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// Header file for this class
#include "ImplicitSolveOperator.h"
// Other ATC includes
#include "ATC_Coupling.h"
#include "FE_Engine.h"
#include "PhysicsModel.h"
#include "PrescribedDataManager.h"
using std::set;
using std::vector;
namespace ATC {
// --------------------------------------------------------------------
// --------------------------------------------------------------------
// ImplicitSolveOperator
// --------------------------------------------------------------------
// --------------------------------------------------------------------
ImplicitSolveOperator::
ImplicitSolveOperator(double alpha, double dt)
: n_(0),
dof_(0),
dt_(dt),
alpha_(alpha),
epsilon0_(1.0e-8)
{
// Nothing else to do here
}
// --------------------------------------------------------------------
// operator *
// --------------------------------------------------------------------
DENS_VEC
ImplicitSolveOperator::operator * (const DENS_VEC & x) const
{
// This method uses a matrix-free approach to approximate the
// multiplication by matrix A in the matrix equation Ax=b, where the
// matrix equation results from an implicit treatment of the
// fast field. In brief, if the ODE for the fast field can be written:
//
// dx/dt = R(x)
//
// A generalized discretization can be written:
//
// 1/dt * (x^n+1 - x^n) = alpha * R(x^n+1) + (1-alpha) * R(x^n)
//
// Taylor expanding the R(x^n+1) term and rearranging gives the
// equation to be solved for dx at each timestep:
//
// [1 - dt * alpha * dR/dx] * dx = dt * R(x^n)
//
// The operator defined in this method computes the left-hand side,
// given a vector dx. It uses a finite difference, matrix-free
// approximation of dR/dx * dx, giving:
//
// [1 - dt * alpha * dR/dx] * dx = dt * R(x^n)
// ~= dx - dt*alpha/epsilon * ( R(x^n + epsilon*dx) - R(x^n) )
//
// Compute epsilon
double epsilon = (x.norm()>0.0) ? epsilon0_*x0_.norm()/x.norm():epsilon0_;
// Compute incremented vector x^n+1 = x^n + epsilon*dx
x_ = x0_ + epsilon * x;
// Evaluate R(x)
this->R(x_,R_);
// Compute full left hand side and return it
DENS_VEC Ax = x - dt_ * alpha_ / epsilon * (R_ - R0_);
return Ax;
}
// --------------------------------------------------------------------
// rhs of Ax = r
// --------------------------------------------------------------------
DENS_VEC
ImplicitSolveOperator::r() const
{
return dt_ * R0_; // dt * R(T^n)
}
// --------------------------------------------------------------------
// preconditioner
// --------------------------------------------------------------------
DIAG_MAT
ImplicitSolveOperator::preconditioner() const
{
DENS_VEC diag(n_);
diag = 1.0;
DIAG_MAT preconditioner(diag);
return preconditioner;
}
// --------------------------------------------------------------------
// --------------------------------------------------------------------
// FieldImplicitSolveOperator
// --------------------------------------------------------------------
// --------------------------------------------------------------------
FieldImplicitSolveOperator::
FieldImplicitSolveOperator(ATC_Coupling * atc,
FIELDS & fields,
const FieldName fieldName,
const Array2D< bool > & rhsMask,
const PhysicsModel * physicsModel,
double simTime,
double dt,
double alpha)
: ImplicitSolveOperator(alpha, dt),
fieldName_(fieldName),
atc_(atc),
physicsModel_(physicsModel),
fields0_(fields), // ref to fields
fields_ (fields), // copy of fields
rhsMask_(rhsMask),
time_(simTime)
{
const DENS_MAT & f = fields0_[fieldName_].quantity();
dof_ = f.nCols();
if (dof_ > 1) throw ATC_Error("Implicit solver operator can only handle scalar fields");
// create all to free map
int nNodes = f.nRows();
set<int> fixedNodes_ = atc_->prescribed_data_manager()->fixed_nodes(fieldName_);
n_ = nNodes;
vector<bool> tag(nNodes);
set<int>::const_iterator it; int i = 0;
for (i = 0; i < nNodes; ++i) { tag[i] = true; }
for (it=fixedNodes_.begin();it!=fixedNodes_.end();++it) {tag[*it]=false;}
int m = 0;
for (i = 0; i < nNodes; ++i) { if (tag[i]) freeNodes_[i]= m++; }
//std::cout << " nodes " << n_ << " " << nNodes << "\n";
// Save current field
x0_.reset(n_);
to_free(f,x0_);
x_ = x0_; // initialize
// righthand side/forcing vector
rhsMask_.reset(NUM_FIELDS,NUM_FLUX);
rhsMask_ = false;
for (int i = 0; i < rhsMask.nCols(); i++) {
rhsMask_(fieldName_,i) = rhsMask(fieldName_,i);
}
//std::cout << print_mask(rhsMask_) << "\n";
massMask_.reset(1);
massMask_(0) = fieldName_;
rhs_[fieldName_].reset(nNodes,dof_);
// Compute the RHS vector R(T^n)
R0_.reset(n_);
R_ .reset(n_);
R(x0_, R0_);
}
void FieldImplicitSolveOperator::to_all(const VECTOR &x, MATRIX &f) const
{
f.reset(x.nRows(),1);
for (int i = 0; i < x.nRows(); ++i) {
f(i,0) = x(i);
}
}
void FieldImplicitSolveOperator::to_free(const MATRIX &r, VECTOR &v) const
{
v.reset(r.nRows());
for (int i = 0; i < r.nRows(); ++i) {
v(i) = r(i,0);
}
}
void
FieldImplicitSolveOperator::R(const DENS_VEC &x, DENS_VEC &v ) const
{
DENS_MAT & f = fields_[fieldName_].set_quantity();
atc_->prescribed_data_manager()->set_fixed_field(time_, fieldName_, f);
to_all(x,f);
atc_->compute_rhs_vector(rhsMask_,fields_,rhs_,FULL_DOMAIN,physicsModel_);
DENS_MAT & r = rhs_[fieldName_].set_quantity();
atc_->prescribed_data_manager()->set_fixed_dfield(time_, fieldName_, r);
atc_->apply_inverse_mass_matrix(r,fieldName_);
to_free(r,v);
#if 0
int n = 6;
//std::cout << "# x "; for (int i = 0; i < n_; ++i) std::cout << x(i) << " "; std::cout << "\n";
//std::cout << "# f "; for (int i = 0; i < n; ++i) std::cout << f(i,0) << " "; std::cout << "\n";
std::cout << "# r "; for (int i = 0; i < n; ++i) std::cout << r(i,0) << " "; std::cout << "\n";
//std::cout << "# v "; for (int i = 0; i < n; ++i) std::cout << v(i) << " "; std::cout << "\n";
#endif
}
void FieldImplicitSolveOperator::solution(const DENS_MAT & dx, DENS_MAT &f) const
{
DENS_MAT & df = fields_[fieldName_].set_quantity();
to_all(column(dx,0),df);
atc_->prescribed_data_manager()->set_fixed_dfield(time_, fieldName_, df);
f += df;
}
void FieldImplicitSolveOperator::rhs(const DENS_MAT & r, DENS_MAT &rhs) const
{
to_all(column(r,0),rhs);
}
} // namespace ATC
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