void
DrivenCavity<Dim>::Jacobian(const vector_ptrtype& X, sparse_matrix_ptrtype& J)
{
auto U = Vh->element( "(u,p)" );
auto V = Vh->element( "(v,q)" );
auto u = U.template element<0>( "u" );
auto v = V.template element<0>( "u" );
auto p = U.template element<1>( "p" );
auto q = V.template element<1>( "p" );
//#if defined( FEELPP_USE_LM )
auto lambda = U.template element<2>();
auto nu = V.template element<2>();
//#endif
if (!J) J = backend(_name="newtonns")->newMatrix( Vh, Vh );
auto a = form2( _test=Vh, _trial=Vh, _matrix=J );
a = integrate( elements( mesh ), inner(gradt( u ),grad( v ))/Re );
a += integrate( elements( mesh ), id(q)*divt(u) -idt(p)*div(v) );
// Convective terms
a += integrate( elements( mesh ), trans(id(v))*gradv(u)*idt(u));
a += integrate( elements( mesh ), trans(id(v))*gradt(u)*idv(u));
//#if defined( FEELPP_USE_LM )
a += integrate(elements(mesh), id(q)*idt(lambda)+idt(p)*id(nu));
//#elif
//a += integrate(elements(mesh), idt(p)*id(nu));
//Weak Dirichlet conditions
a += integrate( boundaryfaces( mesh ),-trans( -idt(p)*N()+gradt(u)*N()/Re )*id( v ));//
a += integrate( boundaryfaces( mesh ),-trans( -id(p)*N()+grad(u)*N()/Re )*idt( u ));//
a += integrate( boundaryfaces( mesh ), +penalbc*inner( idt( u ),id( v ) )/hFace() );
}
void
TestInterpolationHCurl::testInterpolation( std::string one_element_mesh )
{
// expr to interpolate
auto myexpr = unitX() + unitY(); //(1,1)
// one element mesh
auto mesh_name = one_element_mesh + ".msh"; //create the mesh and load it
fs::path mesh_path( mesh_name );
mesh_ptrtype oneelement_mesh = loadMesh( _mesh=new mesh_type,
_filename=mesh_name);
// refined mesh (export)
auto refine_level = std::floor(1 - math::log( 0.1 )); //Deduce refine level from meshSize (option)
mesh_ptrtype mesh = loadMesh( _mesh=new mesh_type,
_filename=mesh_name,
_refine=( int )refine_level);
space_ptrtype Xh = space_type::New( oneelement_mesh );
std::vector<std::string> faces, edges; //list of edges
edges = {"hypo","vert","hor"};
element_type U_h_int = Xh->element();
element_type U_h_on = Xh->element();
element_type U_h_on_boundary = Xh->element();
// handly computed interpolant coeff (in hcurl basis)
for ( int i = 0; i < Xh->nLocalDof(); ++i )
{
CHECK( oneelement_mesh->hasMarkers( {edges[i]} ) );
U_h_int(i) = integrate( markedfaces( oneelement_mesh, edges[i] ), trans( T() )*myexpr ).evaluate()(0,0);
}
// nedelec interpolant using on
U_h_on.zero();
U_h_on.on(_range=elements(oneelement_mesh), _expr=myexpr);
U_h_on_boundary.on(_range=boundaryfaces(oneelement_mesh), _expr=myexpr);
auto exporter_proj = exporter( _mesh=mesh, _name=( boost::format( "%1%" ) % this->about().appName() ).str() );
exporter_proj->step( 0 )->add( "U_interpolation_handly_"+mesh_path.stem().string(), U_h_int );
exporter_proj->step( 0 )->add( "U_interpolation_on_"+mesh_path.stem().string(), U_h_on );
exporter_proj->save();
// print coefficient only for reference element
U_h_int.printMatlab( "U_h_int_" + mesh_path.stem().string() + ".m" );
U_h_on.printMatlab( "U_h_on_" + mesh_path.stem().string() + ".m" );
U_h_on_boundary.printMatlab( "U_h_on_boundary_" + mesh_path.stem().string() + ".m" );
//L2 norm of error
auto error = vf::project(_space=Xh, _range=elements(oneelement_mesh), _expr=idv(U_h_int) - idv(U_h_on) );
double L2error = error.l2Norm();
std::cout << "L2 error (elements) = " << L2error << std::endl;
auto error_boundary = vf::project(_space=Xh, _range=boundaryfaces(oneelement_mesh), _expr=idv(U_h_int) - idv(U_h_on_boundary) );
double L2error_boundary = error_boundary.l2Norm();
std::cout << "L2 error (boundary) = " << L2error_boundary << std::endl;
BOOST_CHECK_SMALL( L2error_boundary - L2error, 1e-13 );
}
// <int Order_s, int Order_p, int Order_t>
void Convection::updateJacobian2( const vector_ptrtype& X,
sparse_matrix_ptrtype& D )
{
mesh_ptrtype mesh = Xh->mesh();
element_type U( Xh, "u" );
U = *X;
LOG(INFO) << "[updateJacobian] ||X|| = " << U.l2Norm() << "\n";
element_type V( Xh, "v" );
element_type W( Xh, "v" );
element_0_type u = U. element<0>(); // fonction vitesse
element_0_type v = V. element<0>(); // fonction test vitesse
element_1_type p = U. element<1>(); // fonction pression
element_1_type q = V. element<1>(); // fonction test pression
element_2_type t = U. element<2>(); // fonction temperature
element_2_type s = V. element<2>(); // fonction test temperature
#if defined( FEELPP_USE_LM )
element_3_type xi = U. element<3>(); // fonction multipliers
element_3_type eta = V. element<3>(); // fonction test multipliers
#endif
double gr= M_current_Grashofs;
double sqgr( 1/math::sqrt( gr ) );
double pr = M_current_Prandtl;
double sqgrpr=( 1/( pr*math::sqrt( gr ) ) );
double gamma( this->vm()["penalbc"]. as<double>() );
double dt=this->vm()["dt"]. as<double>();
int adim=this->vm()["adim"]. as<int>();
double pC=1;
if ( adim == 0 ) pC = this->vm()["pC"]. as<double>();
//
// temperature derivatives
//
// heat convection by the fluid: attention 2 terms
form2( _test=Xh, _trial=Xh, _matrix=D ) +=
integrate ( elements( mesh ),
pC*grad( s )*( idv( t )*idt( u ) ) );
form2( _test=Xh, _trial=Xh, _matrix=D ) +=
integrate ( elements( mesh ),
pC*grad( s )*( idt( t )*idv( u ) ) );
form2( _test=Xh, _trial=Xh, _matrix=D ) +=
integrate ( boundaryfaces( mesh ),
pC*( trans( idv( u ) )*N() )*id( s )*idt( t ) );
form2( _test=Xh, _trial=Xh, _matrix=D ) +=
integrate ( boundaryfaces( mesh ),
pC*( trans( idt( u ) )*N() )*id( s )*idv( t ) );
LOG(INFO) << "[updateJacobian2] Temperature convection terms done\n";
LOG(INFO) << "[updateJacobian2] Temperature weak Dirichlet BC terms done\n";
}
boost::tuple<mpl::size_t<MESH_FACES>,
typename MeshTraits<MeshType>::location_face_const_iterator,
typename MeshTraits<MeshType>::location_face_const_iterator>
boundaryfaces( MeshType const& mesh, rank_type __pid, mpl::bool_<true> )
{
return boundaryfaces( *mesh, __pid, mpl::bool_<false>() );
}
void
DrivenCavity<Dim>::Residual(const vector_ptrtype& X, vector_ptrtype& R)
{
auto U = Vh->element( "(u,p)" );
auto V = Vh->element( "(v,q)" );
auto u = U.template element<0>( "u" );
//auto u_exact = U.template element<0>( "u_exact" );
auto v = V.template element<0>( "u" );
auto p = U.template element<1>( "p" );
auto q = V.template element<1>( "p" );
//#if defined( FEELPP_USE_LM )
auto lambda = U.template element<2>();
auto nu = V.template element<2>();
//#endif
auto uex=unitX();
auto u_exact=vf::project(Vh->template functionSpace<0>(), markedfaces(mesh, "wall2"), uex );
U=*X;
auto r = form1( _test=Vh, _vector=R );
//r += integrate( elements( mesh ),-inner( f,id( v ) ) );
r = integrate( elements( mesh ), trans(gradv( u )*idv(u))*id(v));//convective term
r += integrate( elements( mesh ), inner(gradv( u ),grad( v ))/Re );
r += integrate( elements( mesh ),-idv(p)*div(v) + id(q)*divv(u));
//#if defined( FEELPP_USE_LM )
r += integrate ( elements( mesh ), +id( q )*idv( lambda )+idv( p )*id( nu ) );
//#endif
//Weak Dirichlet
auto SigmaNv = ( -idv( p )*N() + gradv( u )*N()/Re );
auto SigmaN = ( -id( q )*N() + grad( v )*N()/Re );
r +=integrate ( boundaryfaces(mesh), - trans( SigmaNv )*id( v ) - trans( SigmaN )*( idv( u ) -idv(u_exact) ) + penalbc*trans( idv( u ) - idv(u_exact) )*id( v )/hFace() );
}
int
PreconditionerAS<space_type,coef_space_type>::applyInverse ( const vector_type& X /*R*/, vector_type& Y /*W*/) const
{
/*
* We solve Here P_v w = r
* With P_v^-1 = diag(P_m)^-1 (=A)
* + P (\bar L + g \bar Q) P^t (=B)
* + C (L^-1) C^T (=C)
*/
U = X;
U.close();
// solve equ (12)
if ( this->type() == AS )
{
tic();
*M_r = U;
M_r->close();
// step A : diag(Pm)^-1*r
A->pointwiseDivide(*M_r,*M_diagPm);
A->close();
// s = P^t r
M_Pt->multVector(M_r,M_s);
// Impose boundary conditions on M_s
#if 1
M_qh3_elt = *M_s;
M_qh3_elt.close();
#if FEELPP_DIM == 3
M_qh3_elt.on( _range=boundaryfaces( M_Qh3->mesh() ), _expr=vec(cst(0.), cst(0.), cst(0.)) );
#else
M_qh3_elt.on( _range=boundaryfaces( M_Qh3->mesh() ), _expr=vec(cst(0.), cst(0.)) );
#endif
*M_s = M_qh3_elt;
M_s->close();
#endif
#if 1
// Subvectors for M_s (per component) need to be updated
M_s1 = M_s->createSubVector(M_Qh3_indices[0], true);
M_s2 = M_s->createSubVector(M_Qh3_indices[1], true);
#if FEELPP_DIM == 3
M_s3 = M_s->createSubVector(M_Qh3_indices[2], true);
#endif
#else
// s = [ s1, s2, s3 ]
M_s->updateSubVector(M_s1, M_Qh3_indices[0]);
M_s->updateSubVector(M_s2, M_Qh3_indices[1]);
#if FEELPP_DIM == 3
M_s->updateSubVector(M_s3, M_Qh3_indices[2]);
#endif
#endif
M_s->close();
/*
* hat(L) + g Q is a (Qh,Qh) matrix
* [[ hat(L) + g Q, 0 , 0 ], [ y1 ] [ s1 ]
* [ 0, hat(L) + g Q, 0 ], * [ y2 ] = [ s2 ]
* [ 0, 0 , hat(L) + g Q ]] [ y3 ] [ s3 ]
*/
M_lgqOp->applyInverse(M_s1,M_y1);
M_lgqOp->applyInverse(M_s2,M_y2);
#if FEELPP_DIM == 3
M_lgqOp->applyInverse(M_s3,M_y3);
#endif
// y = [ y1, y2, y3 ]
M_y->updateSubVector(M_y1, M_Qh3_indices[0]);
M_y->updateSubVector(M_y2, M_Qh3_indices[1]);
#if FEELPP_DIM == 3
M_y->updateSubVector(M_y3, M_Qh3_indices[2]);
#endif
M_y->close();
// step B : P*y
M_P->multVector(M_y,B);
// Impose boundary conditions on B = Py
#if 1
M_vh_elt = *B;
M_vh_elt.close();
#if FEELPP_DIM == 3
M_vh_elt.on( _range=boundaryfaces( M_Qh3->mesh() ), _expr=vec(cst(0.), cst(0.), cst(0.)) );
#else
M_vh_elt.on( _range=boundaryfaces( M_Qh3->mesh() ), _expr=vec(cst(0.), cst(0.)) );
#endif
*B = M_vh_elt;
B->close();
#endif
// t = C^t r
M_Ct->multVector(M_r,M_t);
// Impose boundary conditions on M_t
#if 1
M_qh_elt = *M_t;
M_qh_elt.close();
M_qh_elt.on( _range=boundaryfaces( M_Qh3->mesh() ), _expr=cst(0.) );
*M_t = M_qh_elt;
M_t->close();
#endif
// 14.b : hat(L) z = t
M_lOp->applyInverse(M_t,M_z);
M_z->close();
// step C : M_C z
M_C->multVector(M_z,C);
C->scale(1./M_g);
// Impose boundary conditions on C = Cz
#if 1
M_vh_elt = *C;
M_vh_elt.close();
#if FEELPP_DIM == 3
M_vh_elt.on( _range=boundaryfaces( M_Qh3->mesh() ), _expr=vec(cst(0.), cst(0.), cst(0.)) );
#else
M_vh_elt.on( _range=boundaryfaces( M_Qh3->mesh() ), _expr=vec(cst(0.), cst(0.)) );
#endif
*C = M_vh_elt;
C->close();
#endif
//if(M_g != 1.0)
A->add(*C);
A->add(*B);
C->close();
B->close();
A->close();
toc("assemble preconditioner AS",FLAGS_v>0);
*M_uout = *A; // 15 : w = A + B + C
}
else if( this->type() == SIMPLE )
{
SimpleOp->applyInverse(X, Y);
*M_uout = Y;
}
else
{
Y=U;
*M_uout = Y;
}
M_uout->close();
tic();
Y=*M_uout;
Y.close();
toc("PreconditionerAS::applyInverse", FLAGS_v>0 );
return 0;
}
void run()
{
Environment::changeRepository( boost::format( "/testsuite/feeldiscr/%1%/P%2%/" )
% Environment::about().appName()
% OrderPoly );
/* change parameters below */
const int nDim = 2;
const int nOrderPoly = OrderPoly;
const int nOrderGeo = 1;
//------------------------------------------------------------------------------//
typedef Mesh< Simplex<nDim, 1,nDim> > mesh_type;
typedef Mesh< Simplex<nDim, 1,nDim> > mesh_bis_type;
double meshSize = option("hsize").as<double>();
double meshSizeBis = option("hsize-bis").as<double>();
// mesh
GeoTool::Node x1( 0,0 );
GeoTool::Node x2( 4,1 );
GeoTool::Rectangle Omega( meshSize,"Omega",x1,x2 );
Omega.setMarker( _type="line",_name="Entree",_marker4=true );
Omega.setMarker( _type="line",_name="Sortie",_marker2=true );
Omega.setMarker( _type="line",_name="Paroi",_marker1=true,_marker3=true );
Omega.setMarker( _type="surface",_name="Fluid",_markerAll=true );
auto mesh = Omega.createMesh(_mesh=new mesh_type,_name="omega_"+ mesh_type::shape_type::name() );
LOG(INFO) << "created mesh\n";
GeoTool::Rectangle OmegaBis( meshSizeBis,"Omega",x1,x2 );
OmegaBis.setMarker( _type="line",_name="Entree",_marker4=true );
OmegaBis.setMarker( _type="line",_name="Sortie",_marker2=true );
OmegaBis.setMarker( _type="line",_name="Paroi",_marker1=true,_marker3=true );
OmegaBis.setMarker( _type="surface",_name="Fluid",_markerAll=true );
auto meshBis = OmegaBis.createMesh(_mesh=new mesh_bis_type,_name="omegaBis_"+ mesh_type::shape_type::name() );
//auto meshBis= mesh->createP1mesh();
LOG(INFO) << "created meshBis\n";
typedef Lagrange<nOrderPoly,Scalar,Continuous,PointSetFekete> basis_type;
typedef FunctionSpace<mesh_type, bases<basis_type> > space_type;
auto Xh = space_type::New( mesh );
auto u = Xh->element();
auto v = Xh->element();
auto u2 = Xh->element();
LOG(INFO) << "created space and elements\n";
auto mybackend = backend();
//--------------------------------------------------------------//
auto A = mybackend->newMatrix( Xh, Xh );
auto F = mybackend->newVector( Xh );
auto pi = cst( M_PI );
auto u_exact = cos( pi*Px() )*sin( pi*Py() );
auto dudx = -pi*sin( pi*Px() )*sin( pi*Py() );
auto dudy = pi*cos( pi*Px() )*cos( pi*Py() );
auto grad_u_uexact = vec( dudx,dudy );
auto lap = -2*pi*pi*cos( pi*Px() )*sin( pi*Py() );
//auto lap = -pi*pi*cos(pi*Px())*sin(pi*Py())
// -pi*pi*cos(pi*Px())*sin(pi*Py());
LOG(INFO) << "created exact data and matrix/vector\n";
auto f = -lap;//cst(1.);
double gammabc=10;
// assemblage
form2( Xh, Xh, A, _init=true ) =
integrate( elements( mesh ), //_Q<15>(),
+ gradt( u )*trans( grad( v ) ) );
form2( Xh, Xh, A ) +=
integrate( boundaryfaces( mesh ),
- gradt( u )*N()*id( v )
+ gammabc*idt( u )*id( v )/hFace() );
form1( Xh, F, _init=true ) =
integrate( elements( mesh ), // _Q<10>(),
trans( f )*id( v ) );
form1( Xh, F ) +=
integrate( boundaryfaces( mesh ),
+ gammabc*u_exact*id( v )/hFace() );
LOG(INFO) << "A,F assembled\n";
//form2( Xh, Xh, A ) +=
// on( boundaryfaces(mesh) , u, F, u_exact );
// solve system
mybackend->solve( A,u,F );
LOG(INFO) << "A u = F solved\n";
//--------------------------------------------------------------//
auto a2 = form2( _test=Xh, _trial=Xh );
auto f2 = form1( _test=Xh );
LOG(INFO) << "created form2 a2 and form1 F2\n";
// assemblage
a2 = integrate( elements( meshBis ),
+ gradt( u2 )*trans( grad( v ) ),
_Q<10>() );
LOG(INFO) << "a2 grad.grad term\n";
a2 += integrate( boundaryfaces( meshBis ),
- gradt( u2 )*N()*id( v )
+ gammabc*idt( u2 )*id( v )/hFace(),
_Q<10>() );
LOG(INFO) << "a2 weak dirichlet terms\n";
f2 = integrate( elements( meshBis ),
trans( f )*id( v ),
_Q<10>() );
LOG(INFO) << "f2 source term\n";
f2 += integrate( boundaryfaces( meshBis ),
+ gammabc*u_exact*id( v )/hFace(),
_Q<10>() );
LOG(INFO) << "f2 dirichlet terms\n";
LOG(INFO) << "a2,f2 assembled\n";
//form2( Xh, Xh, A2 ) +=
// on( boundaryfaces(mesh) , u2, F2, u_exact );
#if 0
for ( size_type i = 0 ; i< F->size() ; ++i )
{
auto errOnF = std::abs( ( *F )( i )-( *F2 )( i ) );
if ( errOnF > 1e-8 )
std::cout << "\nerrOnF : " << errOnF;
}
std::cout << "\nFin errOnF !!!!\n";
#endif
// solve system
a2.solve( _rhs=f2, _solution=u2 );
auto diff = std::sqrt( integrate( elements( mesh ), ( idv( u )-idv( u2 ) )*( idv( u )-idv( u2 ) ) ).evaluate()( 0,0 ) );
#if 0
auto int1 = integrate( elements( mesh ), abs( idv( u ) ) ).evaluate()( 0,0 );
auto int2 = integrate( elements( mesh ), abs( idv( u2 ) ) ).evaluate()( 0,0 );
std::cout << "\nThe diff : " << diff
<< " int1 :" << int1
<< " int2 :" << int2
<< "\n";
#endif
#if USE_BOOST_TEST
BOOST_CHECK_SMALL( diff,1e-2 );
#endif
//--------------------------------------------------------------//
if ( option("exporter.export").as<bool>() )
{
// export
auto ex = exporter( _mesh=mesh );
ex->add( "u", u );
ex->add( "ubis", u2 );
ex->save();
}
}
void
NavierStokes::run()
{
this->init();
auto U = Xh->element( "(u,p)" );
auto V = Xh->element( "(u,q)" );
auto u = U.element<0>( "u" );
auto v = V.element<0>( "u" );
auto p = U.element<1>( "p" );
auto q = V.element<1>( "p" );
#if defined( FEELPP_USE_LM )
auto lambda = U.element<2>();
auto nu = V.element<2>();
#endif
//# endmarker4 #
LOG(INFO) << "[dof] number of dof: " << Xh->nDof() << "\n";
LOG(INFO) << "[dof] number of dof/proc: " << Xh->nLocalDof() << "\n";
LOG(INFO) << "[dof] number of dof(U): " << Xh->functionSpace<0>()->nDof() << "\n";
LOG(INFO) << "[dof] number of dof/proc(U): " << Xh->functionSpace<0>()->nLocalDof() << "\n";
LOG(INFO) << "[dof] number of dof(P): " << Xh->functionSpace<1>()->nDof() << "\n";
LOG(INFO) << "[dof] number of dof/proc(P): " << Xh->functionSpace<1>()->nLocalDof() << "\n";
LOG(INFO) << "Data Summary:\n";
LOG(INFO) << " hsize = " << meshSize << "\n";
LOG(INFO) << " export = " << this->vm().count( "export" ) << "\n";
LOG(INFO) << " mu = " << mu << "\n";
LOG(INFO) << " bccoeff = " << penalbc << "\n";
//# marker5 #
auto deft = gradt( u )+trans(gradt(u));
auto def = grad( v )+trans(grad(v));
//# endmarker5 #
//# marker6 #
// total stress tensor (trial)
auto SigmaNt = -idt( p )*N()+mu*deft*N();
// total stress tensor (test)
auto SigmaN = -id( p )*N()+mu*def*N();
//# endmarker6 #
auto F = M_backend->newVector( Xh );
auto D = M_backend->newMatrix( Xh, Xh );
// right hand side
auto ns_rhs = form1( _test=Xh, _vector=F );
LOG(INFO) << "[navier-stokes] vector local assembly done\n";
// construction of the BDF
auto bdfns=bdf(_space=Xh);
/*
* Construction of the left hand side
*/
auto navierstokes = form2( _test=Xh, _trial=Xh, _matrix=D );
mpi::timer chrono;
navierstokes += integrate( elements( mesh ), mu*inner( deft,def )+ trans(idt( u ))*id( v )*bdfns->polyDerivCoefficient( 0 ) );
LOG(INFO) << "mu*inner(deft,def)+(bdf(u),v): " << chrono.elapsed() << "\n";
chrono.restart();
navierstokes +=integrate( elements( mesh ), - div( v )*idt( p ) + divt( u )*id( q ) );
LOG(INFO) << "(u,p): " << chrono.elapsed() << "\n";
chrono.restart();
#if defined( FEELPP_USE_LM )
navierstokes +=integrate( elements( mesh ), id( q )*idt( lambda ) + idt( p )*id( nu ) );
LOG(INFO) << "(lambda,p): " << chrono.elapsed() << "\n";
chrono.restart();
#endif
std::for_each( inflow_conditions.begin(), inflow_conditions.end(),
[&]( BoundaryCondition const& bc )
{
// right hand side
ns_rhs += integrate( markedfaces( mesh, bc.marker() ), inner( idf(&bc,BoundaryCondition::operator()),-SigmaN+penalbc*id( v )/hFace() ) );
navierstokes +=integrate( boundaryfaces( mesh ), -inner( SigmaNt,id( v ) ) );
navierstokes +=integrate( boundaryfaces( mesh ), -inner( SigmaN,idt( u ) ) );
navierstokes +=integrate( boundaryfaces( mesh ), +penalbc*inner( idt( u ),id( v ) )/hFace() );
});
std::for_each( wall_conditions.begin(), wall_conditions.end(),
[&]( BoundaryCondition const& bc )
{
navierstokes +=integrate( boundaryfaces( mesh ), -inner( SigmaNt,id( v ) ) );
navierstokes +=integrate( boundaryfaces( mesh ), -inner( SigmaN,idt( u ) ) );
navierstokes +=integrate( boundaryfaces( mesh ), +penalbc*inner( idt( u ),id( v ) )/hFace() );
});
std::for_each( outflow_conditions.begin(), outflow_conditions.end(),
[&]( BoundaryCondition const& bc )
{
ns_rhs += integrate( markedfaces( mesh, bc.marker() ), inner( idf(&bc,BoundaryCondition::operator()),N() ) );
});
LOG(INFO) << "bc: " << chrono.elapsed() << "\n";
chrono.restart();
u = vf::project( _space=Xh->functionSpace<0>(), _expr=cst(0.) );
p = vf::project( _space=Xh->functionSpace<1>(), _expr=cst(0.) );
M_bdf->initialize( U );
for( bdfns->start(); bdfns->isFinished(); bdfns->next() )
{
// add time dependent terms
auto bdf_poly = bdfns->polyDeriv();
form1( _test=Xh, _vector=Ft ) =
integrate( _range=elements(mesh), _expr=trans(idv( bdf_poly ))*id( v ) );
// add convective terms
form1( _test=Xh, _vector=Ft ) +=
integrate( _range=elements(mesh), _expr=trans(gradv(u)*idv( u ))*id(v) );
// add contrib from time independent terms
Ft->add( 1., F );
// add time stepping terms from BDF to right hand side
backend()->solve( _matrix=D, _solution=U, _rhs=Ft );
this->exportResults( bdfns->time(), U );
}
} // NavierNavierstokes::run
void
TestInterpolationHCurl3D::testInterpolation( std::string one_element_mesh )
{
//auto myexpr = unitX() + unitY() + unitZ() ; //(1,1,1)
auto myexpr = vec( cst(1.), cst(1.), cst(1.));
// one element mesh
auto mesh_name = one_element_mesh + ".msh"; //create the mesh and load it
fs::path mesh_path( mesh_name );
mesh_ptrtype oneelement_mesh = loadMesh( _mesh=new mesh_type,
_filename=mesh_name);
// refined mesh (export)
auto refine_level = std::floor(1 - math::log( 0.1 )); //Deduce refine level from meshSize (option)
mesh_ptrtype mesh = loadMesh( _mesh=new mesh_type,
_filename=mesh_name,
_refine=( int )refine_level);
space_ptrtype Xh = space_type::New( oneelement_mesh );
std::vector<std::string> faces = {"yzFace","xyzFace","xyFace"};
std::vector<std::string> edges = {"zAxis","yAxis","yzAxis","xyAxis","xzAxis","xAxis"};
element_type U_h_int = Xh->element();
element_type U_h_on = Xh->element();
element_type U_h_on_boundary = Xh->element();
submesh1d_ptrtype edgeMesh( new submesh1d_type );
edgeMesh = createSubmesh(oneelement_mesh, boundaryedges(oneelement_mesh) ); //submesh of edges
// Tangents on ref element
auto t0 = vec(cst(0.),cst(0.),cst(-2.));
auto t1 = vec(cst(0.),cst(2.),cst(0.));
auto t2 = vec(cst(0.),cst(-2.),cst(2.));
auto t3 = vec(cst(2.),cst(-2.),cst(0.));
auto t4 = vec(cst(2.),cst(0.),cst(-2.));
auto t5 = vec(cst(2.),cst(0.),cst(0.));
// Jacobian of geometrical transforms
std::string jac;
if(mesh_path.stem().string() == "one-elt-ref-3d" || mesh_path.stem().string() == "one-elt-real-h**o-3d" )
jac = "{1,0,0,0,1,0,0,0,1}:x:y:z";
else if(mesh_path.stem().string() == "one-elt-real-rotx" )
jac = "{1,0,0,0,0,-1,0,1,0}:x:y:z";
else if(mesh_path.stem().string() == "one-elt-real-roty" )
jac = "{0,0,1,0,1,0,-1,0,0}:x:y:z";
else if(mesh_path.stem().string() == "one-elt-real-rotz" )
jac = "{0,-1,0,1,0,0,0,0,1}:x:y:z";
U_h_int(0) = integrate( markedelements(edgeMesh, edges[0]), trans(expr<3,3>(jac)*t0)*myexpr ).evaluate()(0,0);
U_h_int(1) = integrate( markedelements(edgeMesh, edges[1]), trans(expr<3,3>(jac)*t1)*myexpr ).evaluate()(0,0);
U_h_int(2) = integrate( markedelements(edgeMesh, edges[2]), trans(expr<3,3>(jac)*t2)*myexpr ).evaluate()(0,0);
U_h_int(3) = integrate( markedelements(edgeMesh, edges[3]), trans(expr<3,3>(jac)*t3)*myexpr ).evaluate()(0,0);
U_h_int(4) = integrate( markedelements(edgeMesh, edges[4]), trans(expr<3,3>(jac)*t4)*myexpr ).evaluate()(0,0);
U_h_int(5) = integrate( markedelements(edgeMesh, edges[5]), trans(expr<3,3>(jac)*t5)*myexpr ).evaluate()(0,0);
for(int i=0; i<edges.size(); i++)
{
double edgeLength = integrate( markedelements(edgeMesh, edges[i]), cst(1.) ).evaluate()(0,0);
U_h_int(i) /= edgeLength;
}
#if 0 //Doesn't work for now
for(int i=0; i<Xh->nLocalDof(); i++)
{
CHECK( edgeMesh->hasMarkers( {edges[i]} ) );
U_h_int(i) = integrate( markedelements(edgeMesh, edges[i]), trans( print(T(),"T=") )*myexpr ).evaluate()(0,0);
std::cout << "U_h_int(" << i << ")= " << U_h_int(i) << std::endl;
}
#endif
// nedelec interpolant using on keyword
// interpolate on element
U_h_on.zero();
U_h_on.on(_range=elements(oneelement_mesh), _expr=myexpr);
U_h_on_boundary.on(_range=boundaryfaces(oneelement_mesh), _expr=myexpr);
auto exporter_proj = exporter( _mesh=mesh, _name=( boost::format( "%1%" ) % this->about().appName() ).str() );
exporter_proj->step( 0 )->add( "U_interpolation_handly_"+mesh_path.stem().string(), U_h_int );
exporter_proj->step( 0 )->add( "U_interpolation_on_"+mesh_path.stem().string(), U_h_on );
exporter_proj->save();
// print coefficient only for reference element
U_h_int.printMatlab( "U_h_int_" + mesh_path.stem().string() + ".m" );
U_h_on.printMatlab( "U_h_on_" + mesh_path.stem().string() + ".m" );
U_h_on_boundary.printMatlab( "U_h_on_boundary_" + mesh_path.stem().string() + ".m" );
//L2 norm of error
auto error = vf::project(_space=Xh, _range=elements(oneelement_mesh), _expr=idv(U_h_int) - idv(U_h_on) );
double L2error = error.l2Norm();
std::cout << "L2 error (elements) = " << L2error << std::endl;
auto error_boundary = vf::project(_space=Xh, _range=elements(oneelement_mesh), _expr=idv(U_h_int) - idv(U_h_on_boundary) );
double L2error_boundary = error_boundary.l2Norm();
std::cout << "L2 error (boundary) = " << L2error_boundary << std::endl;
BOOST_CHECK_SMALL( L2error_boundary - L2error, 1e-13 );
}
void
Partitioning<Dim>::run()
{
int p = 2;
int* pm = new int[p];
for(unsigned short i = 0; i < p; ++i)
pm[i] = i * (Environment::numberOfProcessors() / p);
bool excluded = std::binary_search(pm, pm + p, Environment::rank());
mpi::group new_group;
if(excluded)
new_group = Environment::worldComm().group().include(pm,pm+p);
else
new_group = Environment::worldComm().group().exclude(pm,pm+p);
delete [] pm;
boost::mpi::communicator bComm(Environment::worldComm(), new_group);
std::vector<int> active( bComm.size(), true );
WorldComm wComm(bComm,bComm,bComm,bComm.rank(),active);
//wComm.showMe();
boost::shared_ptr<Mesh<Simplex<Dim>>> mesh;
if(!excluded)
{
std::cout << "proc " << Environment::rank()
<< " is not excluded and is locally rank " << wComm.rank() << " and loads mesh with "
<< wComm.globalSize() << " partitions\n";
// mesh = loadMesh(_mesh = new Mesh<Simplex<Dim>>(wComm), _worldcomm=wComm );
mesh = createGMSHMesh(_mesh = new Mesh<Simplex<Dim>>(wComm),
_worldcomm = wComm,
_desc = domain(_worldcomm = wComm, _name = "hypercube", _shape = "hypercube",
_xmin = 0.0, _xmax = 1.0,
_ymin = 0.0, _ymax = 1.0,
_zmin = 0.0, _zmax = 1.0));
std::cout << " - nelement(mesh)=" << nelements(elements(mesh)) << "\n";
std::cout << " - loading space\n";
auto Vh = Pch<2>( mesh );
auto u = Vh->element("u");
auto f = expr( soption(_name="functions.f"), "f", wComm );
auto g = expr( soption(_name="functions.g"), "g", wComm );
auto v = Vh->element( g, "g" );
auto l = form1( _test=Vh );
l = integrate(_range=elements(mesh),_expr=f*id(v));
auto a = form2( _trial=Vh, _test=Vh);
a = integrate(_range=elements(mesh),
_expr=gradt(u)*trans(grad(v)) );
if(boption("gmsh.domain.usenames")) {
if(nelements(markedfaces(mesh, "Dirichlet"), boption("use_global")) > 0)
a+=on(_range=markedfaces(mesh, "Dirichlet"), _rhs=l, _element=u, _expr=g);
}
else
a+=on(_range=boundaryfaces(mesh), _rhs=l, _element=u, _expr=g);
a.solve(_rhs=l,_solution=u);
auto e = exporter( _mesh=mesh );
//e->addRegions();
e->add( "u", u );
e->add( "g", v );
e->save();
}
else
{
std::cout << "proc " << Environment::rank()
<< " is excluded and does not load mesh";
int np = 0;
mpi::all_reduce(wComm, 1, np, std::plus<int>());
std::cout << "proc " << Environment::rank()
<< " - nb proc = " << np << "\n";
}
} // Partitioning::run
