NAG Library Function Document

nag_mesh2d_smooth (d06cac)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{nv}$ – IntegerInput

On entry: the total number of vertices in the input mesh.

Constraint: $\mathbf{nv}\ge 3$.

2:    $\mathbf{nelt}$ – IntegerInput

On entry: the number of triangles in the input mesh.

Constraint: $\mathbf{nelt}\le 2\times \mathbf{nv}-1$.

3:    $\mathbf{nedge}$ – IntegerInput

On entry: the number of the boundary and interface edges in the input mesh.

Constraint: $\mathbf{nedge}\ge 1$.

4:    $\mathbf{coor}\left[2\times \mathbf{nv}\right]$ – doubleInput/Output

Note: the $\left(i,j\right)$th element of the matrix is stored in $\mathbf{coor}\left[\left(j-1\right)\times 2+i-1\right]$.

On entry: $\mathbf{coor}\left[\left(\mathit{i}-1\right)\times 2\right]$ contains the $x$ coordinate of the $\mathit{i}$th input mesh vertex, for $\mathit{i}=1,2,\dots ,\mathbf{nv}$; while $\mathbf{coor}\left[\left(\mathit{i}-1\right)\times 2+1\right]$ contains the corresponding $y$ coordinate.

On exit: $\mathbf{coor}\left[\left(\mathit{i}-1\right)\times 2\right]$ will contain the $x$ coordinate of the $\mathit{i}$th smoothed mesh vertex, for $\mathit{i}=1,2,\dots ,\mathbf{nv}$; while $\mathbf{coor}\left[\left(\mathit{i}-1\right)\times 2+1\right]$ will contain the corresponding $y$ coordinate. Note that the coordinates of boundary and interface edge vertices, as well as those specified by you (see the description of numfix), are unchanged by the process.

5:    $\mathbf{edge}\left[3\times \mathbf{nedge}\right]$ – const IntegerInput

Note: the $\left(i,j\right)$th element of the matrix is stored in $\mathbf{edge}\left[\left(j-1\right)\times 3+i-1\right]$.

On entry: the specification of the boundary or interface edges. $\mathbf{edge}\left[\left(j-1\right)\times 3\right]$ and $\mathbf{edge}\left[\left(j-1\right)\times 3+1\right]$ contain the vertex numbers of the two end points of the $j$th boundary edge. $\mathbf{edge}\left[\left(j-1\right)\times 3+2\right]$ is a user-supplied tag for the $j$th boundary or interface edge: $\mathbf{edge}\left[\left(j-1\right)\times 3+2\right]=0$ for an interior edge and has a nonzero tag otherwise. Note that the edge vertices are numbered from $1$ to nv.

Constraint: $1\le \mathbf{edge}\left[\left(\mathit{j}-1\right)\times 3+\mathit{i}-1\right]\le \mathbf{nv}$ and $\mathbf{edge}\left[\left(\mathit{j}-1\right)\times 3\right]\ne \mathbf{edge}\left[\left(\mathit{j}-1\right)\times 3+1\right]$, for $\mathit{i}=1,2$ and $\mathit{j}=1,2,\dots ,\mathbf{nedge}$.

6:    $\mathbf{conn}\left[3\times \mathbf{nelt}\right]$ – const IntegerInput

Note: the $\left(i,j\right)$th element of the matrix is stored in $\mathbf{conn}\left[\left(j-1\right)\times 3+i-1\right]$.

On entry: the connectivity of the mesh between triangles and vertices. For each triangle $\mathit{j}$, $\mathbf{conn}\left[\left(\mathit{j}-1\right)\times 3+\mathit{i}-1\right]$ gives the indices of its three vertices (in anticlockwise order), for $\mathit{i}=1,2,3$ and $\mathit{j}=1,2,\dots ,\mathbf{nelt}$. Note that the mesh vertices are numbered from $1$ to nv.

Constraint: $1\le \mathbf{conn}\left[\left(\mathit{j}-1\right)\times 3+\mathit{i}-1\right]\le \mathbf{nv}$ and $\mathbf{conn}\left[\left(\mathit{j}-1\right)\times 3\right]\ne \mathbf{conn}\left[\left(\mathit{j}-1\right)\times 3+1\right]$ and $\mathbf{conn}\left[\left(\mathit{j}-1\right)\times 3\right]\ne \mathbf{conn}\left[\left(\mathit{j}-1\right)\times 3+2\right]$ and $\mathbf{conn}\left[\left(\mathit{j}-1\right)\times 3+1\right]\ne \mathbf{conn}\left[\left(\mathit{j}-1\right)\times 3+2\right]$, for $\mathit{i}=1,2,3$ and $\mathit{j}=1,2,\dots ,\mathbf{nelt}$.

7:    $\mathbf{nvfix}$ – IntegerInput

On entry: the number of fixed vertices in the input mesh.

Constraint: $0\le \mathbf{nvfix}\le \mathbf{nv}$.

8:    $\mathbf{numfix}\left[\mathit{dim}\right]$ – const IntegerInput

Note: the dimension, dim, of the array numfix must be at least $\max \left(1,\mathbf{nvfix}\right)$.

On entry: the indices in coor of fixed interior vertices of the input mesh.

Constraint: if $\mathbf{nvfix}>0$, $1\le \mathbf{numfix}\left[\mathit{i}-1\right]\le \mathbf{nv}$, for $\mathit{i}=1,2,\dots ,\mathbf{nvfix}$.

9:    $\mathbf{itrace}$ – IntegerInput

On entry: the level of trace information required from nag_mesh2d_smooth (d06cac).

$\mathbf{itrace}\le 0$

No output is generated.

$\mathbf{itrace}=1$

A histogram of the triangular element qualities is printed before and after smoothing. This histogram gives the lowest and the highest triangle quality as well as the number of elements lying in each of the nqint equal intervals between the extremes.

$\mathbf{itrace}>1$

The output is similar to that produced when $\mathbf{itrace}=1$ but the connectivity between vertices and triangles (for each vertex, the list of triangles in which it appears) is given.

You are advised to set $\mathbf{itrace}=0$, unless you are experienced with finite element meshes.

10:  $\mathbf{outfile}$ – const char *Input

On entry: the name of a file to which diagnostic output will be directed. If outfile is NULL the diagnostic output will be directed to standard output.

11:  $\mathbf{nqint}$ – IntegerInput

On entry: the number of intervals between the extreme quality values for the input and the smoothed mesh.

If $\mathbf{itrace}=0$, nqint is not referenced.

12:  $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

On entry, $\mathbf{nedge}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nedge}\ge 1$.

On entry, $\mathbf{nv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nv}\ge 3$.

NE_INT_2

On entry, $\mathbf{nelt}=〈\mathit{\text{value}}〉$ and $\mathbf{nv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nelt}\le 2\times \mathbf{nv}-1$.

On entry, $\mathbf{nv}=〈\mathit{\text{value}}〉$ and $\mathbf{nvfix}=〈\mathit{\text{value}}〉$.
Constraint: $0\le \mathbf{nvfix}\le \mathbf{nv}$.

On entry, the end points of the edge $\mathit{J}$ have the same index $\mathit{I}$: $\mathit{J}=〈\mathit{\text{value}}〉$ and $\mathit{I}=〈\mathit{\text{value}}〉$.

On entry, vertices $1$ and $2$ of the triangle $\mathit{K}$ have the same index $\mathit{I}$: $\mathit{K}=〈\mathit{\text{value}}〉$ and $\mathit{I}=〈\mathit{\text{value}}〉$.

On entry, vertices $1$ and $3$ of the triangle $\mathit{K}$ have the same index $\mathit{I}$: $\mathit{K}=〈\mathit{\text{value}}〉$ and $\mathit{I}=〈\mathit{\text{value}}〉$.

On entry, vertices $2$ and $3$ of the triangle $\mathit{K}$ have the same index $\mathit{I}$: $\mathit{K}=〈\mathit{\text{value}}〉$ and $\mathit{I}=〈\mathit{\text{value}}〉$.

NE_INT_3

On entry, $\mathbf{numfix}\left[\mathit{I}-1\right]=〈\mathit{\text{value}}〉$, $\mathit{I}=〈\mathit{\text{value}}〉$ and $\mathbf{nv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{numfix}\left[\mathit{I}-1\right]\ge 1$ and $\mathbf{numfix}\left[\mathit{I}-1\right]\le \mathbf{nv}$.

NE_INT_4

On entry, $\mathbf{conn}\left(\mathit{I},\mathit{J}\right)=〈\mathit{\text{value}}〉$, $\mathit{I}=〈\mathit{\text{value}}〉$, $\mathit{J}=〈\mathit{\text{value}}〉$ and $\mathbf{nv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{conn}\left(\mathit{I},\mathit{J}\right)\ge 1$ and $\mathbf{conn}\left(\mathit{I},\mathit{J}\right)\le \mathbf{nv}$, where $\mathbf{conn}\left(\mathit{I},\mathit{J}\right)$ denotes $\mathbf{conn}\left[\left(\mathit{J}-1\right)\times 3+\mathit{I}-1\right]$.

On entry, $\mathbf{edge}\left(\mathit{I},\mathit{J}\right)=〈\mathit{\text{value}}〉$, $\mathit{I}=〈\mathit{\text{value}}〉$, $\mathit{J}=〈\mathit{\text{value}}〉$ and $\mathbf{nv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{edge}\left(\mathit{I},\mathit{J}\right)\ge 1$ and $\mathbf{edge}\left(\mathit{I},\mathit{J}\right)\le \mathbf{nv}$, where $\mathbf{edge}\left(\mathit{I},\mathit{J}\right)$ denotes $\mathbf{edge}\left[\left(\mathit{J}-1\right)\times 3+\mathit{I}-1\right]$.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

A serious error has occurred in an internal call to an auxiliary function. Check the input mesh especially the connectivity. Seek expert help.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_NOT_CLOSE_FILE

Cannot close file $〈\mathit{\text{value}}〉$.

NE_NOT_WRITE_FILE

Cannot open file $〈\mathit{\text{value}}〉$ for writing.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (d06cace.c)

10.2

Program Data

Program Data (d06cace.d)

10.3

Program Results

Program Results (d06cace.r)