//fill a vector to have the container
virtual void containerPtr( vector_ptrtype & vector_to_fill )
{
auto vector = M_backend->newVector( this->space() );
form1( _test=this->space(),_vector=vector) = M_expr;
vector->close();
vector_to_fill = vector;
}
static inline void assemble(boost::shared_ptr<Mesh<Simplex<Dim>>>& mesh, double* vec) {
boost::timer time;
auto Vh = FunctionSpace<Mesh<Simplex<Dim>>, bases<Lagrange<Order, Type>>>::New(_mesh = mesh);
vec[2] = time.elapsed();
vec[1] = Vh->nDof();
Environment::logMemoryUsage( "Assemble Laplacian Memory Usage: FunctionSpace" );
time.restart();
auto v = Vh->element();
auto f = backend()->newVector(Vh);
auto l = form1(_test = Vh, _vector = f);
l = integrate(_range = elements(mesh), _expr = id(v));
vec[4] = time.elapsed();
Environment::logMemoryUsage( "Assemble Laplacian Memory Usage: Form1" );
time.restart();
auto u = Vh->element();
auto A = backend()->newMatrix(Vh, Vh);
vec[5] = time.elapsed();
Environment::logMemoryUsage( "Assemble Laplacian Memory Usage: Matrix" );
time.restart();
auto a = form2(_trial = Vh, _test = Vh, _matrix = A);
a = integrate(_range = elements(mesh), _expr = inner(gradt(u),grad(v)));
a += on(_range = markedfaces(mesh, "Dirichlet"), _rhs = l, _element = u, _expr = cst(0.0));
vec[3] = time.elapsed();
auto mem = Environment::logMemoryUsage( "Assemble Laplacian Memory Usage: form2" );
v[6] = mem.memory_usage/1e9;
LOG(INFO) << "v[6] = " << v[6];
cleanup();
}
void
PreconditionerBlockMS<space_type>::init( void )
{
if( Environment::worldComm().isMasterRank() )
std::cout << "Init preconditioner blockms\n";
LOG(INFO) << "Init ...\n";
tic();
BoundaryConditions M_bc = M_model.boundaryConditions();
LOG(INFO) << "Create sub Matrix\n";
map_vector_field<FEELPP_DIM,1,2> m_dirichlet_u { M_bc.getVectorFields<FEELPP_DIM> ( "u", "Dirichlet" ) };
map_scalar_field<2> m_dirichlet_p { M_bc.getScalarFields<2> ( "phi", "Dirichlet" ) };
/*
* AA = [[ A - k^2 M, B^t],
* [ B , 0 ]]
* We need to extract A-k^2 M and add it M to form A+(1-k^2) M = A+g M
*/
// Is the zero() necessary ?
M_11->zero();
this->matrix()->updateSubMatrix(M_11, M_Vh_indices, M_Vh_indices, false); // M_11 = A-k^2 M
LOG(INFO) << "Use relax = " << M_relax << std::endl;
M_11->addMatrix(M_relax,M_mass); // A-k^2 M + M_relax*M = A+(M_relax-k^2) M
auto f2A = form2(_test=M_Vh, _trial=M_Vh,_matrix=M_11);
auto f1A = form1(_test=M_Vh);
for(auto const & it : m_dirichlet_u )
f2A += on(_range=markedfaces(M_Vh->mesh(),it.first), _expr=it.second,_rhs=f1A, _element=u, _type="elimination_symmetric");
/*
* Rebuilding sub-backend
*/
backend(_name=M_prefix_11, _rebuild=true);
backend(_name=M_prefix_22, _rebuild=true);
// We have to set the G, Px,Py,Pz or X,Y,Z matrices to AMS
if(soption(_name="pc-type", _prefix=M_prefix_11) == "ams")
{
#if FEELPP_DIM == 3
initAMS();
{
if(boption(_name="setAlphaBeta",_prefix=M_prefix_11))
{
auto prec = preconditioner(_pc=pcTypeConvertStrToEnum(soption(M_prefix_11+".pc-type")),
_backend=backend(_name=M_prefix_11),
_prefix=M_prefix_11,
_matrix=M_11
);
prec->setMatrix(M_11);
prec->attachAuxiliarySparseMatrix("a_alpha",M_a_alpha);
prec->attachAuxiliarySparseMatrix("a_beta",M_a_beta);
}
}
#else
std::cerr << "ams preconditioner is not interfaced in two dimensions\n";
#endif
}
toc("[PreconditionerBlockMS] Init",FLAGS_v>0);
LOG(INFO) << "Init done\n";
}
// apply the functional
virtual value_type
operator()( const element_type& x ) const
{
auto vector = M_backend->newVector( this->space() );
form1( _test=this->space(),_vector=vector) = M_expr;
vector->close();
return M_backend->dot( *vector, x.container() );
}
int main(void)
{
Form form1("form1", 5, 5);
Form form2("form2", 10, 5);
Bureaucrat bob("bob", 1);
Bureaucrat roger("roger", 6);
std::cout << form1 << form2 << bob << roger;
bob.signForm(form1);
std::cout << form1 << form2 << bob << roger;
bob.signForm(form2);
std::cout << form1 << form2 << bob << roger;
roger.signForm(form1);
std::cout << form1 << form2 << bob << roger;
roger.signForm(form2);
std::cout << form1 << form2 << bob << roger;
return (0);
}
static inline void assemble(boost::shared_ptr<Mesh<Simplex<Dim>>>& mesh, double* vec) {
boost::timer time;
auto Vh = FunctionSpace<Mesh<Simplex<Dim>>, bases<Lagrange<Order, Type>, Lagrange<OrderBis, TypeBis>>>::New(_mesh = mesh,
_worldscomm = std::vector<WorldComm>(2, mesh->worldComm()),
_extended_doftable = std::vector<bool>(2, false));
vec[2] = time.elapsed();
Environment::logMemoryUsage( "Assemble Stokes Memory Usage: FunctionSpace" );
vec[1] = Vh->nDof();
time.restart();
auto V = Vh->element();
auto v = V.template element<0>();
auto f = backend()->newVector(Vh);
auto l = form1(_test = Vh, _vector = f);
l = integrate(_range = elements(mesh),
_expr = trans(oneY()) * id(v));
vec[4] = time.elapsed();
Environment::logMemoryUsage( "Assemble Stokes Memory Usage: Form1" );
time.restart();
auto U = Vh->element();
auto u = U.template element<0>();
auto p = U.template element<1>();
auto q = V.template element<1>();
auto A = backend()->newMatrix(Vh, Vh);
vec[5] = time.elapsed();
Environment::logMemoryUsage( "Assemble Stokes Memory Usage: Matrix" );
time.restart();
auto a = form2(_trial = Vh, _test = Vh, _matrix = A);
a = integrate(_range = elements(mesh),
_expr = trace(gradt(u) * trans(grad(v))));
a += integrate(_range = elements(mesh),
_expr = - div(v) * idt(p) );
a += integrate(_range = elements(mesh),
_expr = - divt(u) * id(q));
a += on(_range = markedfaces(mesh, "Dirichlet"), _rhs = l, _element = u, _expr = zero<Dim, 1>());
vec[3] = time.elapsed();
auto mem = Environment::logMemoryUsage( "Assemble Stokes Memory Usage: Form2" );
v[6] = mem.memory_usage/1.e9;
cleanup();
}
bool exprs_for_24(int a1, int a2, int a3, int a4)
{
int ar[4] = {a1, a2, a3, a4};
sort_quick(4, ar);
int ops[4] = {'+', '-', '*', '/'};
int opr[3];
Rpermut rp(3, opr, sizeof(ops)/sizeof(int), ops);
int a, b, c, d;
int op1, op2, op3;
bool found = false;
for (; std::next_permutation(ar, ar+4); ) {
a = ar[0];
b = ar[1];
c = ar[2];
d = ar[3];
for (rp.begin(); !rp.ended; rp.next()) {
op1 = opr[0];
op2 = opr[1];
op3 = opr[2];
if (form1(a, b, c, d, op1, op2, op3) ||
form2(a, b, c, d, op1, op2, op3) ||
form3(a, b, c, d, op1, op2, op3) ||
form4(a, b, c, d, op1, op2, op3) ||
form5(a, b, c, d, op1, op2, op3))
found = true;
}
}
return found;
}
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() );
}
static inline void assemble(boost::shared_ptr<Mesh<Simplex<Dim>>>& mesh, double* vec) {
boost::timer time;
//HeapProfilerStart("FunctionSpace");
auto Vh = FunctionSpace<Mesh<Simplex<Dim>>, bases<Lagrange<Order, Type>>>::New(_mesh = mesh);
//HeapProfilerDump("dump");
//HeapProfilerStop();
vec[2] = time.elapsed();
Environment::logMemoryUsage( "Assemble Elasticity Memory Usage: FunctionSpace" );
vec[1] = Vh->nDof();
auto E = 1e+8;
auto nu = 0.25;
auto mu = E / (2 * (1 + nu));
auto lambda = E * nu / ((1 + nu) * (1 - 2 * nu));
time.restart();
auto v = Vh->element();
auto f = backend()->newVector(Vh);
auto l = form1(_test = Vh, _vector = f);
l = integrate(_range = elements(mesh), _expr = -1e+3 * trans(oneY()) * id(v));
vec[4] = time.elapsed();
Environment::logMemoryUsage( "Assemble Elasticity Memory Usage: Form1" );
time.restart();
auto u = Vh->element();
auto A = backend()->newMatrix(Vh, Vh);
vec[5] = time.elapsed();
Environment::logMemoryUsage( "Assemble Elasticity Memory Usage: Matrix" );
time.restart();
auto a = form2(_trial = Vh, _test = Vh, _matrix = A);
a = integrate(_range = elements(mesh),
_expr = lambda * divt(u) * div(v) +
2 * mu * trace(trans(sym(gradt(u))) * sym(grad(u))));
a += on(_range = markedfaces(mesh, "Dirichlet"), _rhs = l, _element = u, _expr = zero<Dim, 1>());
vec[3] = time.elapsed();
auto mem = Environment::logMemoryUsage( "Assemble Elasticity Memory Usage: Form2" );
v[6] = mem.memory_usage/1e9;
cleanup();
}
this_type& operator+=( ExprT const& e )
{
form1( _test=this->space(), _vector=M_vector ) += e;
return *this;
}
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
PreconditionerBlockMS<space_type>::PreconditionerBlockMS(space_ptrtype Xh, // (u)x(p)
ModelProperties model, // model
std::string const& p, // prefix
sparse_matrix_ptrtype AA ) // The matrix
:
M_backend(backend()), // the backend associated to the PC
M_Xh( Xh ),
M_Vh( Xh->template functionSpace<0>() ), // Potential
M_Qh( Xh->template functionSpace<1>() ), // Lagrange
M_Vh_indices( M_Vh->nLocalDofWithGhost() ),
M_Qh_indices( M_Qh->nLocalDofWithGhost() ),
M_uin( M_backend->newVector( M_Vh ) ),
M_uout( M_backend->newVector( M_Vh ) ),
M_pin( M_backend->newVector( M_Qh ) ),
M_pout( M_backend->newVector( M_Qh ) ),
U( M_Xh, "U" ),
M_mass(M_backend->newMatrix(M_Vh,M_Vh)),
M_L(M_backend->newMatrix(M_Qh,M_Qh)),
M_er( 1. ),
M_model( model ),
M_prefix( p ),
M_prefix_11( p+".11" ),
M_prefix_22( p+".22" ),
u(M_Vh, "u"),
ozz(M_Vh, "ozz"),
zoz(M_Vh, "zoz"),
zzo(M_Vh, "zzo"),
M_ozz(M_backend->newVector( M_Vh )),
M_zoz(M_backend->newVector( M_Vh )),
M_zzo(M_backend->newVector( M_Vh )),
X(M_Qh, "X"),
Y(M_Qh, "Y"),
Z(M_Qh, "Z"),
M_X(M_backend->newVector( M_Qh )),
M_Y(M_backend->newVector( M_Qh )),
M_Z(M_backend->newVector( M_Qh )),
phi(M_Qh, "phi")
{
tic();
LOG(INFO) << "[PreconditionerBlockMS] setup starts";
this->setMatrix( AA );
this->setName(M_prefix);
/* Indices are need to extract sub matrix */
std::iota( M_Vh_indices.begin(), M_Vh_indices.end(), 0 );
std::iota( M_Qh_indices.begin(), M_Qh_indices.end(), M_Vh->nLocalDofWithGhost() );
M_11 = AA->createSubMatrix( M_Vh_indices, M_Vh_indices, true, true);
/* Boundary conditions */
BoundaryConditions M_bc = M_model.boundaryConditions();
map_vector_field<FEELPP_DIM,1,2> m_dirichlet_u { M_bc.getVectorFields<FEELPP_DIM> ( "u", "Dirichlet" ) };
map_scalar_field<2> m_dirichlet_p { M_bc.getScalarFields<2> ( "phi", "Dirichlet" ) };
/* Compute the mass matrix (needed in first block, constant) */
auto f2A = form2(_test=M_Vh, _trial=M_Vh, _matrix=M_mass);
auto f1A = form1(_test=M_Vh);
f2A = integrate(_range=elements(M_Vh->mesh()), _expr=inner(idt(u),id(u))); // M
for(auto const & it : m_dirichlet_u )
{
LOG(INFO) << "Applying " << it.second << " on " << it.first << " for "<<M_prefix_11<<"\n";
f2A += on(_range=markedfaces(M_Vh->mesh(),it.first), _expr=it.second,_rhs=f1A, _element=u, _type="elimination_symmetric");
}
/* Compute the L (= er * grad grad) matrix (the second block) */
auto f2L = form2(_test=M_Qh,_trial=M_Qh, _matrix=M_L);
for(auto it : M_model.materials() )
{
f2L += integrate(_range=markedelements(M_Qh->mesh(),marker(it)), _expr=M_er*inner(gradt(phi), grad(phi)));
}
auto f1LQ = form1(_test=M_Qh);
for(auto const & it : m_dirichlet_p)
{
LOG(INFO) << "Applying " << it.second << " on " << it.first << " for "<<M_prefix_22<<"\n";
f2L += on(_range=markedfaces(M_Qh->mesh(),it.first),_element=phi, _expr=it.second, _rhs=f1LQ, _type="elimination_symmetric");
}
if(soption(_name="pc-type", _prefix=M_prefix_11) == "ams")
#if FEELPP_DIM == 3
{
M_grad = Grad( _domainSpace=M_Qh, _imageSpace=M_Vh);
// This preconditioner is linked to that backend : the backend will
// automatically use the preconditioner.
auto prec = preconditioner(_pc=pcTypeConvertStrToEnum(soption(M_prefix_11+".pc-type")),
_backend=backend(_name=M_prefix_11),
_prefix=M_prefix_11,
_matrix=M_11
);
prec->setMatrix(M_11);
prec->attachAuxiliarySparseMatrix("G",M_grad.matPtr());
if(boption(M_prefix_11+".useEdge"))
{
LOG(INFO) << "[ AMS ] : using SetConstantEdgeVector \n";
ozz.on(_range=elements(M_Vh->mesh()),_expr=vec(cst(1),cst(0),cst(0)));
zoz.on(_range=elements(M_Vh->mesh()),_expr=vec(cst(0),cst(1),cst(0)));
zzo.on(_range=elements(M_Vh->mesh()),_expr=vec(cst(0),cst(0),cst(1)));
*M_ozz = ozz; M_ozz->close();
*M_zoz = zoz; M_zoz->close();
*M_zzo = zzo; M_zzo->close();
prec->attachAuxiliaryVector("Px",M_ozz);
prec->attachAuxiliaryVector("Py",M_zoz);
prec->attachAuxiliaryVector("Pz",M_zzo);
}
else
{
LOG(INFO) << "[ AMS ] : using SetCoordinates \n";
X.on(_range=elements(M_Vh->mesh()),_expr=Px());
Y.on(_range=elements(M_Vh->mesh()),_expr=Py());
Z.on(_range=elements(M_Vh->mesh()),_expr=Pz());
*M_X = X; M_X->close();
*M_Y = Y; M_Y->close();
*M_Z = Z; M_Z->close();
prec->attachAuxiliaryVector("X",M_X);
prec->attachAuxiliaryVector("Y",M_Y);
prec->attachAuxiliaryVector("Z",M_Z);
}
}
#else
std::cerr << "ams preconditioner is not interfaced in two dimensions\n";
#endif
toc( "[PreconditionerBlockMS] setup done ", FLAGS_v > 0 );
}
PreconditionerBlockMS<space_type>::PreconditionerBlockMS(space_ptrtype Xh, // (u)x(p)
ModelProperties model, // model
std::string const& p, // prefix
sparse_matrix_ptrtype AA, value_type relax ) // The matrix
:
M_backend(backend()), // the backend associated to the PC
M_Xh( Xh ),
M_Vh( Xh->template functionSpace<0>() ), // Potential
M_Qh( Xh->template functionSpace<1>() ), // Lagrange
M_Vh_indices( M_Vh->nLocalDofWithGhost() ),
M_Qh_indices( M_Qh->nLocalDofWithGhost() ),
M_uin( M_backend->newVector( M_Vh ) ),
M_uout( M_backend->newVector( M_Vh ) ),
M_pin( M_backend->newVector( M_Qh ) ),
M_pout( M_backend->newVector( M_Qh ) ),
U( M_Xh, "U" ),
M_mass(M_backend->newMatrix(M_Vh,M_Vh)),
M_L(M_backend->newMatrix(M_Qh,M_Qh)),
M_er( 1. ),
M_model( model ),
M_prefix( p ),
M_prefix_11( p+".11" ),
M_prefix_22( p+".22" ),
u(M_Vh, "u"),
ozz(M_Vh, "ozz"),
zoz(M_Vh, "zoz"),
zzo(M_Vh, "zzo"),
M_ozz(M_backend->newVector( M_Vh )),
M_zoz(M_backend->newVector( M_Vh )),
M_zzo(M_backend->newVector( M_Vh )),
X(M_Qh, "X"),
Y(M_Qh, "Y"),
Z(M_Qh, "Z"),
M_X(M_backend->newVector( M_Qh )),
M_Y(M_backend->newVector( M_Qh )),
M_Z(M_backend->newVector( M_Qh )),
phi(M_Qh, "phi"),
M_relax(relax)
{
tic();
LOG(INFO) << "[PreconditionerBlockMS] setup starts";
this->setMatrix( AA );
this->setName(M_prefix);
/* Indices are need to extract sub matrix */
std::iota( M_Vh_indices.begin(), M_Vh_indices.end(), 0 );
std::iota( M_Qh_indices.begin(), M_Qh_indices.end(), M_Vh->nLocalDofWithGhost() );
M_11 = AA->createSubMatrix( M_Vh_indices, M_Vh_indices, true, true);
/* Boundary conditions */
BoundaryConditions M_bc = M_model.boundaryConditions();
map_vector_field<FEELPP_DIM,1,2> m_dirichlet_u { M_bc.getVectorFields<FEELPP_DIM> ( "u", "Dirichlet" ) };
map_scalar_field<2> m_dirichlet_p { M_bc.getScalarFields<2> ( "phi", "Dirichlet" ) };
/* Compute the mass matrix (needed in first block, constant) */
auto f2A = form2(_test=M_Vh, _trial=M_Vh, _matrix=M_mass);
auto f1A = form1(_test=M_Vh);
f2A = integrate(_range=elements(M_Vh->mesh()), _expr=inner(idt(u),id(u))); // M
for(auto const & it : m_dirichlet_u )
{
LOG(INFO) << "Applying " << it.second << " on " << it.first << " for "<<M_prefix_11<<"\n";
f2A += on(_range=markedfaces(M_Vh->mesh(),it.first), _expr=it.second,_rhs=f1A, _element=u, _type="elimination_symmetric");
}
/* Compute the L (= er * grad grad) matrix (the second block) */
auto f2L = form2(_test=M_Qh,_trial=M_Qh, _matrix=M_L);
#if 0
//If you want to manage the relative permittivity materials per material,
//here is the entry to deal with.
for(auto it : M_model.materials() )
{
f2L += integrate(_range=markedelements(M_Qh->mesh(),marker(it)), _expr=M_er*inner(gradt(phi), grad(phi)));
}
#else
f2L += integrate(_range=elements(M_Qh->mesh()), _expr=M_er*inner(gradt(phi), grad(phi)));
#endif
auto f1LQ = form1(_test=M_Qh);
for(auto const & it : m_dirichlet_p)
{
LOG(INFO) << "Applying " << it.second << " on " << it.first << " for "<<M_prefix_22<<"\n";
f2L += on(_range=markedfaces(M_Qh->mesh(),it.first),_element=phi, _expr=it.second, _rhs=f1LQ, _type="elimination_symmetric");
}
toc( "[PreconditionerBlockMS] setup done ", FLAGS_v > 0 );
}
void
ThermalBlockMinimalVersion::initModel()
{
gamma_dir=option(_name="gamma_dir").template as<double>();
this->setFunctionSpaces( Pch<1>( loadMesh( _mesh=new Mesh<Simplex<2>> ) ) );
auto mesh = Xh->mesh();
if( Environment::worldComm().isMasterRank() )
{
std::cout << "Number of local dof " << Xh->nLocalDof() << "\n";
std::cout << "Number of dof " << Xh->nDof() << "\n";
}
auto mu_min = Dmu->element();
auto mu_max = Dmu->element();
mu_min << 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 ;
mu_max << 10 , 10 , 10 , 10 , 10 , 10 , 10 , 10 ;
Dmu->setMin( mu_min );
Dmu->setMax( mu_max );
auto u = Xh->element();
auto v = Xh->element();
auto M = backend()->newMatrix( Xh , Xh );
double mu_min_coeff=0.1;
// on boundary north we have u=0 so term from weak dirichlet condition
// vanish in the right hand side
//rhs
auto f0 = form1( _test=Xh );
f0 = integrate( _range=markedfaces( mesh,"south_domain-1" ), _expr= id( v ) )
+ integrate( _range=markedfaces( mesh,"south_domain-2" ), _expr= id( v ) )
+ integrate( _range=markedfaces( mesh,"south_domain-3" ), _expr= id( v ) );
this->addRhs( { f0, "1" } );
//lhs
auto a0 = form2( _trial=Xh, _test=Xh);
a0 = integrate( markedelements( mesh, "domain-1" ), gradt( u )*trans( grad( v ) ) );
this->addLhs( { a0 , "1" } );
auto a1 = form2( _trial=Xh, _test=Xh);
a1 = integrate( markedelements( mesh, "domain-2" ), gradt( u )*trans( grad( v ) ) );
this->addLhs( { a1 , "mu0" } );
auto a2 = form2( _trial=Xh, _test=Xh);
a2 = integrate( markedelements( mesh, "domain-3" ), gradt( u )*trans( grad( v ) ) );
this->addLhs( { a2 , "mu1" } );
auto a3 = form2( _trial=Xh, _test=Xh);
a3 = integrate( markedelements( mesh, "domain-4" ), gradt( u )*trans( grad( v ) ) );
this->addLhs( { a3 , "mu2" } );
auto a4 = form2( _trial=Xh, _test=Xh);
a4 = integrate( markedelements( mesh, "domain-5" ), gradt( u )*trans( grad( v ) ) );
this->addLhs( { a4 , "mu3" } );
auto a5 = form2( _trial=Xh, _test=Xh);
a5 = integrate( markedelements( mesh, "domain-6" ), gradt( u )*trans( grad( v ) ) );
this->addLhs( { a5 , "mu4" } );
auto a6 = form2( _trial=Xh, _test=Xh);
a6 = integrate( markedelements( mesh, "domain-7" ), gradt( u )*trans( grad( v ) ) )
+integrate( markedfaces( mesh, "north_domain-7" ),
-gradt( u )*vf::N()*id( v )
-grad( u )*vf::N()*idt( v )
);
this->addLhs( { a6 , "mu5" } );
auto a7 = form2( _trial=Xh, _test=Xh);
a7 = integrate( markedelements( mesh, "domain-8" ), gradt( u )*trans( grad( v ) ) )
+integrate( markedfaces( mesh, "north_domain-8" ),
-gradt( u )*vf::N()*id( v )
-grad( u )*vf::N()*idt( v )
);
this->addLhs( { a7 , "mu6" } );
auto a8 = form2( _trial=Xh, _test=Xh);
a8 = integrate( markedelements( mesh, "domain-9" ), gradt( u )*trans( grad( v ) ) )
+integrate( markedfaces( mesh, "north_domain-9" ),
-gradt( u )*vf::N()*id( v )
-grad( u )*vf::N()*idt( v )
);
this->addLhs( { a8 , "mu7" } );
auto a9 = form2( _trial=Xh, _test=Xh);
a9 = integrate( markedfaces( mesh, "north_domain-7" ),gamma_dir*idt( u )*id( v )/h() )
+integrate( markedfaces( mesh, "north_domain-8" ),gamma_dir*idt( u )*id( v )/h() )
+integrate( markedfaces( mesh, "north_domain-9" ),gamma_dir*idt( u )*id( v )/h() );
this->addLhs( { a9 , "1" } );
form2( Xh, Xh, M ) = integrate( markedelements( mesh, "domain-1" ), gradt( u )*trans( grad( v ) ) );
form2( Xh, Xh, M ) += integrate( markedelements( mesh, "domain-2" ), gradt( u )*trans( grad( v ) ) * mu_min_coeff );
form2( Xh, Xh, M ) += integrate( markedelements( mesh, "domain-3" ), gradt( u )*trans( grad( v ) ) * mu_min_coeff );
form2( Xh, Xh, M ) += integrate( markedelements( mesh, "domain-4" ), gradt( u )*trans( grad( v ) ) * mu_min_coeff );
form2( Xh, Xh, M ) += integrate( markedelements( mesh, "domain-5" ), gradt( u )*trans( grad( v ) ) * mu_min_coeff );
form2( Xh, Xh, M ) += integrate( markedelements( mesh, "domain-6" ), gradt( u )*trans( grad( v ) ) * mu_min_coeff );
form2( Xh, Xh, M ) += integrate( markedelements( mesh, "domain-7" ), gradt( u )*trans( grad( v ) ) * mu_min_coeff );
form2( Xh, Xh, M ) += integrate( markedelements( mesh, "domain-8" ), gradt( u )*trans( grad( v ) ) * mu_min_coeff );
form2( Xh, Xh, M ) += integrate( markedelements( mesh, "domain-9" ), gradt( u )*trans( grad( v ) ) * mu_min_coeff );
form2( Xh, Xh, M ) += integrate( markedfaces( mesh, "north_domain-7" ),
-gradt( u )*vf::N()*id( v ) * mu_min_coeff
-grad( u )*vf::N()*idt( v ) * mu_min_coeff
);
form2( Xh, Xh, M ) += integrate( markedfaces( mesh, "north_domain-8" ),
-gradt( u )*vf::N()*id( v ) * mu_min_coeff
-grad( u )*vf::N()*idt( v ) * mu_min_coeff
);
form2( Xh, Xh, M ) += integrate( markedfaces( mesh, "north_domain-9" ),
-gradt( u )*vf::N()*id( v ) * mu_min_coeff
-grad( u )*vf::N()*idt( v ) * mu_min_coeff
);
form2( Xh, Xh, M ) += integrate( markedfaces( mesh, "north_domain-7" ),gamma_dir*idt( u )*id( v )/h() );
form2( Xh, Xh, M ) += integrate( markedfaces( mesh, "north_domain-8" ),gamma_dir*idt( u )*id( v )/h() );
form2( Xh, Xh, M ) += integrate( markedfaces( mesh, "north_domain-9" ),gamma_dir*idt( u )*id( v )/h() );
this->addEnergyMatrix( M );
}//initModel()
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
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
