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TyingsPeriodic.h
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/**
Tools to store and apply nodal/DOF tyings.
\file TyingsPeriodic.h
\copyright Copyright 2017. Tom de Geus. All rights reserved.
\license This project is released under the GNU Public License (GPLv3).
*/
#ifndef GOOSEFEM_TYINGSPERIODIC_H
#define GOOSEFEM_TYINGSPERIODIC_H
#include "config.h"
#include <Eigen/Eigen>
#include <Eigen/Sparse>
namespace GooseFEM {
/**
Tools to store and apply nodal/DOF tyings.
*/
namespace Tyings {
/**
Nodal tyings per periodic boundary conditions.
The idea is that the displacement of all DOFs of a node are tied to another node
and to the average displacement gradient.
The latter is applied/measured using 'virtual' control nodes.
Consider the DOF list \f$ u \f$ renumbered such that it is split up in
independent and dependent DOFs as follows
\f$ u = \begin{bmatrix} u_i \\ u_d \end{bmatrix}\f$
whereby the independent DOFs are furthermore split up in unknown and prescribed nodes as follows
\f$ u_i = \begin{bmatrix} u_u \\ u_p \end{bmatrix}\f$
such that
\f$ u = \begin{bmatrix} u_u \\ u_p \\ u_d \end{bmatrix}\f$
\todo Document how the DOFs are tied to the control nodes, and what the has to do with the mean.
*/
class Periodic {
public:
Periodic() = default;
/**
Constructor.
\param coor Nodal coordinates [nnode, ndim].
\param dofs DOF-numbers per node [nnode, ndim].
\param control_dofs DOF-numbers per control node [ndim, ndim].
\param nodal_tyings List of nodal tyings, see nodal_tyings(). [ntyings, 2].
*/
Periodic(
const xt::xtensor<double, 2>& coor,
const xt::xtensor<size_t, 2>& dofs,
const xt::xtensor<size_t, 2>& control_dofs,
const xt::xtensor<size_t, 2>& nodal_tyings);
/**
Constructor.
\param coor Nodal coordinates [nnode, ndim].
\param dofs DOF-numbers per node [nnode, ndim].
\param control_dofs DOF-numbers per control node [ndim, ndim].
\param nodal_tyings List of nodal tyings, see nodal_tyings(). [ntyings, 2].
\param iip List of prescribed DOF-numbers.
*/
Periodic(
const xt::xtensor<double, 2>& coor,
const xt::xtensor<size_t, 2>& dofs,
const xt::xtensor<size_t, 2>& control_dofs,
const xt::xtensor<size_t, 2>& nodal_tyings,
const xt::xtensor<size_t, 1>& iip);
/**
Number of dependent DOFs.
\return unsigned int
*/
size_t nnd() const;
/**
Number of independent DOFs.
\return unsigned int
*/
size_t nni() const;
/**
Number of independent unknown DOFs.
\return unsigned int
*/
size_t nnu() const;
/**
Number of independent prescribed DOFs.
\return unsigned int
*/
size_t nnp() const;
/**
Return the DOF-numbers per node, as used internally (after renumbering).
\return [nnode, ndim].
*/
xt::xtensor<size_t, 2> dofs() const;
/**
Return the DOF-numbers for each control node, as used internally (after renumbering).
\return [ndim, ndim].
*/
xt::xtensor<size_t, 2> control() const;
/**
Return the applied nodal tyings.
Per tying (row) two node numbers are specified,
according to the convention (independent, dependent).
\return [ntyings, 2].
*/
xt::xtensor<size_t, 2> nodal_tyings() const;
/**
Dependent DOFs.
\return List of DOF numbers.
*/
xt::xtensor<size_t, 1> iid() const;
/**
Independent DOFs.
\return List of DOF numbers.
*/
xt::xtensor<size_t, 1> iii() const;
/**
Independent unknown DOFs.
\return List of DOF numbers.
*/
xt::xtensor<size_t, 1> iiu() const;
/**
Independent prescribed DOFs.
\return List of DOF numbers.
*/
xt::xtensor<size_t, 1> iip() const;
/**
Return tying matrix such as to get the dependent DOFs \f$ u_d \f$ from
the independent DOFs \f$ u_i \f$ as follows
\f$ u_d = C_{di} u_i \f$
Note that this can be further partitioned in
\f$ u_d = C_{du} u_u + C_{dp} u_p \f$
See Cdu() and Cdp().
\return Sparse matrix.
*/
Eigen::SparseMatrix<double> Cdi() const;
/**
Unknown part of the partitioned tying matrix, see Cdi().
\return Sparse matrix.
*/
Eigen::SparseMatrix<double> Cdu() const;
/**
Prescribed part of the partitioned tying matrix, see Cdi().
\return Sparse matrix.
*/
Eigen::SparseMatrix<double> Cdp() const;
private:
size_t m_nnu; ///< See nnu().
size_t m_nnp; ///< See nnp().
size_t m_nni; ///< See nni().
size_t m_nnd; ///< See nnd().
size_t m_ndim; ///< Number of dimensions.
size_t m_nties; ///< Number of nodal ties.
xt::xtensor<size_t, 2> m_dofs; ///< See dofs().
xt::xtensor<size_t, 2> m_control; ///< See control().
xt::xtensor<size_t, 2> m_tyings; ///< See nodal_tyings().
xt::xtensor<double, 2> m_coor; ///< Nodal coordinates [nnode, ndim].
};
/**
Add control nodes to an existing system.
*/
class Control {
public:
Control() = default;
/**
Constructor.
\param coor Nodal coordinates [nnode, ndim].
\param dofs DOF-numbers per node [nnode, ndim].
*/
Control(const xt::xtensor<double, 2>& coor, const xt::xtensor<size_t, 2>& dofs);
/**
Nodal coordinates, for the system with control nodes added to it.
\param [nnode + ndim, ndim], with nnode the number of nodes of the original system.
*/
xt::xtensor<double, 2> coor() const;
/**
DOF-numbers per node, for the system with control nodes added to it.
\param [nnode + ndim, ndim], with nnode the number of nodes of the original system.
*/
xt::xtensor<size_t, 2> dofs() const;
/**
DOF-numbers of each control node.
\param [ndim, ndim].
*/
xt::xtensor<size_t, 2> controlDofs() const;
/**
Node-numbers of the control nodes.
\param [ndim].
*/
xt::xtensor<size_t, 1> controlNodes() const;
private:
xt::xtensor<double, 2> m_coor; ///< See coor().
xt::xtensor<size_t, 2> m_dofs; ///< See dofs().
xt::xtensor<size_t, 2> m_control_dofs; ///< See controlDofs().
xt::xtensor<size_t, 1> m_control_nodes; ///< See controlNodes().
};
} // namespace Tyings
} // namespace GooseFEM
#include "TyingsPeriodic.hpp"
#endif

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