CenterMF2D Class Reference

#include <TMPQualityMetricTest.hpp>

Inheritance diagram for CenterMF2D:

Collaboration diagram for CenterMF2D:

Public Member Functions
	CenterMF2D (const MappingFunction2D *real_mf)
EntityTopology	element_topology () const
	Get MBMesquite::EntityTopology handled by this mapping function.
int	num_nodes () const
	Get number of nodes in the element type.
NodeSet	sample_points (NodeSet) const
	Get sample points at which to evaluate mapping function.
void	coefficients (Sample l, NodeSet s, double *c, size_t *i, size_t &n, MsqError &e) const
	Mapping Function Coefficients.
void	derivatives (Sample l, NodeSet s, size_t *i, MsqVector< 2 > *c, size_t &n, MsqError &e) const
	Mapping Function Derivatives.
Private Attributes
const MappingFunction2D *	myFunc

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Detailed Description

Definition at line 228 of file TMPQualityMetricTest.hpp.

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Constructor & Destructor Documentation

CenterMF2D::CenterMF2D

(

const MappingFunction2D *

real_mf

)

[inline]

Definition at line 231 of file TMPQualityMetricTest.hpp.

: myFunc( real_mf ){};

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Member Function Documentation

void CenterMF2D::coefficients	(	Sample	location,
		NodeSet	nodeset,
		double *	coeff_out,
		size_t *	indices_out,
		size_t &	num_coeff_out,
		MsqError &	err
	)		const [inline, virtual]

Mapping Function Coefficients.

This function returns the list of scalar values ( \(N_i\)'s) resulting from the evaluation of the mapping function coefficient terms \(N_1(\vec{\xi}), N_2(\vec{\xi}), \ldots, N_n(\vec{\xi})\) for a given \(\vec{\xi}\).

Parameters:

location	Where within the element at which to evaluate the coefficients.
nodeset	List of which nodes are present in the element.
coefficients_out	The coefficients ( \(N_i(\vec{\xi})\)) for each vertex in the element.
indices_out	The index ($i$ in $N_i$) for each term in 'coeffs_out'. The assumption is that mapping function implementations will not return zero coefficients. This is not required, but for element types with large numbers of nodes it may have a significant impact on performance.

Implements MBMesquite::MappingFunction.

Definition at line 246 of file TMPQualityMetricTest.hpp.

    {
        myFunc->coefficients( l, s, c, i, n, e );
    }

void CenterMF2D::derivatives	(	Sample	location,
		NodeSet	nodeset,
		size_t *	vertex_indices_out,
		MsqVector< 2 > *	d_coeff_d_xi_out,
		size_t &	num_vtx,
		MsqError &	err
	)		const [inline, virtual]

Mapping Function Derivatives.

This function returns the partial derivatives of the mapping function coefficient terms \(\nabla N_1(\vec{\xi}), \nabla N_2(\vec{\xi}), \ldots, \nabla N_n(\vec{\xi})\) evaluated for a given \(\vec{\xi}\), where \(\vec{x_i}\) is a point in \(\mathbf{R}^3\) (i.e. \(x_i,y_i,z_i\)). \(\vec{\xi_i} = \left\{\begin{array}{c}\xi_i\\ \eta_i\\ \end{array}\right\}\) for surface elements and \(\vec{\xi_i} = \left\{\begin{array}{c}\xi_i\\ \eta_i\\ \zeta_i\\ \end{array}\right\}\) for volume elements.

The list of returned partial derivatives may be considered list of elements of a matrix \(\mathbf{D}\) in row major order. For surface elements, \(\mathbf{D}\) is a \(n\times 2\) matrix and for volume elements it is a \(n \times 3\) matrix. Each row of \(\mathbf{D}\) corresponds to one of the coefficient functions \(N_i(\vec{\xi})\) and each column corresponds to one of the components of \(\vec{\xi}\) that the corresponding coefficient function is differentiated with respect to.

\( \mathbf{D} = \left[ \begin{array}{ccc} \frac{\delta N_1}{\delta \xi} & \frac{\delta N_1}{\delta \eta} & \ldots \\ \frac{\delta N_2}{\delta \xi} & \frac{\delta N_2}{\delta \eta} & \ldots \\ \vdots & \vdots & \ddots \end{array} \right]\)

The Jacobian matrix ( \(\mathbf{J}\)) of the mapping function can be calculated as follows. Define a matrix \(\mathbf{X}\) such that each column contains the coordinates of the element nodes.

\( \mathbf{X} = \left[ \begin{array}{ccc} x_1 & x_2 & \ldots \\ y_1 & y_2 & \ldots \\ z_1 & z_2 & \ldots \end{array}\right]\)

The Jacobian matrix is then:

\(\mathbf{J} = \mathbf{X} \times \mathbf{D}\)

\(\mathbf{X}\) is always \(3\times n\), so \(\mathbf{J}\) is either \(3\times 2\) (surface elements) or \(3\times 3\) (volume elements) depending on the dimensions of \(\mathbf{D}\).

If the Jacobian matrix of the mapping function is considered as a function of the element vertex coordinates \(\mathbf{J}(\vec{x_1},\vec{x_2},\ldots)\) with \(\vec{\xi}\) constant, then the gradient of that Jacobian matrix function (with respect to the vertex coordinates) can be obtained from the same output list of partial deravitves.

\(\frac{\delta \mathbf{J}}{\delta x_i} = \left[ \begin{array}{ccc} \frac{\delta N_i}{\delta \xi} & \frac{\delta N_i}{\delta \eta} & \ldots \\ 0 & 0 & \ldots \\ 0 & 0 & \ldots \end{array} \right]\) \(\frac{\delta \mathbf{J}}{\delta y_i} = \left[ \begin{array}{ccc} 0 & 0 & \ldots \\ \frac{\delta N_i}{\delta \xi} & \frac{\delta N_i}{\delta \eta} & \ldots \\ 0 & 0 & \ldots \end{array} \right]\) \(\frac{\delta \mathbf{J}}{\delta z_i} = \left[ \begin{array}{ccc} 0 & 0 & \ldots \\ 0 & 0 & \ldots \\ \frac{\delta N_i}{\delta \xi} & \frac{\delta N_i}{\delta \eta} & \ldots \end{array} \right]\)

Parameters:

location	Where within the element at which to evaluate the derivatives.
nodeset	List of which nodes are present in the element.
vertices_out	The list of vertices for which the corresponding coefficient in the mapping function is non-zero. The vertices are specified by their index in the canonical ordering for an element with all mid-nodes present (i.e. first all the corner nodes, then the mid-edge nodes, ...).
d_coeff_d_xi_out	The mapping function is composed of a series of coefficient functions \(N_i(\vec{\xi})\), one correspoding to the position \(\vec{x_i}\) of each node in the element such that the mapping function is of the form: \(\vec{x}(\vec{\xi})=\sum_{i=1}^n N_i(\vec{\xi})\vec{x_i}\). For each vertex indicated in vertex_indices_out, this list contains the partial derivatives of the cooresponding coefficient function \(N_i\) with respect to each component of \(\vec{\xi}\) in the same order as the corresponding nodes in vertex_indices_out.
num_vtx	Output: The number of vertex indices and derivitive tuples returned in vertices_out and d_coeff_d_xi_out, respectively.

Implements MBMesquite::MappingFunction2D.

Definition at line 250 of file TMPQualityMetricTest.hpp.

    {
        myFunc->derivatives( l, s, i, c, n, e );
    }

EntityTopology CenterMF2D::element_topology

(

)

const [inline, virtual]

Get MBMesquite::EntityTopology handled by this mapping function.

Implements MBMesquite::MappingFunction.

Definition at line 232 of file TMPQualityMetricTest.hpp.

    {
        return myFunc->element_topology();
    }

int CenterMF2D::num_nodes

(

)

const [inline, virtual]

Get number of nodes in the element type.

Get the number of nodes in the element type that the mapping function implements. It is assumed that the result of this function, in combination with the element topology, is sufficient to determine the element type.

Implements MBMesquite::MappingFunction.

Definition at line 236 of file TMPQualityMetricTest.hpp.

    {
        return myFunc->num_nodes();
    }

NodeSet CenterMF2D::sample_points

(

NodeSet

higher_order_nodes

)

const [inline, virtual]

Get sample points at which to evaluate mapping function.

Get the points within the element at which TMP quality metrics that are a function of the mapping function Jacobian should be evaluated. The default (which may be overridden by individual mapping functions) is to evaluate at all nodes.

Reimplemented from MBMesquite::MappingFunction.

Definition at line 240 of file TMPQualityMetricTest.hpp.

References MBMesquite::NodeSet::set_mid_face_node().

    {
        NodeSet s;
        s.set_mid_face_node( 0 );
        return s;
    }

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Member Data Documentation

const MappingFunction2D* CenterMF2D::myFunc [private]

Definition at line 256 of file TMPQualityMetricTest.hpp.

List of all members.

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

• TMPQualityMetricTest.hpp