Detailed Description

template<typename ShapeFunction>
class ApplicationUtils::ComputeNaturalCoordsRootFindingProblem< ShapeFunction >

Models the computation of natural coordinates inside a given mesh element for some given real coordinates as a root finding problem.

That root finding problem is designed such that it can be easily used/solved by the NumLib::NewtonRaphson solver.

Definition at line 28 of file ComputeNaturalCoordsRootFindingProblem.h.

#include <ComputeNaturalCoordsRootFindingProblem.h>

Collaboration diagram for ApplicationUtils::ComputeNaturalCoordsRootFindingProblem< ShapeFunction >:

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Public Types
using	LocalJacobianMatrix
using	LocalResidualVector = Eigen::Matrix<double, Dim, 1>

Public Member Functions
	ComputeNaturalCoordsRootFindingProblem (MeshLib::Element const &e, LocalResidualVector const &x_expected)
void	updateJacobian (LocalJacobianMatrix &J) const
void	updateResidual (LocalResidualVector &res) const
void	updateSolution (LocalResidualVector const &delta_r)
LocalResidualVector const &	getNaturalCoordinates () const

Private Types
using	ShapeMatricesType = ShapeMatrixPolicyType<ShapeFunction, Dim>
using	NodeCoordsMatrix

Private Member Functions
void	updateShp ()

Static Private Member Functions
static NodeCoordsMatrix	getNodeCoords (MeshLib::Element const &e)
static constexpr LocalResidualVector	initialGuess ()

Private Attributes
MeshLib::Element const &	e_
NodeCoordsMatrix const	node_coords_
LocalResidualVector const	x_expected_
ShapeMatricesType::ShapeMatrices	sm_
LocalResidualVector	r_ = initialGuess()

Static Private Attributes
static constexpr int	Dim = ShapeFunction::DIM

Member Typedef Documentation

◆ LocalJacobianMatrix

template<typename ShapeFunction>

using ApplicationUtils::ComputeNaturalCoordsRootFindingProblem< ShapeFunction >::LocalJacobianMatrix

Initial value:

Eigen::Matrix<double, Dim, Dim, Eigen::RowMajor>

Definition at line 34 of file ComputeNaturalCoordsRootFindingProblem.h.

◆ LocalResidualVector

template<typename ShapeFunction>

using ApplicationUtils::ComputeNaturalCoordsRootFindingProblem< ShapeFunction >::LocalResidualVector = Eigen::Matrix<double, Dim, 1>

Used for the residuum ("res"), the solution vector ("r", natural coordinates) and real coordinates ("x").

Definition at line 38 of file ComputeNaturalCoordsRootFindingProblem.h.

◆ NodeCoordsMatrix

template<typename ShapeFunction>

using ApplicationUtils::ComputeNaturalCoordsRootFindingProblem< ShapeFunction >::NodeCoordsMatrix

private

Initial value:

Eigen::Matrix<double, Dim, ShapeFunction::NPOINTS, Eigen::RowMajor>

Definition at line 79 of file ComputeNaturalCoordsRootFindingProblem.h.

◆ ShapeMatricesType

template<typename ShapeFunction>

using ApplicationUtils::ComputeNaturalCoordsRootFindingProblem< ShapeFunction >::ShapeMatricesType = ShapeMatrixPolicyType<ShapeFunction, Dim>

private

Definition at line 31 of file ComputeNaturalCoordsRootFindingProblem.h.

Constructor & Destructor Documentation

◆ ComputeNaturalCoordsRootFindingProblem()

template<typename ShapeFunction>

ApplicationUtils::ComputeNaturalCoordsRootFindingProblem< ShapeFunction >::ComputeNaturalCoordsRootFindingProblem	(	MeshLib::Element const &	e,
		LocalResidualVector const &	x_expected )

inline

Definition at line 40 of file ComputeNaturalCoordsRootFindingProblem.h.

        : e_{e},
          node_coords_{getNodeCoords(e)},
          x_expected_{x_expected},
          // TODO 2D elements with 3D coordinates etc.
          // TODO check all dims
          sm_{ShapeFunction::DIM, e.getDimension(), ShapeFunction::NPOINTS}
    {
        updateShp();
    }

References e_, getNodeCoords(), node_coords_, sm_, updateShp(), and x_expected_.

Member Function Documentation

◆ getNaturalCoordinates()

template<typename ShapeFunction>

LocalResidualVector const & ApplicationUtils::ComputeNaturalCoordsRootFindingProblem< ShapeFunction >::getNaturalCoordinates ( ) const

inline

Definition at line 76 of file ComputeNaturalCoordsRootFindingProblem.h.

76{ return r_; }

ApplicationUtils::ComputeNaturalCoordsRootFindingProblem::r_

LocalResidualVector r_

Definition ComputeNaturalCoordsRootFindingProblem.h:116

References r_.

◆ getNodeCoords()

template<typename ShapeFunction>

NodeCoordsMatrix ApplicationUtils::ComputeNaturalCoordsRootFindingProblem< ShapeFunction >::getNodeCoords ( MeshLib::Element const & e )

inlinestaticprivate

Definition at line 93 of file ComputeNaturalCoordsRootFindingProblem.h.

    {
        NodeCoordsMatrix node_coords;
 
        for (std::size_t n = 0; n < ShapeFunction::NPOINTS; ++n)
        {
            node_coords.col(n) = Eigen::Map<const Eigen::Vector<double, Dim>>(
                e.getNode(n)->data());
        }
 
        return node_coords;
    }

References MeshLib::Element::getNode().

Referenced by ComputeNaturalCoordsRootFindingProblem().

◆ initialGuess()

template<typename ShapeFunction>

constexpr LocalResidualVector ApplicationUtils::ComputeNaturalCoordsRootFindingProblem< ShapeFunction >::initialGuess ( )

inlinestaticconstexprprivate

Definition at line 106 of file ComputeNaturalCoordsRootFindingProblem.h.

    {
        return LocalResidualVector::Constant(0.5);
    }

◆ updateJacobian()

template<typename ShapeFunction>

void ApplicationUtils::ComputeNaturalCoordsRootFindingProblem< ShapeFunction >::updateJacobian ( LocalJacobianMatrix & J ) const

inline

Definition at line 52 of file ComputeNaturalCoordsRootFindingProblem.h.

    {
        auto const& dNdr = sm_.dNdr;
 
        for (int comp = 0; comp < Dim; ++comp)
        {
            J.row(comp) = node_coords_.row(comp) * dNdr.transpose();
        }
    }

References Dim, node_coords_, and sm_.

◆ updateResidual()

template<typename ShapeFunction>

void ApplicationUtils::ComputeNaturalCoordsRootFindingProblem< ShapeFunction >::updateResidual ( LocalResidualVector & res ) const

inline

Definition at line 62 of file ComputeNaturalCoordsRootFindingProblem.h.

    {
        res = node_coords_ * sm_.N.transpose() - x_expected_;
    }

References node_coords_, sm_, and x_expected_.

◆ updateShp()

template<typename ShapeFunction>

void ApplicationUtils::ComputeNaturalCoordsRootFindingProblem< ShapeFunction >::updateShp ( )

inlineprivate

Definition at line 82 of file ComputeNaturalCoordsRootFindingProblem.h.

    {
        auto const fe =
            NumLib::createIsoparametricFiniteElement<ShapeFunction,
                                                     ShapeMatricesType>(e_);
 
        constexpr auto GlobalDim = Dim;
        fe.template computeShapeFunctions<NumLib::ShapeMatrixType::N_J>(
            r_.data(), sm_, GlobalDim, false);
    }

References NumLib::createIsoparametricFiniteElement(), Dim, e_, r_, and sm_.

Referenced by ComputeNaturalCoordsRootFindingProblem(), and updateSolution().

◆ updateSolution()

template<typename ShapeFunction>

void ApplicationUtils::ComputeNaturalCoordsRootFindingProblem< ShapeFunction >::updateSolution ( LocalResidualVector const & delta_r )

inline

Updates the current guess.

Parameters

delta_r the solution increment (natural coordinates)

Definition at line 70 of file ComputeNaturalCoordsRootFindingProblem.h.

    {
        r_ += delta_r;
        updateShp();
    }

References r_, and updateShp().

Member Data Documentation

◆ Dim

template<typename ShapeFunction>

int ApplicationUtils::ComputeNaturalCoordsRootFindingProblem< ShapeFunction >::Dim = ShapeFunction::DIM

staticconstexprprivate

Definition at line 30 of file ComputeNaturalCoordsRootFindingProblem.h.

Referenced by updateJacobian(), and updateShp().

◆ e_

template<typename ShapeFunction>

MeshLib::Element const& ApplicationUtils::ComputeNaturalCoordsRootFindingProblem< ShapeFunction >::e_

private

Definition at line 111 of file ComputeNaturalCoordsRootFindingProblem.h.

Referenced by ComputeNaturalCoordsRootFindingProblem(), and updateShp().

◆ node_coords_

template<typename ShapeFunction>

NodeCoordsMatrix const ApplicationUtils::ComputeNaturalCoordsRootFindingProblem< ShapeFunction >::node_coords_

private

Definition at line 112 of file ComputeNaturalCoordsRootFindingProblem.h.

Referenced by ComputeNaturalCoordsRootFindingProblem(), updateJacobian(), and updateResidual().

◆ r_

template<typename ShapeFunction>

LocalResidualVector ApplicationUtils::ComputeNaturalCoordsRootFindingProblem< ShapeFunction >::r_ = initialGuess()

private

Definition at line 116 of file ComputeNaturalCoordsRootFindingProblem.h.

Referenced by getNaturalCoordinates(), updateShp(), and updateSolution().

◆ sm_

template<typename ShapeFunction>

ShapeMatricesType::ShapeMatrices ApplicationUtils::ComputeNaturalCoordsRootFindingProblem< ShapeFunction >::sm_

private

Definition at line 115 of file ComputeNaturalCoordsRootFindingProblem.h.

Referenced by ComputeNaturalCoordsRootFindingProblem(), updateJacobian(), updateResidual(), and updateShp().

◆ x_expected_

template<typename ShapeFunction>

LocalResidualVector const ApplicationUtils::ComputeNaturalCoordsRootFindingProblem< ShapeFunction >::x_expected_

private

Definition at line 113 of file ComputeNaturalCoordsRootFindingProblem.h.

Referenced by ComputeNaturalCoordsRootFindingProblem(), and updateResidual().

The documentation for this class was generated from the following file:

ComputeNaturalCoordsRootFindingProblem.h

Detailed Description

Public Types

Public Member Functions

Private Types

Private Member Functions

Static Private Member Functions

Private Attributes

Static Private Attributes

Member Typedef Documentation

◆ LocalJacobianMatrix

◆ LocalResidualVector

◆ NodeCoordsMatrix

◆ ShapeMatricesType

Constructor & Destructor Documentation

◆ ComputeNaturalCoordsRootFindingProblem()

Member Function Documentation

◆ getNaturalCoordinates()

◆ getNodeCoords()

◆ initialGuess()

◆ updateJacobian()

◆ updateResidual()

◆ updateShp()

◆ updateSolution()

Member Data Documentation

◆ Dim

◆ e_

◆ node_coords_

◆ r_

◆ sm_

◆ x_expected_