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linear.cpp
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linear.cpp
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#include"main.h"
#include"linear.h"
#include"sim_pars.h"
//#include"periodic.h"
#define TOL 1e-12
// quite dirty
//#define LOAD
extern sim_pars simu;
void linear::save_matrices(void){
if(stiff.size()==0) fill_stiff();
if(mass.size()==0) fill_mass();
if(lambda_x.size()==0) fill_lambda();
std::cout << "Saving matrices" << std::endl;
saveMarket(stiff, "stiff.mtx");
saveMarket(mass, "mass.mtx");
saveMarket(stiffp1, "stiffp1.mtx");
saveMarket(lambda_x, "lambda_x.mtx");
saveMarket(lambda_y, "lambda_y.mtx");
return;
}
void linear::load_matrices(void){
loadMarket(stiff, "stiff.mtx");
loadMarket(stiffp1, "stiffp1.mtx");
loadMarket(mass, "mass.mtx");
return;
}
void linear::fill_stiff(void){
#ifdef LOAD
std::cout << " Reading stiffness matrix" << std::endl;
loadMarket(stiff, "stiff.mtx");
loadMarket(stiffp1, "stiffp1.mtx");
#else
std::cout << " Filling stiffness matrix" << std::endl;
// int n=simu.no_of_points();
std::vector<triplet> aa , bb ; // list of non-zeros coefficients
int N=0;
for(F_v_it fv=T.finite_vertices_begin();
fv!=T.finite_vertices_end();
fv++) {
++N;
int vi=fv->idx.val();
typedef Vertex::scalar_link scalar_link;
// typedef std::map<Vertex_handle,Vector_2> vector_link;
scalar_link stiffs=fv->stiff();
for(
scalar_link::iterator nn= stiffs.begin();
nn!=stiffs.end(); ++nn) {
int vj=nn->first->idx.val();
FT ddelta = nn->second; // wrong sign here ???
// Aqui con Ada
// cout << vi << " , " << vj << " " << ddelta << endl;
aa.push_back( triplet(vi,vj, -ddelta ));
if( (vi!=0) && (vj!=0) ) bb.push_back( triplet(vi - 1 , vj -1 , -ddelta ));
}
}
stiff.resize(N,N);
stiff.setFromTriplets(aa.begin(), aa.end());
std::cout << " Filled stiffness matrix" << std::endl;
cout << "matrix size " << stiff.rows() << " x " << stiff.cols() << endl;
// F_v_it fv=T.finite_vertices_begin();
// int i0=fv->idx.val();
// aa.push_back( triplet( N , i0 , 1 ) ); // anchor particle 0 to have fixed pressure
// //aa.push_back( triplet( N , 0 , 1 ) ); // anchor particle 0 to have fixed pressure
// stiffp1.resize(N+1,N+1);
// stiffp1.setFromTriplets(aa.begin(), aa.end());
stiffp1.resize(N-1,N-1);
stiffp1.setFromTriplets(bb.begin(), bb.end());
std::cout << " Filled stiffness plus 1 matrix" << std::endl;
cout << "matrix size " << stiffp1.rows() << " x " << stiffp1.cols() << endl;
#endif
// Only non-direct iterative solvers
#ifndef DIRECT_SOLVER
solver_stiffp1.setTolerance( TOL );
solver_stiffp1.setMaxIterations( 40 * N );
#endif
solver_stiffp1.compute(stiffp1);
if(solver_stiffp1.info()!=Eigen::Success) {
std::cout << "Failure decomposing stiff plus 1 matrix\n";
}
return;
}
void linear::fill_lambda(){
#ifdef LOAD
std::cout << " Reading labmda matrices" << std::endl;
loadMarket(lambda_x, "lambda_x.mtx");
loadMarket(lambda_y, "lambda_y.mtx");
#else
// div( vectorf, inter_scalarf );
std::cout << " Filling lambda matrices" << std::endl;
std::vector<triplet> ax; // list of non-zeros coefficients
std::vector<triplet> ay; // list of non-zeros coefficients
int N=0;
for(F_v_it fv=T.finite_vertices_begin();
fv!=T.finite_vertices_end();
fv++) {
++N;
int vi=fv->idx.val();
typedef Vertex::vector_link vector_link;
vector_link nabla=fv->nabla();
for(
vector_link::iterator nn= nabla.begin();
nn!=nabla.end(); ++nn) {
int vj=nn->first->idx.val();
Vector_2 nnabla=nn->second;
ax.push_back( triplet(vi,vj, nnabla.x() ));
ay.push_back( triplet(vi,vj, nnabla.y() ));
}
}
lambda_x.resize(N,N);
lambda_y.resize(N,N);
lambda_x.setFromTriplets(ax.begin(), ax.end());
lambda_y.setFromTriplets(ay.begin(), ay.end());
#endif
std::cout << " Filled lambda matrices" << std::endl;
cout << "matrix size " << lambda_x.rows() << " x " << lambda_x.cols() << endl;
return;
}
void linear::fill_mass() {
#ifdef LOAD
std::cout << " Reading mass matrix" << std::endl;
loadMarket(mass, "mass.mtx");
#else
std::cout << " Filling mass matrix" << std::endl;
std::vector<triplet> aa; // list of non-zeros coefficients
int N=0;
for(F_v_it fv=T.finite_vertices_begin();
fv!=T.finite_vertices_end();
fv++) {
++N;
int vi=fv->idx.val();
typedef Vertex::scalar_link scalar_link;
scalar_link masss=fv->mass();
for(
scalar_link::iterator nn= masss.begin();
nn!=masss.end(); ++nn) {
int vj=nn->first->idx.val();
FT mm = nn->second;
aa.push_back( triplet(vi,vj, mm ));
}
}
mass.resize(N,N);
mass.setFromTriplets(aa.begin(), aa.end());
std::cout << " Filled mass matrix" << std::endl;
cout << "matrix size " << mass.rows() << " x " << mass.cols() << endl;
#endif
// Only non-direct iterative solvers
#ifndef DIRECT_SOLVER
solver_mass.setTolerance( TOL );
#endif
solver_mass.compute(mass);
if(solver_mass.info()!=Eigen::Success) {
std::cout << "Failure decomposing mass matrix\n";
}
return;
}
void linear::fill_mas( const FT& dt ){
#ifdef LOAD
std::cout << " Reading mas matrix" << std::endl;
loadMarket(mas, "mas.mtx");
std::cout << " Read mas matrix" << std::endl;
#else
if(stiff.size()==0) fill_stiff();
if(mass.size()==0) fill_mass();
std::cout << " Building MAS matrix: " ;
FT a = dt * simu.mu() ;
cout << " (mass - " << a << " x stiff) " << endl;
mas = mass - a * stiff;
#endif
solver_mas.compute(mas);
if(solver_mas.info()!=Eigen::Success) {
std::cout << "Failure decomposing mass minus a stiff matrix\n";
}
}
void linear::fill_mbs( const FT& b ){
if(stiff.size()==0) fill_stiff();
if(mass.size()==0) fill_mass();
std::cout << " Building MbS matrix: " ;
// // Model A dynamics:
// cout << "( " << 1 - b << " mass - " << 0.5 * b << " x stiff) " << endl;
// mbs = ( 1 - b ) * mass - ( 0.5 * b ) * stiff;
// Model B dynamics:
cout << " (mass + " << b << " x stiff) " << endl;
mbs = mass + b * stiff;
solver_mbs.compute(mbs);
if(solver_mbs.info()!=Eigen::Success) {
std::cout << "Failure decomposing mass minus b stiff matrix\n";
}
}
VectorXd linear::field_to_vctr(const kind::f scalarf ) {
std::vector<int> indices;
std::vector<FT> ff;
for(F_v_it fv=T.finite_vertices_begin();
fv!=T.finite_vertices_end();
fv++) {
indices.push_back( fv->idx.val() );
ff.push_back( fv->sf(scalarf).val() );
}
int N=indices.size();
VectorXd vctr;
vctr.resize(N);
for(int nn=0; nn<indices.size(); nn++) {
vctr(indices[nn])=ff[nn];
// cout << indices[nn] << " : "
// << ff[nn] << endl;
}
return vctr;
}
void linear::vctr_to_field(const VectorXd& vv, const kind::f scalarf ) {
// int nn=0;
for(F_v_it fv=T.finite_vertices_begin();
fv!=T.finite_vertices_end();
fv++) {
// check (only makes sense if vertices are re-labeled at every step)
int index = fv->idx.val();
// if(index!=nn) {
// std::cout << "Error transfering from vector onto field " << scalarf << std::endl;
// }
fv->sf(scalarf).set(vv[index]);
// ++nn;
// cout << index << " : "
// << vv[index] << endl;
}
return;
}
void linear::vctr_to_vfield(const VectorXd& vv, const kind::f vectorf, const int comp ) {
for(F_v_it fv=T.finite_vertices_begin();
fv!=T.finite_vertices_end();
fv++) {
int index = fv->idx.val();
// TODO: define changes on each component of a vector field
if(comp==0) {
FT vvy = fv->vf(vectorf).val().y() ;
fv->vf(vectorf).set( Vector_2 ( vv[index] , vvy ) );
} else {
FT vvx = fv->vf(vectorf).val().x() ;
fv->vf(vectorf).set( Vector_2 ( vvx , vv[index] ) );
}
}
return;
}
VectorXd linear::vfield_to_vctr(const kind::f vectorf , int comp ) {
std::vector<int> indices;
std::vector<FT> ff;
for(F_v_it fv=T.finite_vertices_begin();
fv!=T.finite_vertices_end();
fv++) {
indices.push_back( fv->idx.val() );
if(comp==0)
ff.push_back( fv->vf(vectorf).val().x() );
else
ff.push_back( fv->vf(vectorf).val().y() );
}
int N=indices.size();
VectorXd vctr(N);
for(int nn=0; nn<indices.size(); nn++)
vctr(indices[nn])=ff[nn];
return vctr;
}
// solves for f in
// stiffp1 x f = lapl
void linear::poisson(const VectorXd& lapl, VectorXd& f) {
if(stiffp1.size()==0) fill_stiff();
if(mass.size()==0) fill_mass();
VectorXd massl = mass * lapl ;
int N=massl.size();
VectorXd massll = massl.tail( N-1 );
VectorXd ff= solver_stiffp1.solve( massll );
f(0) = 0;
f.tail(N-1) = ff;
// zero mean
f = f.array() - f.mean();
return;
}
// solves for scalarf in
// stiffp1 x scalarf = lambda · vectorf
// inter_scalarf is lambda · vectorf
void linear::laplace_div(
const kind::f velocity ,
const FT dt,
const kind::f divvel,
const kind::f pressure ) {
if(stiffp1.size()==0) fill_stiff();
cout << "Solving Lapl of field " << pressure
<< " = div of field " << velocity
<< ", with intermediate field " << divvel
<< '\n';
if(lambda_x.size()==0) fill_lambda();
VectorXd vx = vfield_to_vctr( velocity ,0 );
VectorXd vy = vfield_to_vctr( velocity ,1 );
VectorXd div1 = lambda_x * vx + lambda_y * vy ;
vctr_to_field( div1 , divvel );
// divv.conservativeResize(N+1);
// divv[N]=0;
// {
// MatrixXd dstiff = MatrixXd(stiff);
// cout << "s =" << dstiff.format(OctaveFmt) ;
// }
cout << "matrix size " << stiffp1.rows() << " x " << stiffp1.cols() << endl;
// cout << "d = " << divv.format(OctaveFmt) ;
// x = solver.solveWithGuess(b,x0);
// if(mass.size()==0) fill_mass();
// VectorXd div2 = mass * div1;
int N=div1.size();
VectorXd divv = div1.tail( N-1 );
cout << "rhs vector of size " << divv.rows() << endl;
VectorXd lapl= solver_stiffp1.solve( divv );
// Only non-direct iterative solvers
// cout << "Solver iterations: " << solver_stiffp1.iterations()
// << " , max: " << solver_stiffp1.maxIterations()
// << endl ;
if(solver_stiffp1.info()!=Eigen::Success)
cout << "Warning: unsucessful stiffp1 solve, error code "
<< solver_stiffp1.info() << endl ;
// cout << "l = " << lapl.format(OctaveFmt) ;
// vctr_to_field(lapl, scalarf);
// mass_s(scalarf); //it's the other way around
VectorXd lapl2(N);
lapl2(0) = 0;
lapl2.tail(N-1) = ( 1.0 / dt ) * lapl;
vctr_to_field( lapl2 , pressure );
return;
}
// lumped mass "inversion"
void linear::mass_v_lumped(const kind::f vectorf ) {
for(F_v_it vit=T.vertices_begin();
vit != T.vertices_end();
vit++) {
FT V=vit->vol();
vit->vf(vectorf) /= V;
}
// VectorXd mm = field_to_vctr( kind::VOL );
// VectorXd lambda_v_x = vfield_to_vctr( vectorf , 0 );
// lambda_v_x.cwiseQuotient( mm ) ;
// VectorXd lambda_v_y = vfield_to_vctr( vectorf , 1 );
// lambda_v_y.cwiseQuotient( mm ) ;
// vctr_to_vfield( lambda_v_x , vectorf , 0 );
// vctr_to_vfield( lambda_v_y , vectorf , 1 );
return;
}
// solves mass x vectorf = vectorf
// vectorf is I/O
// full mass matrix inversion
// void linear::mass_v( VectorXd& fx , VectorXd& fy ) {
// cout << "Mass - inverting vector x,y couple " << endl;
// if(mass.size()==0) fill_mass();
// cout << "matrix vector of size " << mass.rows() << " x " << mass.cols() << endl;
// cout << "x component" << endl;
// // x component.-
// VectorXd grad_x= solver_mass.solve(fx);
// if(solver_mass.info()!=Eigen::Success)
// cout << "Warning: unsucessful mass x solve, error code "
// << solver_mass.info() << endl ;
// // y component.-
// cout << "y component" << endl;
// VectorXd grad_y= solver_mass.solve(fy);
// if(solver_mass.info()!=Eigen::Success)
// cout << "Warning: unsucessful mass y solve, error code "
// << solver_mass.info() << endl ;
// fx=grad_x;
// fy=grad_y;
// cout << "Mass invertion done " << endl;
// return;
// }
void linear::mass_v(const kind::f vectorf ) {
cout << "Mass - inverting vector field " << vectorf
<< '\n';
VectorXd lambda_v_x = vfield_to_vctr( vectorf , 0 );
VectorXd lambda_v_y = vfield_to_vctr( vectorf , 1 );
mass_s(lambda_v_x);
mass_s(lambda_v_y);
vctr_to_vfield( lambda_v_x , vectorf , 0 );
vctr_to_vfield( lambda_v_y , vectorf , 1 );
cout << "Mass invertion of vector field " << vectorf << " done " << endl;
return;
}
void linear::mass_s( VectorXd& lambda ) {
cout << "Mass - inverting scalar field " << endl;
if(mass.size()==0) fill_mass();
VectorXd mm = solver_mass.solve(lambda);
if(solver_mass.info()!=Eigen::Success)
cout << "Warning: unsucessful mass x solve, error code "
<< solver_mass.info() << endl ;
lambda = mm;
return;
}
void linear::mass_s(const kind::f scalarf ) {
cout << "Mass - inverting scalar field " << scalarf
<< '\n';
VectorXd lambda = field_to_vctr( scalarf );
mass_s( lambda );
vctr_to_field( lambda , scalarf );
return;
}
// TODO, not needed after all
// set u_star as the force due to chem pot gradients
// void linear::ustar_is_force( const kind::f Ustar) {
// chem_pot_force();
// // TODO ...
// return;
// }
// add chem pot force to already existing force
void linear::chem_pot_force(void){
gradient(kind::CHEMPOT, kind::GRADCHEMPOT);
VectorXd al = field_to_vctr( kind::ALPHA );
VectorXd grad_cp_x = vfield_to_vctr( kind::GRADCHEMPOT , 0 );
VectorXd f_x = vfield_to_vctr( kind::FORCE , 0 );
f_x -= VectorXd( al.array() * grad_cp_x.array() ); // array: for el-wise *
vctr_to_vfield( f_x , kind::FORCE , 0 );
VectorXd f_y = vfield_to_vctr( kind::FORCE , 1 );
VectorXd grad_cp_y = vfield_to_vctr( kind::GRADCHEMPOT , 1 );
f_y -= VectorXd( al.array() * grad_cp_y.array() ); // array: for el-wise *
vctr_to_vfield( f_y , kind::FORCE , 1 );
return;
}
// Overdamped-only u inversion (Stokes' equation)
// Reduced units!
// TODO : largely redundant with laplace_div
void linear::u_inv_od(const kind::f velocity) {
if(stiffp1.size()==0) fill_stiff();
if(mass.size()==0) fill_mass();
//void linear::laplace_div_v_xy(
// cout << "Solving Lapl of field " << pressure
// << " = div of field " << velocity
// << ", with intermediate field " << divvel
// << '\n';
if(lambda_x.size()==0) fill_lambda();
VectorXd p = field_to_vctr( kind::P );
VectorXd f_x = vfield_to_vctr( kind::FORCE , 0 );
VectorXd rhs_x = lambda_x * p - mass * f_x;
int N=rhs_x.size();
VectorXd rhs2_x = (rhs_x.tail( N-1 ));
VectorXd u_x= solver_stiffp1.solve( rhs2_x );
if(solver_stiffp1.info()!=Eigen::Success)
cout << "Warning: unsucessful stiffp1 solve, error code "
<< solver_stiffp1.info() << endl ;
VectorXd u2_x(N);
u2_x(0) = 0;
u2_x.tail(N-1) = u_x;
vctr_to_vfield( u2_x , velocity , 0 );
VectorXd f_y = vfield_to_vctr( kind::FORCE , 1 );
VectorXd rhs_y = lambda_y * p - mass * f_y;
// int N=rhs_y.size();
VectorXd rhs2_y = (rhs_y.tail( N-1 ));
VectorXd u_y= solver_stiffp1.solve( rhs2_y );
if(solver_stiffp1.info()!=Eigen::Success)
cout << "Warning: unsucessful stiffp1 solve, error code "
<< solver_stiffp1.info() << endl ;
VectorXd u2_y(N);
u2_y(0) = 0;
u2_y.tail(N-1) = u_y;
vctr_to_vfield( u2_y , velocity , 1 );
return;
}
void linear::ustar_inv_cp(
const kind::f Ustar,
const FT dt,
const kind::f U0 ,
const bool overdamped, const bool semi) {
if(mas.size()==0) fill_mas( dt );
// if(lambda_x.size()==0) fill_lambda();
// FT eps=1e-1;
//// x
// gradient of chem pot .-
chem_pot_force();
VectorXd U0_x = vfield_to_vctr( kind::FORCE , 0 ); // = dt *
// U0_x *= a;
U0_x *= dt;
if(!overdamped) {
// VectorXd force_x
U0_x += vfield_to_vctr( U0 , 0 );
}
VectorXd massU0_x;
if (semi) {
VectorXd grad_x = vfield_to_vctr( kind::GRADP , 0 );
massU0_x = mass * U0_x - dt * grad_x;
} else
massU0_x = mass * U0_x ;
// massU0_x = (-dt) * mass * al * grad_cp_x ;
VectorXd Ustarx= solver_mas.solve(massU0_x);
if(solver_mas.info()!=Eigen::Success)
cout << "Warning: unsucessful mas x solve, error code "
<< solver_mas.info() << endl ;
vctr_to_vfield( Ustarx , Ustar , 0 );
//// y
VectorXd U0_y = vfield_to_vctr( kind::FORCE , 1 ); // = dt *
// U0_y -= eps * al * vfield_to_vctr( kind::GRADALPHA , 1 );
// U0_y *= a;
U0_y *= dt;
if(!overdamped) {
// VectorXd force_y = vfield_to_vctr( kind::FORCE , 1 );
U0_y += vfield_to_vctr( U0 , 1 );
}
VectorXd massU0_y;
if (semi) {
VectorXd grad_y = vfield_to_vctr( kind::GRADP , 1 );
massU0_y = mass * U0_y - dt * grad_y;
} else
massU0_y = mass * U0_y ;
// massU0_y = (-dt) * mass * al * grad_cp_y ;
VectorXd Ustary= solver_mas.solve(massU0_y);
if(solver_mas.info()!=Eigen::Success)
cout << "Warning: unsucessful mas y solve, error code "
<< solver_mas.info() << endl ;
vctr_to_vfield( Ustary , Ustar , 1);
return;
}
// solves (mass - dt x mu x stiff) ustar = mass ( dt x force + u0 )
void linear::ustar_inv(
const kind::f Ustar,
const FT dt,
const kind::f U0 ,
const bool overdamped, const bool semi) {
if(mas.size()==0) fill_mas( dt );
VectorXd U0_x = vfield_to_vctr( kind::FORCE , 0 ); // = dt *
U0_x *= dt;
if(!overdamped) {
// VectorXd force_x
U0_x += vfield_to_vctr( U0 , 0 );
}
VectorXd massU0_x;
if (semi) {
VectorXd grad_x = vfield_to_vctr( kind::GRADP , 0 );
massU0_x = mass * U0_x - dt * grad_x;
} else
massU0_x = mass * U0_x ;
VectorXd Ustarx= solver_mas.solve(massU0_x);
if(solver_mas.info()!=Eigen::Success)
cout << "Warning: unsucessful mas x solve, error code "
<< solver_mas.info() << endl ;
vctr_to_vfield( Ustarx , Ustar , 0 );
//// y
VectorXd U0_y = vfield_to_vctr( kind::FORCE , 1 ); // = dt *
U0_y *= dt;
if(!overdamped) {
// VectorXd force_y = vfield_to_vctr( kind::FORCE , 1 );
U0_y += vfield_to_vctr( U0 , 1 );
}
VectorXd massU0_y;
if (semi) {
VectorXd grad_y = vfield_to_vctr( kind::GRADP , 1 );
massU0_y = mass * U0_y - dt * grad_y;
} else
massU0_y = mass * U0_y ;
VectorXd Ustary= solver_mas.solve(massU0_y);
if(solver_mas.info()!=Eigen::Success)
cout << "Warning: unsucessful mas y solve, error code "
<< solver_mas.info() << endl ;
vctr_to_vfield( Ustary , Ustar , 1);
return;
}
// solves ( mass )^-1 s alpha = lapl_alpha, with
// lapl_alpha s.t. mu = - alpha + alpha^3 - (1/2) lapl_alpha
void linear::alpha_inv_cp2(const kind::f alpha,
const FT dt,
const kind::f alpha0 ) {
VectorXd al = field_to_vctr( alpha );
VectorXd cp = field_to_vctr( kind::CHEMPOT ) ;
VectorXd alal3 = - al.array() * ( 1 - al.array() * al.array() ); // - al + al^3
VectorXd lapl= 2*( alal3 - cp );
poisson( lapl , al );
vctr_to_field( al , alpha);
return;
}
void linear::chempot_inv(const kind::f alpha,
const FT dt,
const kind::f alpha0 ) {
const FT D=0.04;
VectorXd al = field_to_vctr( alpha );
VectorXd al0 = field_to_vctr( alpha0 );
VectorXd diff = (1.0/ ( D * dt ) ) * ( al - al0) ;
VectorXd cp( diff.size() );
poisson( diff , cp );
vctr_to_field( cp , kind::CHEMPOT );
return;
}
// solves (mass - dt x mu x stiff) alpha = alpha0
void linear::alpha_inv_cp(const kind::f alpha,
const FT dt,
const kind::f alpha0 ) {
const FT D=0.04;
FT b = D * dt ;
VectorXd al0 = field_to_vctr( alpha0 );
VectorXd al = field_to_vctr( alpha );
VectorXd cp = field_to_vctr( kind::CHEMPOT ); // + al ;
//VectorXd al3 = al.array().pow(3);
//VectorXd mass0 = mass * al0 + b * stiff * al3;
// VectorXd al = solver_mbs.solve(mass0);
// // Model A dynamics, no diff
// VectorXd new_al0 = (1.0 / (1.0 - b)) * ( al0 + b * cp );
// vctr_to_field( new_al0 , alpha );
// return;
// VectorXd cp2 = chempot2( al );
// // model A dynamics