def make_data(switch):
u = sympy.Matrix(sympy.sympify(
"""
((cos(pi*x)+3)*sin(pi*y)*sin(pi*z),
sin(pi*x)*(cos(pi*y)+2)*sin(pi*z),
sin(pi*x)*sin(pi*y)*(cos(pi*z)+2))
"""))
if switch[0] == "T":
l1 = sympy.Matrix(sympy.sympify("(sin(pi*x), -sin(pi*y), 0)"))
else:
l1 = sympy.zeros(3, 1)
if switch[1] == "T":
l2 = sympy.Matrix(sympy.sympify(
"""
(( 1, 2, -1),
( 2, -2, 0),
( 1, 3, 1))
"""))
else:
l2 = sympy.zeros(3, 3)
if switch[2] == "T":
l3 = sympy.Matrix(sympy.sympify(
"""
(( 1, 0, -1),
( 0, -1, 0),
( 1, 2, 1))
"""))
else:
l3 = sympy.zeros(3, 3)
if switch[3] == "T":
l4 = sympy.Matrix(sympy.sympify("(1, 2, -1)"))
else:
l4 = sympy.zeros(3, 1)
if switch[4] == "T":
l5 = sympy.Matrix(sympy.sympify(
"""
(( 10, 0, 0),
( 0, 10, 0),
( 0, 0, 0))
"""))
else:
l5 = sympy.zeros(3, 3)
# compute data in sympy
du = S.div(u)
sigma = S.curl(u) + l2 * u
dsigma = S.curl(sigma)
f = dsigma + l3 * sigma - S.grad(du) - S.grad(l1.dot(u)) + l4 * du + l5 * u
# convert to FEniCS
f = Expression(S.sympy2exp(f))
ext_sols = map(Expression, map(S.sympy2exp, (sigma, dsigma, u, du)))
lots = map(Expression, map(S.sympy2exp, (l1, l2, l3, l4, l5)))
return (f, lots, ext_sols)
def make_data(switch):
u = sympy.Matrix(
sympy.sympify("""
((cos(pi*x)+3)*sin(pi*y)*sin(pi*z),
sin(pi*x)*(cos(pi*y)+2)*sin(pi*z),
sin(pi*x)*sin(pi*y)*(cos(pi*z)+2))
"""))
if switch[0] == "T":
l1 = sympy.Matrix(sympy.sympify("(sin(pi*x), -sin(pi*y), 0)"))
else:
l1 = sympy.zeros(3, 1)
if switch[1] == "T":
l2 = sympy.Matrix(
sympy.sympify("""
(( 1, 2, -1),
( 2, -2, 0),
( 1, 3, 1))
"""))
else:
l2 = sympy.zeros(3, 3)
if switch[2] == "T":
l3 = sympy.Matrix(
sympy.sympify("""
(( 1, 0, -1),
( 0, -1, 0),
( 1, 2, 1))
"""))
else:
l3 = sympy.zeros(3, 3)
if switch[3] == "T":
l4 = sympy.Matrix(sympy.sympify("(1, 2, -1)"))
else:
l4 = sympy.zeros(3, 1)
if switch[4] == "T":
l5 = sympy.Matrix(
sympy.sympify("""
(( 10, 0, 0),
( 0, 10, 0),
( 0, 0, 0))
"""))
else:
l5 = sympy.zeros(3, 3)
# compute data in sympy
du = S.div(u)
sigma = S.curl(u) + l2 * u
dsigma = S.curl(sigma)
f = dsigma + l3 * sigma - S.grad(du) - S.grad(l1.dot(u)) + l4 * du + l5 * u
# convert to FEniCS
f = Expression(S.sympy2exp(f))
ext_sols = map(Expression, map(S.sympy2exp, (sigma, dsigma, u, du)))
lots = map(Expression, map(S.sympy2exp, (l1, l2, l3, l4, l5)))
return (f, lots, ext_sols)
def make_data(switch):
u = sympy.Matrix(sympy.sympify(
"""
(sin(pi*x)*cos(pi*z),
cos(pi*x)*sin(pi*y),
cos(pi*y)*sin(pi*z))
"""))
if switch[0] == "T":
l1 = sympy.Matrix(sympy.sympify(
"""
((sin(pi*y)*sin(pi*z), sin(pi*z), sin(pi*y)),
(sin(pi*z), sin(pi*x)*sin(pi*z), sin(pi*x)),
(sin(pi*y), sin(pi*x), sin(pi*x)*sin(pi*y)))
"""))
else:
l1 = sympy.zeros(3, 3)
if switch[1] == "T":
l2 = sympy.Matrix(sympy.sympify("(2, 0, 1)"))
else:
l2 = sympy.zeros(3, 1)
if switch[2] == "T":
l3 = sympy.Matrix(sympy.sympify("(3, 2, -1)"))
else:
l3 = sympy.zeros(3, 1)
if switch[3] == "T":
l4 = sympy.Matrix(sympy.sympify(
"""
(( 1, 2, -1),
( 3, -3, -3),
( 1, 3, 1))
"""))
else:
l4 = sympy.zeros(3, 3)
if switch[4] == "T":
# l5 = sympy.Matrix(sympy.sympify(
# """
# (( 10, 0, 0),
# ( 0, 10, 0),
# ( 0, 0, 0))
# """))
l5 = sympy.Matrix(sympy.sympify(
"""
((10, 0, 0),
( 0, 10, 0),
( 0, 0, 10))
"""))
else:
l5 = sympy.zeros(3, 3)
# compute data in sympy
du = S.curl(u)
sigma = -S.div(u) + l2.dot(u)
dsigma = S.grad(sigma)
f = dsigma + l3 * sigma + S.curl(du) + l4 * du + S.curl(l1 * u) + l5 * u
# convert to FEniCS
f = Expression(S.sympy2exp(f))
ext_sols = map(Expression, map(S.sympy2exp, (sigma, dsigma, u, du)))
lots = map(Expression, map(S.sympy2exp, (l1, l2, l3, l4, l5)))
return (f, lots, ext_sols)
def make_data(switch):
u = sympy.Matrix(
sympy.sympify("""
(sin(pi*x)*cos(pi*z),
cos(pi*x)*sin(pi*y),
cos(pi*y)*sin(pi*z))
"""))
if switch[0] == "T":
l1 = sympy.Matrix(
sympy.sympify("""
((sin(pi*y)*sin(pi*z), sin(pi*z), sin(pi*y)),
(sin(pi*z), sin(pi*x)*sin(pi*z), sin(pi*x)),
(sin(pi*y), sin(pi*x), sin(pi*x)*sin(pi*y)))
"""))
else:
l1 = sympy.zeros(3, 3)
if switch[1] == "T":
l2 = sympy.Matrix(sympy.sympify("(2, 0, 1)"))
else:
l2 = sympy.zeros(3, 1)
if switch[2] == "T":
l3 = sympy.Matrix(sympy.sympify("(3, 2, -1)"))
else:
l3 = sympy.zeros(3, 1)
if switch[3] == "T":
l4 = sympy.Matrix(
sympy.sympify("""
(( 1, 2, -1),
( 3, -3, -3),
( 1, 3, 1))
"""))
else:
l4 = sympy.zeros(3, 3)
if switch[4] == "T":
# l5 = sympy.Matrix(sympy.sympify(
# """
# (( 10, 0, 0),
# ( 0, 10, 0),
# ( 0, 0, 0))
# """))
l5 = sympy.Matrix(
sympy.sympify("""
((10, 0, 0),
( 0, 10, 0),
( 0, 0, 10))
"""))
else:
l5 = sympy.zeros(3, 3)
# compute data in sympy
du = S.curl(u)
sigma = -S.div(u) + l2.dot(u)
dsigma = S.grad(sigma)
f = dsigma + l3 * sigma + S.curl(du) + l4 * du + S.curl(l1 * u) + l5 * u
# convert to FEniCS
f = Expression(S.sympy2exp(f))
ext_sols = map(Expression, map(S.sympy2exp, (sigma, dsigma, u, du)))
lots = map(Expression, map(S.sympy2exp, (l1, l2, l3, l4, l5)))
return (f, lots, ext_sols)