def test_logical_expr_2d_1():
rdim = 2
M = Mapping('M', rdim)
domain = M(Domain('Omega', dim=rdim))
alpha = Constant('alpha')
V = ScalarFunctionSpace('V', domain, kind='h1')
W = VectorFunctionSpace('V', domain, kind='h1')
u, v = [element_of(V, name=i) for i in ['u', 'v']]
w = element_of(W, name='w')
det_M = Jacobian(M).det()
#print('det = ', det_M)
det = Symbol('det')
# ...
expr = 2 * u + alpha * v
expr = LogicalExpr(expr, mapping=M, dim=rdim)
#print(expr)
#print('')
# ...
# ...
expr = dx(u)
expr = LogicalExpr(expr, mapping=M, dim=rdim)
#print(expr.subs(det_M, det))
#print('')
# ...
# ...
expr = dy(u)
expr = LogicalExpr(expr, mapping=M, dim=rdim)
#print(expr.subs(det_M, det))
#print('')
# ...
# ...
expr = dx(det_M)
expr = LogicalExpr(expr, mapping=M, dim=rdim)
expr = expr.subs(det_M, det)
expr = expand(expr)
#print(expr)
#print('')
# ...
# ...
expr = dx(dx(u))
expr = LogicalExpr(expr, mapping=M, dim=rdim)
#print(expr.subs(det_M, det))
#print('')
# ...
# ...
expr = dx(w[0])
expr = LogicalExpr(expr, mapping=M, dim=rdim)
def _visit_PhysicalValueNode(self, expr, **kwargs):
mapping = self.mapping
expr = LogicalExpr(mapping, expr.expr)
expr = SymbolicExpr(expr)
inv_jac = SymbolicInverseDeterminant(mapping)
jac = SymbolicExpr(mapping.det_jacobian)
expr = expr.subs(1 / jac, inv_jac)
return expr
def test_logical_expr_3d_1():
rdim = 3
M = Mapping('M', rdim)
domain = Domain('Omega', dim=rdim)
alpha = Constant('alpha')
V = ScalarFunctionSpace('V', domain)
u, v = [element_of(V, name=i) for i in ['u', 'v']]
det_M = DetJacobian(M)
#print('det = ', det_M)
det = Symbol('det')
# ...
expr = 2 * u + alpha * v
expr = LogicalExpr(M, expr)
#print(expr)
#print('')
# ...
# ...
expr = dx(u)
expr = LogicalExpr(M, expr)
#print(expr.subs(det_M, det))
#print('')
# ...
# ...
expr = dy(u)
expr = LogicalExpr(M, expr)
#print(expr.subs(det_M, det))
#print('')
# ...
# ...
expr = dx(det_M)
expr = LogicalExpr(M, expr)
expr = expr.subs(det_M, det)
expr = expand(expr)
#print(expr)
#print('')
# ...
# ...
expr = dx(dx(u))
expr = LogicalExpr(M, expr)
def test_logical_expr_3d_1():
dim = 3
M = Mapping('M', dim=dim)
domain = M(Domain('Omega', dim=dim))
alpha = Constant('alpha')
V = ScalarFunctionSpace('V', domain, kind='h1')
u, v = [element_of(V, name=i) for i in ['u', 'v']]
det_M = Jacobian(M).det()
#print('det = ', det_M)
det = Symbol('det')
# ...
expr = 2 * u + alpha * v
expr = LogicalExpr(expr, domain)
#print(expr)
#print('')
# ...
# ...
expr = dx(u)
expr = LogicalExpr(expr, domain)
#print(expr.subs(det_M, det))
#print('')
# ...
# ...
expr = dy(u)
expr = LogicalExpr(expr, domain)
#print(expr.subs(det_M, det))
#print('')
# ...
# ...
expr = dx(det_M)
expr = LogicalExpr(expr, domain)
expr = expr.subs(det_M, det)
#print(expr)
#print('')
# ...
# ...
expr = dx(dx(u))
expr = LogicalExpr(expr, domain)
def test_symbolic_expr_1d_1():
rdim = 1
M = Mapping('M', rdim)
domain = M(Domain('Omega', dim=rdim))
alpha = Constant('alpha')
V = ScalarFunctionSpace('V', domain, kind='h1')
u = element_of(V, name='u')
det_M = Jacobian(M).det()
det_M = SymbolicExpr(det_M)
#print('>>> ', det_M)
det = Symbol('det')
# ...
expr = u
expr = LogicalExpr(expr, mapping=M, dim=rdim)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx1(u)
expr = LogicalExpr(expr, mapping=M, dim=rdim)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx1(M[0])
expr = LogicalExpr(expr, mapping=M, dim=rdim)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx(u)
expr = LogicalExpr(expr, mapping=M, dim=rdim)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
#print(expr)
# ...
# ...
expr = dx(Jacobian(M).det())
expr = LogicalExpr(expr, mapping=M, dim=rdim)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
#print(expand(expr))
# ...
# ...
expr = dx(dx(u))
expr = LogicalExpr(expr, mapping=M, dim=rdim)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
#print(expand(expr))
# ...
# ...
expr = dx(dx(dx(u)))
expr = LogicalExpr(expr, mapping=M, dim=rdim)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
def test_symbolic_expr_3d_1():
dim = 3
M = Mapping('M', dim=dim)
domain = M(Domain('Omega', dim=dim))
V = ScalarFunctionSpace('V', domain, kind='h1')
u = element_of(V, 'u')
det_M = Jacobian(M).det()
det_M = SymbolicExpr(det_M)
#print('>>> ', det_M)
det = Symbol('det')
# ...
expr = u
expr = LogicalExpr(expr, domain)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx1(u)
expr = LogicalExpr(expr, domain)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx1(dx2(u))
expr = LogicalExpr(expr, domain)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx1(M[0])
expr = LogicalExpr(expr, domain)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx(u)
expr = LogicalExpr(expr, domain)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
#print(expr)
# ...
# ...
expr = dx(Jacobian(M).det())
expr = LogicalExpr(expr, domain)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
#print(expand(expr))
# ...
# ...
expr = dx(dx(u))
expr = LogicalExpr(expr, domain)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
#print(expand(expr))
# ...
# ...
expr = dx(dx(dx(u)))
expr = LogicalExpr(expr, domain)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
def test_symbolic_expr_3d_1():
rdim = 3
M = Mapping('M', rdim)
domain = Domain('Omega', dim=rdim)
alpha = Constant('alpha')
V = ScalarFunctionSpace('V', domain)
u = element_of(V, 'u')
det_M = DetJacobian(M)
det_M = SymbolicExpr(det_M)
#print('>>> ', det_M)
det = Symbol('det')
# ...
expr = u
expr = LogicalExpr(M, expr)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx1(u)
expr = LogicalExpr(M, expr)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx1(dx2(u))
expr = LogicalExpr(M, expr)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx1(M[0])
expr = LogicalExpr(M, expr)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx(u)
expr = LogicalExpr(M, expr)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
#print(expr)
# ...
# ...
expr = dx(DetJacobian(M))
expr = LogicalExpr(M, expr)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
#print(expand(expr))
# ...
# ...
expr = dx(dx(u))
expr = LogicalExpr(M, expr)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
#print(expand(expr))
# ...
# ...
expr = dx(dx(dx(u)))
expr = LogicalExpr(M, expr)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)