Rheolef  7.1
an efficient C++ finite element environment
neumann-laplace-lambda.cc
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1 #include "rheolef.h"
26 using namespace rheolef;
27 using namespace std;
28 size_t d;
29 Float f (const point& x) { return 1; }
30 Float g (const point& x) { return -0.5/d; }
31 int main(int argc, char**argv) {
32  environment rheolef (argc, argv);
33  geo omega (argv[1]);
34  d = omega.dimension();
35  space Xh (omega, argv[2]);
36  trial u (Xh); test v (Xh);
37  form a = integrate (dot(grad(u),grad(v)));
38  field b = integrate(v);
39  field lh = integrate (f*v) + integrate ("boundary", g*v);
40  form A = {{ a, b},
41  { trans(b), 0}};
42  field B = { lh, 0};
43  A.set_symmetry(true);
44  space IR = space::real();
45  space Yh = Xh*IR;
46  field Uh (Yh,0);
47  problem p (A);
48  p.solve (B, Uh);
49  dout << catchmark("u") << Uh[0];
50  // get lambda:
51  Float lambda = (Uh.comm().rank() == Uh.constraint_process_rank()) ? Uh[1].dof(0) : 0;
52 #ifdef _RHEOLEF_HAVE_MPI
53  mpi::broadcast (Uh.comm(), lambda, Uh.constraint_process_rank());
54 #endif // _RHEOLEF_HAVE_MPI
55  dout << catchmark("lambda") << lambda << endl;
56  check_macro(fabs(lambda) < 1e-10, "unexpected lambda="<<lambda);
57 }
g
Float g(const point &x)
Definition: neumann-laplace-lambda.cc:30
form
see the form page for the full documentation
rheolef::catchmark
see the catchmark page for the full documentation
Definition: catchmark.h:67
mkgeo_ball.b
int b
Definition: mkgeo_ball.sh:152
rheolef::dot
rheolef::std enable_if ::type dot const Expr1 expr1, const Expr2 expr2 dot(const Expr1 &expr1, const Expr2 &expr2)
dot(x,y): see the expression page for the full documentation
Definition: vec_expr_v2.h:415
field
see the field page for the full documentation
rheolef::integrate
std::enable_if< details::is_field_expr_v2_nonlinear_arg< Expr >::value &&! is_undeterminated< Result >::value, Result >::type integrate(const geo_basic< T, M > &omega, const Expr &expr, const integrate_option &iopt, Result dummy=Result())
see the integrate page for the full documentation
Definition: integrate.h:202
main
int main(int argc, char **argv)
Definition: neumann-laplace-lambda.cc:31
d
size_t d
Definition: neumann-laplace-lambda.cc:28
space
see the space page for the full documentation
rheolef::grad
std::enable_if< details::is_field_convertible< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::memory_type,details::differentiate_option::gradient >>::type grad(const Expr &expr)
grad(uh): see the expression page for the full documentation
Definition: field_expr_terminal.h:911
rheolef.h
rheolef - reference manual
p
Definition: sphere.icc:25
a
Definition: diffusion_isotropic.h:25
rheolef::environment
see the environment page for the full documentation
Definition: environment.h:115
lh
field lh(Float epsilon, Float t, const test &v)
Definition: burgers_diffusion_operators.icc:25
rheolef
This file is part of Rheolef.
Definition: compiler_eigen.h:37
test
see the test page for the full documentation
problem
see the problem page for the full documentation
u
Definition: leveque.h:25
Float
see the Float page for the full documentation
point
see the point page for the full documentation
u
Float u(const point &x)
Definition: transmission_error.cc:26
g
Definition: cavity_dg.h:25
trial
see the test page for the full documentation
f
Float f(const point &x)
Definition: neumann-laplace-lambda.cc:29
mkgeo_ball.a
int a
Definition: mkgeo_ball.sh:151
rheolef::dout
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:430
f
Definition: cavity_dg.h:29
rheolef::trans
csr< T, sequential > trans(const csr< T, sequential > &a)
trans(a): see the form page for the full documentation
Definition: csr.h:455
rheolef::std
Definition: vec_expr_v2.h:402
geo
see the geo page for the full documentation
lambda
Definition: yield_slip_circle.h:34