void
TestInterpolationHDiv<Dim>::testInterpolation()
{
// expr to interpolate
int is3D = 0;
if( Dim == 3 )
is3D = 1;
auto myexpr = unitX() + unitY() + is3D*unitZ() ; //(1,1)
auto mesh = loadMesh( _mesh=new Mesh<Simplex<Dim>> );
space_ptrtype Xh = space_type::New( mesh ); // RT function space
auto u_on = Xh->element();
auto u_proj = Xh->element();
//test on keyword
u_on.on(_range=elements(mesh), _expr=myexpr);
//test project keyword
u_proj = vf::project(_space=Xh, _range=elements(mesh), _expr=myexpr);
//L2 norm of error
auto error_on = vf::project(_space=Xh, _range=elements(mesh), _expr=myexpr - idv(u_on) );
double L2error_on = error_on.l2Norm();
std::cout << "[on] L2 error = " << L2error_on << std::endl;
auto error_proj = vf::project(_space=Xh, _range=elements(mesh), _expr=myexpr - idv(u_proj) );
double L2error_proj = error_proj.l2Norm();
std::cout << "[proj] L2 error = " << L2error_proj << std::endl;
}
// <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";
}
double L2_error(const space_ptrtype & Xh, const element_type & T, const double & values) const
{
// replace params by specified values
ex solution = getSolution(values);
auto g = expr(solution,vars);
auto mesh = Xh->mesh();
return math::sqrt( integrate( elements(mesh), Px()*(idv(T) - g)*(idv(T) - g) ).evaluate()(0,0) );
}
void updateCinematicViscosity( std::string const& marker = "" )
{
std::string markerUsed = ( marker.empty() )? self_type::defaultMaterialName() : marker;
M_cstCinematicViscosity[markerUsed] = this->cstMu(markerUsed)/this->cstRho(markerUsed);
if ( M_fieldCinematicViscosity )
{
if ( marker.empty() )
M_fieldCinematicViscosity->on(_range=elements(M_fieldCinematicViscosity->mesh()),
_expr=idv(this->fieldMu())/idv(this->fieldRho()) );
else
M_fieldCinematicViscosity->on(_range=markedelements(M_fieldCinematicViscosity->mesh(),marker),
_expr=idv(this->fieldMu())/idv(this->fieldRho()) );
}
}
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
TestInterpolationHDiv<Dim>::testInterpolationOneElt( std::string one_element_mesh )
{
// expr to interpolate
int is3D = 0;
if( Dim == 3 )
is3D = 1;
auto myexpr = unitX() + unitY() + is3D*unitZ() ; //(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::cout << "nb dof = " << Xh->nDof() << std::endl;
std::vector<std::string> faces;
if(Dim == 2)
faces = { "hypo","vert","hor"};
else if (Dim == 3)
faces = {"xzFace","xyFace","xyzFace","yzFace"};
element_type U_h_int = Xh->element();
element_type U_h_on = Xh->element();
// handly computed interpolant coeff (in hdiv basis)
for ( int i = 0; i < Xh->nLocalDof(); ++i )
{
CHECK( mesh->hasMarkers( {faces[i]} ) );
U_h_int(i) = integrate( markedfaces( oneelement_mesh, faces[i] ), trans( N() )*myexpr ).evaluate()(0,0);
}
// raviart-thomas interpolant using on
U_h_on.zero();
U_h_on.on(_range=elements(oneelement_mesh), _expr=myexpr);
auto exporter_proj = exporter( _mesh=mesh, _name=( boost::format( "%1%-%2%" ) % this->about().appName() %mesh_path.stem().string() ).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();
U_h_int.printMatlab( "U_h_int_" + mesh_path.stem().string() + ".m" );
U_h_on.printMatlab( "U_h_on_" + 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 = " << L2error << std::endl;
}
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 );
}
extern int shapeop_addConstraint(ShapeOpSolver *op, const char *constraintType, int *ids, int nb_ids, ShapeOpScalar weight) {
const std::string ct(constraintType);
std::vector<int> idv(ids, ids + nb_ids);
std::shared_ptr<ShapeOp::Constraint> c = ShapeOp::Constraint::shapeConstraintFactory(ct, idv, weight, op->s->getPoints());
if (!c) { return -1; }
return op->s->addConstraint(c);
}
// Generate 'usage' and 'help' properties for the given object.
// JS_DefineFunctionsWithHelp will define individual function objects with both
// of those properties (eg getpid.usage = "getpid()" and getpid.help = "return
// the process id"). This function will generate strings for an "interface
// object", eg os.file, which contains some number of functions.
//
// .usage will be set to "<name> - interface object".
//
// .help will be set to a newline-separated list of functions that have either
// 'help' or 'usage' properties. Functions are described with their usage
// strings, if they have them, else with just their names.
//
bool
GenerateInterfaceHelp(JSContext* cx, HandleObject obj, const char* name)
{
AutoIdVector idv(cx);
if (!GetPropertyKeys(cx, obj, JSITER_OWNONLY | JSITER_HIDDEN, &idv))
return false;
StringBuffer buf(cx);
int numEntries = 0;
for (size_t i = 0; i < idv.length(); i++) {
RootedId id(cx, idv[i]);
RootedValue v(cx);
if (!JS_GetPropertyById(cx, obj, id, &v))
return false;
if (!v.isObject())
continue;
RootedObject prop(cx, &v.toObject());
RootedValue usage(cx);
RootedValue help(cx);
if (!JS_GetProperty(cx, prop, "usage", &usage))
return false;
if (!JS_GetProperty(cx, prop, "help", &help))
return false;
if (!usage.isString() && !help.isString())
continue;
if (numEntries && !buf.append("\n"))
return false;
numEntries++;
if (!buf.append(" ", 2))
return false;
if (!buf.append(usage.isString() ? usage.toString() : JSID_TO_FLAT_STRING(id)))
return false;
}
RootedString s(cx, buf.finishString());
if (!s || !JS_DefineProperty(cx, obj, "help", s, 0))
return false;
buf.clear();
if (!buf.append(name, strlen(name)) || !buf.append(" - interface object with ", 25))
return false;
char cbuf[100];
SprintfLiteral(cbuf, "%d %s", numEntries, numEntries == 1 ? "entry" : "entries");
if (!buf.append(cbuf, strlen(cbuf)))
return false;
s = buf.finishString();
if (!s || !JS_DefineProperty(cx, obj, "usage", s, 0))
return false;
return true;
}
double
ThermalBlockMinimalVersion::output( int output_index, parameter_type const& mu , element_type& u, bool need_to_solve)
{
double output=0;
auto mesh = Xh->mesh();
if ( output_index==0 )
{
output = integrate( _range=markedfaces( mesh,"south_domain-1" ), _expr= idv( u ) ).evaluate()(0,0)
+ integrate( _range=markedfaces( mesh,"south_domain-2" ), _expr= idv( u ) ).evaluate()(0,0)
+ integrate( _range=markedfaces( mesh,"south_domain-3" ), _expr= idv( u ) ).evaluate()(0,0);
}
else
{
throw std::logic_error( "[ThermalBlock::output] error with output_index : only 0 " );
}
return output;
}//output
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() );
}
void
cv<Dim,Order>::run()
{
auto mesh = loadMesh(_mesh = new mesh_type ,_update = MESH_CHECK|MESH_UPDATE_FACES|MESH_UPDATE_EDGES|MESH_RENUMBER );
auto Xh = space_type::New( mesh );
auto Xhm1 = space_pm1_type::New( mesh );
auto Xhm1vec = space_pm1vec_type::New( mesh );
auto phi = Xh->element();
auto gphi = Xhm1vec->element();
auto gphi0 = Xhm1->element();
phi = vf::project(Xh,elements(mesh), Px()*Px() + Py()*Py() );
// P0 vector
gphi = vf::project(Xhm1vec, elements(mesh), trans( gradv(phi) ) );
// P0 scalar
auto gphi_compx = gphi.comp( ( ComponentType )0 );
gphi0 = vf::project(Xhm1, elements(mesh), idv(gphi_compx) );
auto e = exporter(_mesh = mesh, _name = "myExporter");
e->add( "phi", phi );
e->add( "grad_phi", gphi );
e->add( "grad_phi0", gphi0 );
e->save();
}
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
Beam<nDim,nOrder>::run()
{
this->changeRepository( boost::format( "doc/manual/solid/%1%/%2%/P%3%/h_%4%/" )
% this->about().appName()
% entity_type::name()
% nOrder
% meshSize );
/*
* First we create the mesh
*/
mesh_ptrtype mesh = createGMSHMesh( _mesh=new mesh_type,
_update=MESH_UPDATE_EDGES|MESH_UPDATE_FACES|MESH_CHECK,
_desc=domain( _name=( boost::format( "beam-%1%" ) % nDim ).str() ,
_shape="hypercube",
_xmin=0., _xmax=0.351,
_ymin=0., _ymax=0.02,
_zmin=0., _zmax=0.02,
_h=meshSize ) );
// add marker clamped to the mesh
mesh->addMarkerName( "clamped",( nDim==2 )?1:19, (nDim==2)?1:2);
mesh->addMarkerName( "tip",( nDim==2)?3:27, (nDim==2)?1:2);
/*
* The function space and some associate elements are then defined
*/
timers["init"].first.restart();
space_ptrtype Xh = space_type::New( mesh );
Xh->printInfo();
element_type u( Xh, "u" );
element_type v( Xh, "v" );
timers["init"].second = timers["init"].first.elapsed();
/*
* Data associated with the simulation
*/
auto E = doption(_name="E")*pascal;
const double nu = doption(_name="nu");
auto mu = E/( 2*( 1+nu ) );
auto lambda = E*nu/( ( 1+nu )*( 1-2*nu ) );
auto density = 1e3;
auto gravity = -2*newton/pow<Dim>(meter);//-density*0.05;
LOG(INFO) << "lambda = " << lambda << "\n"
<< "mu = " << mu << "\n"
<< "gravity= " << gravity << "\n";
/*
* Construction of the right hand side
*
* \f$ f = \int_\Omega g * v \f$ where \f$ g \f$ is a vector
* directed in the \f$ y \f$ direction.
*/
auto F = backend()->newVector( Xh );
F->zero();
timers["assembly"].first.restart();
if ( Dim == 3 )
form1( _test=Xh, _vector=F ) = integrate( elements( mesh ), trans( gravity.value()*oneZ() )*id( v ) );
else
form1( _test=Xh, _vector=F ) = integrate( elements( mesh ), trans( gravity.value()*oneY() )*id( v ) );
timers["assembly"].second = timers["assembly"].first.elapsed();
/*
* Construction of the left hand side
*/
auto D = backend()->newMatrix( Xh, Xh );
timers["assembly"].first.restart();
auto deft = sym(gradt(u));
auto def = sym(grad(u));
auto a = form2( _test=Xh, _trial=Xh, _matrix=D );
a = integrate( elements( mesh ),
lambda.value()*divt( u )*div( v ) +
2.*mu.value()*trace( trans( deft )*def ) );
if ( M_bctype == 1 ) // weak Dirichlet bc
{
auto Id = eye<nDim>();
a += integrate( markedfaces( mesh, "clamped" ),
- trans( ( 2.*mu.value()*deft+lambda.value()*trace( deft )*Id )*N() )*id( v )
- trans( ( 2.*mu.value()*def+lambda.value()*trace( def )*Id )*N() )*idt( u )
+ bcCoeff*std::max(2.*mu.value(),lambda.value())*trans( idt( u ) )*id( v )/hFace() );
}
if ( M_bctype == 0 )
a += on( markedfaces( mesh, "clamped" ), u, F, zero<nDim,1>() );
timers["assembly"].second += timers["assembly"].first.elapsed();
backend(_rebuild=true)->solve( _matrix=D, _solution=u, _rhs=F );
v = vf::project( Xh, elements( Xh->mesh() ), P() );
this->exportResults( 0, u, v );
auto i1 = mean( _range=markedfaces( mesh, "tip" ), _expr=idv( u ) );
LOG(INFO) << "deflection: " << i1 << "\n";
} // Beam::run