int RSA::coprime(int e[MAX], int s[MAX]) /*//// 判断两个大数之间是否互质////*/
{
int a[MAX], b[MAX], c[MAX], d[MAX], o[MAX], l[MAX];
int i;
for (i = 0; i<MAX; i++)
l[i] = o[i] = c[i] = d[i] = 0;
o[0] = 0; o[MAX - 1] = 1;
l[0] = 1; l[MAX - 1] = 1;
mov(e, b);
mov(s, a);
do
{
if (cmp(b, l) == 0)
{
return 1;
}
for (i = 0; i<MAX; i++)
c[i] = 0;
divt(a, b, d, c);
mov(b, a);/*b--->a*/
mov(c, b);/*c--->b*/
} while (cmp(c, o) != 0);
/* printf("Ihey are not coprime!\n");*/
return 0;
}
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 RSA::rsad(int e[MAX], int g[MAX], int *d)
{
int r[MAX], n1[MAX], n2[MAX], k[MAX], w[MAX];
int i, t[MAX], b1[MAX], b2[MAX], temp[MAX];
mov(g, n1);
mov(e, n2);
for (i = 0; i<MAX; i++)
k[i] = w[i] = r[i] = temp[i] = b1[i] = b2[i] = t[i] = 0;
b1[MAX - 1] = 0; b1[0] = 0;/*/b1=0;*/
b2[MAX - 1] = 1; b2[0] = 1;/*/b2=1;*/
while (1)
{
for (i = 0; i<MAX; i++)
k[i] = w[i] = 0;
divt(n1, n2, k, w);/*/k=n1/n2;*/
for (i = 0; i<MAX; i++)
temp[i] = 0;
mul(k, n2, temp);/*/temp=k*n2;*/
for (i = 0; i<MAX; i++)
r[i] = 0;
sub(n1, temp, r);
if ((r[MAX - 1] == 1) && (r[0] == 0))/*/r=0*/
{
break;
}
else
{
mov(n2, n1);/*/n1=n2;*/
mov(r, n2);/*/n2=r;*/
mov(b2, t);/*/t=b2;*/
for (i = 0; i<MAX; i++)
temp[i] = 0;
mul(k, b2, temp);/*/b2=b1-k*b2;*/
for (i = 0; i<MAX; i++)
b2[i] = 0;
sub(b1, temp, b2);
mov(t, b1);
}
}
for (i = 0; i<MAX; i++)
t[i] = 0;
add(b2, g, t);
for (i = 0; i<MAX; i++)
temp[i] = d[i] = 0;
divt(t, g, temp, d);
}
/*-------------接下来的重点任务是要着手解决 m=a^p mod n的函数问题------------*/
void RSA::expmod(int a[MAX], int p[MAX], int n[MAX], int *m)
{
int t[MAX], l[MAX], temp[MAX]; /*/t放入2，l放入1；*/
int w[MAX], s[MAX], c[MAX], b[MAX], i;
for (i = 0; i<MAX - 1; i++)
b[i] = l[i] = t[i] = w[i] = 0;
t[0] = 2; t[MAX - 1] = 1;
l[0] = 1; l[MAX - 1] = 1;
mov(l, temp);
mov(a, m);
mov(p, b);
while (cmp(b, l) != 0)
{
for (i = 0; i<MAX; i++)
w[i] = c[i] = 0;
divt(b, t, w, c);/*// c=p mod 2 w= p /2*/
mov(w, b);/*//p=p/2*/
if (cmp(c, l) == 0) /*/余数c==1*/
{
for (i = 0; i<MAX; i++)
w[i] = 0;
mul(temp, m, w);
mov(w, temp);
for (i = 0; i<MAX; i++)
w[i] = c[i] = 0;
divt(temp, n, w, c);/* /c为余c=temp % n，w为商w=temp/n */
mov(c, temp);
}
for (i = 0; i<MAX; i++)
s[i] = 0;
mul(m, m, s);//s=a*a
for (i = 0; i<MAX; i++)
c[i] = 0;
divt(s, n, w, c);/*/w=s/n;c=s mod n*/
mov(c, m);
}
for (i = 0; i<MAX; i++)
s[i] = 0;
mul(m, temp, s);
for (i = 0; i<MAX; i++)
c[i] = 0;
divt(s, n, w, c);
mov(c, m);/*余数s给m*/
m[MAX - 2] = a[MAX - 2];/*为后面的汉字显示需要，用第99位做为标记*/
return;/*/k=temp*k%n;*/
}
void RSA::mulmod(int a[MAX], int b[MAX], int n[MAX], int *m)/*解决 了 m=a*b mod n;*/
{
int c[MAX], d[MAX];
int i;
for (i = 0; i<MAX; i++)
d[i] = c[i] = 0;
mul(a, b, c);
divt(c, n, d, m);
//for(i=0;i<m[MAX-1];i++)
// printf("%d",m[m[MAX-1]-i-1]);
//printf("\nm length is : %d \n",m[MAX-1]);
}
double exponential (double k)
{
int n; /*n es el contador de tÈrminos*/
double f; /*f es el valor del tÈrmino*/
for (n=0;n<15;n++) /*se aproximar· hasta el tÈrmino 15*/
{
double c= expo(k,n); /*se eleva la base x al exponente n*/
long d= fact(n); /*se busca el factorial n*/
double t= divt (c,d); /*se dividen los resultados previos*/
f=f+t; /*se van sumando los tÈrminos sucesivos*/
}
return f;
}
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();
}
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();
}
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
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
