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rGOOSEFEM/src/GooseFEM/DynamicsDiagonalSemiPeriodic.h
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DynamicsDiagonalSemiPeriodic.h
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/* ========================================== DESCRIPTION ==========================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_DYNAMICS_DIAGONAL_SEMIPERIODIC_H
#define GOOSEFEM_DYNAMICS_DIAGONAL_SEMIPERIODIC_H
#include "Macros.h"
#include <cppmat/cppmat.h>
// -------------------------------------------------------------------------------------------------
namespace GooseFEM {
namespace Dynamics {
namespace Diagonal {
// =========================================== OVERVIEW ============================================
template <class Element>
class SemiPeriodic
{
public:
// variables
// ---------
// element/quadrature/material definition
std::unique_ptr<Element> elem;
// mesh: nodal position/displacement/velocity/acceleration, DOF-numbers, connectivity, dimensions
size_t nnode, nelem, nne, ndim, ndof;
MatS conn, dofs;
MatD x, u, v, a;
// fixed DOFs: prescribed velocity/acceleration, DOF-numbers, dimensions
size_t nfixed;
ColS fixedDofs;
ColD fixedV, fixedA;
// linear system: columns (also "M" and "D" which are diagonal)
ColD M, Minv, D, F, V, V_n, A, A_n;
// time integration
double dt, t=0.0;
// constructor
// -----------
SemiPeriodic(){};
SemiPeriodic(
std::unique_ptr<Element> elem, const MatD &x, const MatS &conn, const MatS &dofs,
const ColS &fixedDofs, double dt
);
// functions
// ---------
void velocityVerlet(); // one time step of time integrator
void Verlet(); // one time step of time integrator (no velocity dependence)
void updated_x(); // process update in "x"
void updated_u(bool init=false); // process update in "u", if init all possible updates are made
void updated_v(bool init=false); // process update in "v", if init all possible updates are made
void assemble_M(); // assemble the mass matrix from the element mass matrices
void assemble_D(); // assemble the damping matrix from the element damping matrices
void assemble_F(); // assemble the force from the element forces
};
// ========================================== SOURCE CODE ==========================================
template<class Element>
SemiPeriodic<Element>::SemiPeriodic(
std::unique_ptr<Element> _elem, const MatD &_x, const MatS &_conn, const MatS &_dofs,
const ColS &_fixedDofs, double _dt
)
{
// copy input
elem = std::move(_elem);
x = _x;
conn = _conn;
dofs = _dofs;
dt = _dt;
fixedDofs = _fixedDofs;
// compute sizes
nfixed = static_cast<size_t>(fixedDofs.size());
nnode = static_cast<size_t>(x.rows());
ndim = static_cast<size_t>(x.cols());
nelem = static_cast<size_t>(conn.rows());
nne = static_cast<size_t>(conn.cols());
ndof = dofs.maxCoeff()+1;
// basic checks (mostly the user is 'trusted')
assert( dofs.size() == nnode * ndim );
assert( ndof < nnode * ndim );
#ifndef NDEBUG
for ( size_t i = 0 ; i < nfixed ; ++i ) assert( fixedDofs(i) < ndof );
#endif
// allocate and zero-initialize nodal quantities
u.conservativeResize(nnode,ndim); u.setZero();
v.conservativeResize(nnode,ndim); v.setZero();
a.conservativeResize(nnode,ndim); a.setZero();
// allocate and zero-initialize linear system (DOFs)
Minv.conservativeResize(ndof);
M .conservativeResize(ndof);
D .conservativeResize(ndof);
F .conservativeResize(ndof);
V .conservativeResize(ndof);
V_n .conservativeResize(ndof); V_n .setZero();
A .conservativeResize(ndof);
A_n .conservativeResize(ndof); A_n .setZero();
// fixed DOFs : default zero velocity and acceleration
fixedV.conservativeResize(nfixed); fixedV.setZero();
fixedA.conservativeResize(nfixed); fixedA.setZero();
// initialize all fields
updated_x();
updated_u(true);
updated_v(true);
}
// =================================================================================================
template<class Element>
void SemiPeriodic<Element>::velocityVerlet()
{
// (1) new positions (displacements)
// - apply update (nodal) : x_{n+1} = x_n + dt * v_n + .5 * dt^2 * a_n"
u += dt * v + ( .5 * std::pow(dt,2.) ) * a;
// - process update in displacements
updated_u();
// (2a) estimate new velocities
// - update velocities (DOFs)
V.noalias() = V_n + dt * A;
// - apply the fixed velocities
for ( size_t i=0; i<nfixed; ++i ) V(fixedDofs(i)) = fixedV(i);
// - convert to nodal velocities (periodicity implies that several nodes depend on the same DOF)
for ( size_t i=0; i<nnode*ndim; ++i ) v(i) = V(dofs(i));
// - process update in velocities
updated_v();
// - solve for accelerations (DOFs)
A.noalias() = Minv.cwiseProduct( - F - D.cwiseProduct(V) );
// - update velocities (DOFs)
V.noalias() = V_n + ( .5 * dt ) * ( A_n + A );
// - apply the fixed velocities
for ( size_t i=0; i<nfixed; ++i ) V(fixedDofs(i)) = fixedV(i);
// - convert to nodal velocities (periodicity implies that several nodes depend on the same DOF)
for ( size_t i=0; i<nnode*ndim; ++i ) v(i) = V(dofs(i));
// - process update in velocities
updated_v();
// (2b) new velocities
// - solve for accelerations (DOFs)
A.noalias() = Minv.cwiseProduct( - F - D.cwiseProduct(V) );
// - update velocities (DOFs)
V.noalias() = V_n + ( .5 * dt ) * ( A_n + A );
// - apply the fixed velocities
for ( size_t i=0; i<nfixed; ++i ) V(fixedDofs(i)) = fixedV(i);
// - convert to nodal velocities (periodicity implies that several nodes depend on the same DOF)
for ( size_t i=0; i<nnode*ndim; ++i ) v(i) = V(dofs(i));
// - process update in velocities
updated_v();
// (3) new accelerations
// - solve for accelerations (DOFs)
A.noalias() = Minv.cwiseProduct( - F - D.cwiseProduct(V) );
// - apply the fixed accelerations
for ( size_t i=0; i<nfixed; ++i ) A(fixedDofs(i)) = fixedA(i);
// - convert to nodal acceleration (periodicity implies that several nodes depend on the same DOF)
for ( size_t i=0; i<nnode*ndim; ++i ) a(i) = A(dofs(i));
// store history
A_n = A; // accelerations (DOFs)
V_n = V; // nodal velocities
t += dt; // current time instance
// N.B. at this point:
// "a" == "A" == "A_n" -> new nodal accelerations, their DOF equivalents, and a 'back-up'
// "v" == "V_n" -> new nodal velocities, and a 'back-up'
// "u" -> new nodal displacements
// The forces "F" correspond to this state of the system
}
// =================================================================================================
template<class Element>
void SemiPeriodic<Element>::Verlet()
{
// (1) new nodal positions (displacements)
// - apply update (nodal) : x_{n+1} = x_n + dt * v_n + .5 * dt^2 * a_n"
u += dt * v + ( .5 * std::pow(dt,2.) ) * a;
// - process update in displacements
updated_u();
// - solve for accelerations (DOFs)
A.noalias() = Minv.cwiseProduct( - F );
// - apply the fixed accelerations
for ( size_t i=0; i<nfixed; ++i ) A(fixedDofs(i)) = fixedA(i);
// - convert to nodal acceleration (periodicity implies that several nodes depend on the same DOF)
for ( size_t i=0; i<nnode*ndim; ++i ) a(i) = A(dofs(i));
// (2) propagate velocities
// - update velocities (DOFs)
V.noalias() = V_n + ( .5 * dt ) * ( A_n + A );
// - apply the fixed velocities
for ( size_t i=0; i<nfixed; ++i ) V(fixedDofs(i)) = fixedV(i);
// - convert to nodal velocities (periodicity implies that several nodes depend on the same DOF)
for ( size_t i=0; i<nnode*ndim; ++i ) v(i) = V(dofs(i));
// store history
A_n = A; // accelerations (DOFs)
V_n = V; // nodal velocities
t += dt; // current time instance
// N.B. at this point:
// "a" == "A" == "A_n" -> new nodal accelerations, their DOF equivalents, and a 'back-up'
// "v" == "V_n" -> new nodal velocities, and a 'back-up'
// "u" -> new nodal displacements
// The forces "F" correspond to this state of the system
}
// =================================================================================================
template<class Element>
void SemiPeriodic<Element>::updated_x()
{
// set the nodal positions of all elements (in parallel)
#pragma omp parallel for
for ( size_t e = 0 ; e < nelem ; ++e )
for ( size_t m = 0 ; m < nne ; ++m )
for ( size_t i = 0 ; i < ndim ; ++i )
elem->x(e,m,i) = x(conn(e,m),i);
// signal update
elem->updated_x();
}
// =================================================================================================
template<class Element>
void SemiPeriodic<Element>::updated_u(bool init)
{
// set the nodal displacements of all elements (in parallel)
#pragma omp parallel for
for ( size_t e = 0 ; e < nelem ; ++e )
for ( size_t m = 0 ; m < nne ; ++m )
for ( size_t i = 0 ; i < ndim ; ++i )
elem->u(e,m,i) = u(conn(e,m),i);
// signal update
elem->updated_u();
// update
if ( elem->changed_M or init ) assemble_M();
if ( elem->changed_D or init ) assemble_D();
if ( elem->changed_f or init ) assemble_F();
}
// =================================================================================================
template<class Element>
void SemiPeriodic<Element>::updated_v(bool init)
{
// set the nodal displacements of all elements (in parallel)
#pragma omp parallel for
for ( size_t e = 0 ; e < nelem ; ++e )
for ( size_t m = 0 ; m < nne ; ++m )
for ( size_t i = 0 ; i < ndim ; ++i )
elem->v(e,m,i) = v(conn(e,m),i);
// signal update
elem->updated_v();
// update
if ( elem->changed_M or init ) assemble_M();
if ( elem->changed_D or init ) assemble_D();
if ( elem->changed_f or init ) assemble_F();
}
// =================================================================================================
template<class Element>
void SemiPeriodic<Element>::assemble_M()
{
// zero-initialize
M.setZero();
// temporarily disable parallelization by Eigen
Eigen::setNbThreads(1);
// assemble
#pragma omp parallel
{
// - mass matrix, per thread
ColD M_(ndof);
M_.setZero();
// - assemble diagonal mass matrix, per thread
#pragma omp for
for ( size_t e = 0 ; e < nelem ; ++e )
for ( size_t m = 0 ; m < nne ; ++m )
for ( size_t i = 0 ; i < ndim ; ++i )
M_(dofs(conn(e,m),i)) += elem->M(e,m*ndim+i,m*ndim+i);
// - reduce "M_" per thread to total "M"
#pragma omp critical
M += M_;
}
// automatic parallelization by Eigen
Eigen::setNbThreads(0);
// compute inverse of the mass matrix
Minv = M.cwiseInverse();
}
// =================================================================================================
template<class Element>
void SemiPeriodic<Element>::assemble_D()
{
// zero-initialize
D.setZero();
// temporarily disable parallelization by Eigen
Eigen::setNbThreads(1);
// assemble
#pragma omp parallel
{
// - damping matrix, per thread
ColD D_(ndof);
D_.setZero();
// - assemble diagonal damping matrix, per thread
#pragma omp for
for ( size_t e = 0 ; e < nelem ; ++e )
for ( size_t m = 0 ; m < nne ; ++m )
for ( size_t i = 0 ; i < ndim ; ++i )
D_(dofs(conn(e,m),i)) += elem->D(e,m*ndim+i,m*ndim+i);
// - reduce "D_" per thread to total "D"
#pragma omp critical
D += D_;
}
// automatic parallelization by Eigen
Eigen::setNbThreads(0);
}
// =================================================================================================
template<class Element>
void SemiPeriodic<Element>::assemble_F()
{
// zero-initialize
F.setZero();
// temporarily disable parallelization by Eigen
Eigen::setNbThreads(1);
// assemble
#pragma omp parallel
{
// - force, per thread
ColD F_(ndof);
F_.setZero();
// - assemble force, per thread
#pragma omp for
for ( size_t e = 0 ; e < nelem ; ++e )
for ( size_t m = 0 ; m < nne ; ++m )
for ( size_t i = 0 ; i < ndim ; ++i )
F_(dofs(conn(e,m),i)) += elem->f(e,m,i);
// - reduce "F_" per thread to total "F"
#pragma omp critical
F += F_;
}
// automatic parallelization by Eigen
Eigen::setNbThreads(0);
}
// =================================================================================================
}}} // namespace GooseFEM::Dynamics::Diagonal
#endif
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