,3) ),
( 'chi1', Fra(1,3), Fra(2,3) ) ],
[ ( 'chi0', Fra(2,3), Fra(3,3) ),
( 'chi1', Fra(1,3), Fra(2,3) ) ],
[ ( 'chi0', Fra(0,3), Fra(1,3) ),
( 'chi1', Fra(2,3), Fra(3,3) ) ],
[ ( 'chi0', Fra(1,3), Fra(2,3) ),
( 'chi1', Fra(2,3), Fra(3,3) ) ],
[ ( 'chi0', Fra(2,3), Fra(3,3) ),
( 'chi1', Fra(2,3), Fra(3,3) ) ]
],
[ # DG face 3
[ ( 'chi0', Fra(0,3), Fra(1,3) ),
( 'chi1', Fra(0,3), Fra(1,3) ) ],
[ ( 'chi0', Fra(1,3), Fra(2,3) ),
( 'chi1', Fra(0,3), Fra(1,3) ) ],
[ ( 'chi0', Fra(2,3), Fra(3,3) ),
( 'chi1', Fra(0,3), Fra(1,3) ) ],
[ ( 'chi0', Fra(0,3), Fra(1,3) ),
( 'chi1', Fra(1,3), Fra(2,3) ) ],
[ ( 'chi0', Fra(1,3), Fra(2,3) ),
( 'chi1', Fra(1,3), Fra(2,3) ) ],
[ ( 'chi0', Fra(2,3), Fra(3,3) ),
( 'chi1', Fra(1,3), Fra(2,3) ) ],
[ ( 'chi0', Fra(0,3), Fra(1,3) ),
( 'chi1', Fra(2,3), Fra(3,3) ) ],
[ ( 'chi0', Fra(1,3), Fra(2,3) ),
( 'chi1', Fra(2,3), Fra(3,3) ) ],
[ ( 'chi0', Fra(2,3), Fra(3,3) ),
( 'chi1', Fra(2,3), Fra(3,3) ) ]
],
[ # DG face 4
[ ( 'chi0', Fra(0,3), Fra(1,3) ),
( 'chi1', Fra(0,3), Fra(1,3) ) ],
[ ( 'chi0', Fra(1,3), Fra(2,3) ),
( 'chi1', Fra(0,3), Fra(1,3) ) ],
[ ( 'chi0', Fra(2,3), Fra(3,3) ),
( 'chi1', Fra(0,3), Fra(1,3) ) ],
[ ( 'chi0', Fra(0,3), Fra(1,3) ),
( 'chi1', Fra(1,3), Fra(2,3) ) ],
[ ( 'chi0', Fra(1,3), Fra(2,3) ),
( 'chi1', Fra(1,3), Fra(2,3) ) ],
[ ( 'chi0', Fra(2,3), Fra(3,3) ),
( 'chi1', Fra(1,3), Fra(2,3) ) ],
[ ( 'chi0', Fra(0,3), Fra(1,3) ),
( 'chi1', Fra(2,3), Fra(3,3) ) ],
[ ( 'chi0', Fra(1,3), Fra(2,3) ),
( 'chi1', Fra(2,3), Fra(3,3) ) ],
[ ( 'chi0', Fra(2,3), Fra(3,3) ),
( 'chi1', Fra(2,3), Fra(3,3) ) ]
],
[ # DG face 5
[ ( 'chi0', Fra(0,3), Fra(1,3) ),
( 'chi1', Fra(0,3), Fra(1,3) ) ],
[ ( 'chi0', Fra(1,3), Fra(2,3) ),
( 'chi1', Fra(0,3), Fra(1,3) ) ],
[ ( 'chi0', Fra(2,3), Fra(3,3) ),
( 'chi1', Fra(0,3), Fra(1,3) ) ],
[ ( 'chi0', Fra(0,3), Fra(1,3) ),
( 'chi1', Fra(1,3), Fra(2,3) ) ],
[ ( 'chi0', Fra(1,3), Fra(2,3) ),
( 'chi1', Fra(1,3), Fra(2,3) ) ],
[ ( 'chi0', Fra(2,3), Fra(3,3) ),
( 'chi1', Fra(1,3), Fra(2,3) ) ],
[ ( 'chi0', Fra(0,3), Fra(1,3) ),
( 'chi1', Fra(2,3), Fra(3,3) ) ],
[ ( 'chi0', Fra(1,3), Fra(2,3) ),
( 'chi1', Fra(2,3), Fra(3,3) ) ],
[ ( 'chi0', Fra(2,3), Fra(3,3) ),
( 'chi1', Fra(2,3), Fra(3,3) ) ]
] ] )
def test_gatherLine(self):
#
# 2nd order
#
l_syms, l_basis = edge_pre.dg.basis.Line.gen( 1 )
l_intIn, l_intSend, l_intSurf = edge_pre.sc.grid.Line.intSc( 1, l_syms )
l_gather = Project.gather( l_basis, l_intIn+l_intSend )
l_gatherUt = sympy.Matrix( [ [ Fra(1, 3), 0 ],
[ Fra(1, 3), -Fra(3, 4) ],
[ Fra(1, 3), Fra(3, 4) ]
])
self.assertEqual( l_gather, l_gatherUt )
#
# 3rd order
#
l_syms, l_basis = edge_pre.dg.basis.Line.gen( 2 )
l_intIn, l_intSend, l_intSurf = edge_pre.sc.grid.Line.intSc( 2, l_syms )
l_gather = Project.gather( l_basis, l_intIn+l_intSend )
l_gatherUt = sympy.Matrix( [ [ Fra(1, 5), -Fra(1, 4), -Fra(25, 84) ],
[ Fra(1, 5), 0, -Fra(25, 42) ],
[ Fra(1, 5), Fra(1, 4), -Fra(25, 84) ],
[ Fra(1, 5), -Fra(1, 2), Fra(25, 42) ],
[ Fra(1, 5), Fra(1, 2), Fra(25, 42) ]
])
self.assertEqual( l_gather, l_gatherUt )
def test_intSfDg(self):
l_xi0 = sympy.symbols('xi_0')
l_xi1 = sympy.symbols('xi_1')
l_chi0 = sympy.symbols('chi_0')
# second order
l_subs, l_intSfDg = Tria.intSfDg( 1, [l_chi0], [l_xi0, l_xi1] )
# check substitutions
self.assertEqual( l_subs, (
( ( l_xi0, l_chi0 ),
( l_xi1, 0 ) ),
( ( l_xi0, 1-l_chi0 ),
( l_xi1, l_chi0 ) ),
( ( l_xi0, 0 ),
( l_xi1, l_chi0 ) )
) )
# check intervals
self.assertEqual( l_intSfDg, [ [ # DG face0
[ ( l_chi0, Fra(0,3), Fra(1,3) ) ],
[ ( l_chi0, Fra(1,3), Fra(2,3) ) ],
[ ( l_chi0, Fra(2,3), Fra(3,3) ) ]
],
[ # DG face1
[ ( l_chi0, Fra(0,3), Fra(1,3) ) ],
[ ( l_chi0, Fra(1,3), Fra(2,3) ) ],
[ ( l_chi0, Fra(2,3), Fra(3,3) ) ]
],
[ # DG face3
[ ( l_chi0, Fra(2,3), Fra(3,3) ) ],
[ ( l_chi0, Fra(1,3), Fra(2,3) ) ],
[ ( l_chi0, Fra(0,3), Fra(1,3) ) ]
] ] )
# third order
l_subs, l_intSfDg = Tria.intSfDg( 2, [l_chi0], [l_xi0, l_xi1] )
# check substitutions
self.assertEqual( l_subs, (
( ( l_xi0, l_chi0 ),
( l_xi1, 0 ) ),
( ( l_xi0, 1-l_chi0 ),
( l_xi1, l_chi0 ) ),
( ( l_xi0, 0 ),
( l_xi1, l_chi0 ) )
) )
self.assertEqual( l_intSfDg, [ [ # DG face0
[ ( l_chi0, Fra(0,5), Fra(1,5) ) ],
[ ( l_chi0, Fra(1,5), Fra(2,5) ) ],
[ ( l_chi0, Fra(2,5), Fra(3,5) ) ],
[ ( l_chi0, Fra(3,5), Fra(4,5) ) ],
[ ( l_chi0, Fra(4,5), Fra(5,5) ) ]
],
[ # DG face1
[ ( l_chi0, Fra(0,5), Fra(1,5) ) ],
[ ( l_chi0, Fra(1,5), Fra(2,5) ) ],
[ ( l_chi0, Fra(2,5), Fra(3,5) ) ],
[ ( l_chi0, Fra(3,5), Fra(4,5) ) ],
[ ( l_chi0, Fra(4,5), Fra(5,5) ) ]
],
[ # DG face3
[ ( l_chi0, Fra(4,5), Fra(5,5) ) ],
[ ( l_chi0, Fra(3,5), Fra(4,5) ) ],
[ ( l_chi0, Fra(2,5), Fra(3,5) ) ],
[ ( l_chi0, Fra(1,5), Fra(2,5) ) ],
[ ( l_chi0, Fra(0,5), Fra(1,5) ) ]
] ] )
def test_svs(self):
# 1st order
l_svs = Hex.svs(0)
self.assertEqual(l_svs, [[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0],
[0, 0, 1], [1, 0, 1], [0, 1, 1], [1, 1, 1]])
# 2nd order
l_svs = Hex.svs(1)
self.assertEqual(l_svs, [
[0, 0, 0],
[Fra(1, 3), 0, 0],
[Fra(2, 3), 0, 0],
[Fra(3, 3), 0, 0],
[0, Fra(1, 3), 0],
[Fra(1, 3), Fra(1, 3), 0],
[Fra(2, 3), Fra(1, 3), 0],
[Fra(3, 3), Fra(1, 3), 0],
[0, Fra(2, 3), 0],
[Fra(1, 3), Fra(2, 3), 0],
[Fra(2, 3), Fra(2, 3), 0],
[Fra(3, 3), Fra(2, 3), 0],
[0, Fra(3, 3), 0],
[Fra(1, 3), Fra(3, 3), 0],
[Fra(2, 3), Fra(3, 3), 0],
[Fra(3, 3), Fra(3, 3), 0],
[0, 0, Fra(1, 3)],
[Fra(1, 3), 0, Fra(1, 3)],
[Fra(2, 3), 0, Fra(1, 3)],
[Fra(3, 3), 0, Fra(1, 3)],
[0, Fra(1, 3), Fra(1, 3)],
[Fra(1, 3), Fra(1, 3), Fra(1, 3)],
[Fra(2, 3), Fra(1, 3), Fra(1, 3)],
[Fra(3, 3), Fra(1, 3), Fra(1, 3)],
[0, Fra(2, 3), Fra(1, 3)],
[Fra(1, 3), Fra(2, 3), Fra(1, 3)],
[Fra(2, 3), Fra(2, 3), Fra(1, 3)],
[Fra(3, 3), Fra(2, 3), Fra(1, 3)],
[0, Fra(3, 3), Fra(1, 3)],
[Fra(1, 3), Fra(3, 3), Fra(1, 3)],
[Fra(2, 3), Fra(3, 3), Fra(1, 3)],
[Fra(3, 3), Fra(3, 3), Fra(1, 3)],
[0, 0, Fra(2, 3)],
[Fra(1, 3), 0, Fra(2, 3)],
[Fra(2, 3), 0, Fra(2, 3)],
[Fra(3, 3), 0, Fra(2, 3)],
[0, Fra(1, 3), Fra(2, 3)],
[Fra(1, 3), Fra(1, 3), Fra(2, 3)],
[Fra(2, 3), Fra(1, 3), Fra(2, 3)],
[Fra(3, 3), Fra(1, 3), Fra(2, 3)],
[0, Fra(2, 3), Fra(2, 3)],
[Fra(1, 3), Fra(2, 3), Fra(2, 3)],
[Fra(2, 3), Fra(2, 3), Fra(2, 3)],
[Fra(3, 3), Fra(2, 3), Fra(2, 3)],
[0, Fra(3, 3), Fra(2, 3)],
[Fra(1, 3), Fra(3, 3), Fra(2, 3)],
[Fra(2, 3), Fra(3, 3), Fra(2, 3)],
[Fra(3, 3), Fra(3, 3), Fra(2, 3)],
[0, 0, Fra(3, 3)],
[Fra(1, 3), 0, Fra(3, 3)],
[Fra(2, 3), 0, Fra(3, 3)],
[Fra(3, 3), 0, Fra(3, 3)],
[0, Fra(1, 3), Fra(3, 3)],
[Fra(1, 3), Fra(1, 3), Fra(3, 3)],
[Fra(2, 3), Fra(1, 3), Fra(3, 3)],
[Fra(3, 3), Fra(1, 3), Fra(3, 3)],
[0, Fra(2, 3), Fra(3, 3)],
[Fra(1, 3), Fra(2, 3), Fra(3, 3)],
[Fra(2, 3), Fra(2, 3), Fra(3, 3)],
[Fra(3, 3), Fra(2, 3), Fra(3, 3)],
[0, Fra(3, 3), Fra(3, 3)],
[Fra(1, 3), Fra(3, 3), Fra(3, 3)],
[Fra(2, 3), Fra(3, 3), Fra(3, 3)],
[Fra(3, 3), Fra(3, 3), Fra(3, 3)],
])
def test_svs(self):
# FV
l_svs = Tria.svs( 0 )
self.assertEqual( l_svs, [ [0,0], [1,0], [0,1] ] )
# 2nd order
l_svs = Tria.svs( 1 )
self.assertEqual( l_svs, [ [0, 0 ], [Fra(1,3), 0], [Fra(2,3), 0], [1, 0],
[0, Fra(1,3)], [Fra(1,3), Fra(1,3)], [Fra(2,3), Fra(1,3)],
[0, Fra(2,3)], [Fra(1,3), Fra(2,3)],
[0, 1] ] )
# 3rd order
l_svs = Tria.svs( 2 )
self.assertEqual( l_svs, [ [0, 0], [Fra(1,5), 0], [Fra(2,5), 0],
[Fra(3,5), 0], [Fra(4,5), 0], [1, 0],
[0, Fra(1,5)], [Fra(1,5), Fra(1,5)], [Fra(2,5), Fra(1,5)],
[Fra(3,5), Fra(1,5)], [Fra(4,5), Fra(1,5)],
[0, Fra(2,5)], [Fra(1,5), Fra(2,5)], [Fra(2,5), Fra(2,5)],
[Fra(3,5), Fra(2,5)],
[0, Fra(3,5)], [Fra(1,5), Fra(3,5)], [Fra(2,5), Fra(3,5)],
[0, Fra(4,5)], [Fra(1,5), Fra(4,5)],
[0, 1] ] )
def test_gen(self):
l_xi1 = sympy.symbols('xi_1')
l_xi2 = sympy.symbols('xi_2')
l_syms, l_basis = Quad.gen(0)
self.assertEqual(l_syms, [l_xi1, l_xi2])
self.assertEqual(l_basis, [1])
l_syms, l_basis = Quad.gen(1)
self.assertEqual(l_syms, [l_xi1, l_xi2])
self.assertEqual(l_basis, [
1, 2 * l_xi1 - 1, 2 * l_xi2 - 1, (2 * l_xi1 - 1) * (2 * l_xi2 - 1)
])
l_syms, l_basis = Quad.gen(2)
self.assertEqual(l_syms, [l_xi1, l_xi2])
self.assertEqual(l_basis, [
sympy.sympify(1), 2 * l_xi1 - 1,
Fra(3, 2) * (2 * l_xi1 - 1)**2 - Fra(1, 2), 2 * l_xi2 - 1,
(2 * l_xi1 - 1) * (2 * l_xi2 - 1),
(2 * l_xi2 - 1) * (Fra(3, 2) * (2 * l_xi1 - 1)**2 - Fra(1, 2)),
Fra(3, 2) * (2 * l_xi2 - 1)**2 - Fra(1, 2),
(2 * l_xi1 - 1) * (Fra(3, 2) * (2 * l_xi2 - 1)**2 - Fra(1, 2)),
((Fra(3, 2) * (2 * l_xi2 - 1)**2 - Fra(1, 2))) *
((Fra(3, 2) * (2 * l_xi1 - 1)**2 - Fra(1, 2)))
])
def test_gen(self):
l_xi1 = sympy.symbols('xi_1')
l_xi2 = sympy.symbols('xi_2')
l_xi3 = sympy.symbols('xi_3')
# P3, hierarchical storage
l_basisUt = [
sympy.sympify(1), 4 * l_xi3 - 1, 3 * l_xi2 + l_xi3 - 1,
2 * l_xi1 + l_xi2 + l_xi3 - 1, 15 * l_xi3**2 - 10 * l_xi3 + 1,
(6 * l_xi3 - 1) * (3 * l_xi2 + l_xi3 - 1), 10 * l_xi2**2 +
8 * l_xi2 * l_xi3 - 8 * l_xi2 + l_xi3**2 - 2 * l_xi3 + 1,
(6 * l_xi3 - 1) * (2 * l_xi1 + l_xi2 + l_xi3 - 1),
(5 * l_xi2 + l_xi3 - 1) * (2 * l_xi1 + l_xi2 + l_xi3 - 1),
-Fra(1, 2) * (l_xi2 + l_xi3 - 1)**2 + Fra(3, 2) *
(2 * l_xi1 + l_xi2 + l_xi3 - 1)**2,
56 * l_xi3**3 - 63 * l_xi3**2 + 18 * l_xi3 - 1,
(3 * l_xi2 + l_xi3 - 1) * (14 * l_xi3 + 7 *
(2 * l_xi3 - 1)**2 - 6),
-(8 * l_xi3 - 1) * (4 * l_xi2 * (l_xi3 - 1)**2 + 3 *
(l_xi3 - 1)**3 - 5 * (l_xi3 - 1) *
(2 * l_xi2 + l_xi3 - 1)**2) / (2 * l_xi3 - 2),
35 * l_xi2**3 + 45 * l_xi2**2 * l_xi3 - 45 * l_xi2**2 +
15 * l_xi2 * l_xi3**2 - 30 * l_xi2 * l_xi3 + 15 * l_xi2 +
l_xi3**3 - 3 * l_xi3**2 + 3 * l_xi3 - 1,
(14 * l_xi3 + 7 *
(2 * l_xi3 - 1)**2 - 6) * (2 * l_xi1 + l_xi2 + l_xi3 - 1),
(8 * l_xi3 - 1) * (5 * l_xi2 + l_xi3 - 1) *
(2 * l_xi1 + l_xi2 + l_xi3 - 1),
-(36 * l_xi2 * (l_xi3 - 1)**2 + 17 * (l_xi3 - 1)**3 - 21 *
(l_xi3 - 1) * (2 * l_xi2 + l_xi3 - 1)**2) *
(2 * l_xi1 + l_xi2 + l_xi3 - 1) / (4 * l_xi3 - 4),
Fra(1, 2) * (8 * l_xi3 - 1) * (-(l_xi2 + l_xi3 - 1)**2 + 3 *
(2 * l_xi1 + l_xi2 + l_xi3 - 1)**2),
Fra(1, 2) * (-(l_xi2 + l_xi3 - 1)**2 + 3 *
(2 * l_xi1 + l_xi2 + l_xi3 - 1)**2) *
(7 * l_xi2 + l_xi3 - 1),
-(6 * l_xi1 * (l_xi2 + l_xi3 - 1)**3 + 3 *
(l_xi2 + l_xi3 - 1)**4 - 5 * (l_xi2 + l_xi3 - 1) *
(2 * l_xi1 + l_xi2 + l_xi3 - 1)**3) / (2 * l_xi2 + 2 * l_xi3 - 2)
]
# check FV basis
l_syms, l_basis = Tet.gen(0)
self.assertEqual(l_syms, [l_xi1, l_xi2, l_xi3])
self.assertEqual(l_basis, [sympy.sympify(1)])
# check degree 1
l_syms, l_basis = Tet.gen(1)
self.assertEqual(l_syms, [l_xi1, l_xi2, l_xi3])
self.assertEqual(len(l_basis), 4)
for l_ba in range(4):
self.assertEqual(sympy.simplify(l_basis[l_ba] - l_basisUt[l_ba]),
0)
# check degree 2
l_syms, l_basis = Tet.gen(2)
self.assertEqual(l_syms, [l_xi1, l_xi2, l_xi3])
self.assertEqual(len(l_basis), 10)
for l_ba in range(10):
self.assertEqual(sympy.simplify(l_basis[l_ba] - l_basisUt[l_ba]),
0)
# check degree 3
l_syms, l_basis = Tet.gen(3)
self.assertEqual(l_syms, [l_xi1, l_xi2, l_xi3])
self.assertEqual(len(l_basis), 20)
for l_ba in range(20):
self.assertEqual(sympy.simplify(l_basis[l_ba] - l_basisUt[l_ba]),
0)