NAG Library Function Document

nag_mesh2d_inc (d06aac)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{nvb}$ – IntegerInput

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

Constraint: $3\le \mathbf{nvb}\le \mathbf{nvmax}$.

2:    $\mathbf{nvmax}$ – IntegerInput

On entry: the maximum number of vertices in the mesh to be generated.

3:    $\mathbf{nedge}$ – IntegerInput

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

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

4:    $\mathbf{edge}\left[3\times \mathbf{nedge}\right]$ – 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 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 edge and is not used by nag_mesh2d_inc (d06aac). Note that the edge vertices are numbered from $1$ to nvb.

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

5:    $\mathbf{nv}$ – Integer *Output

On exit: the total number of vertices in the output mesh (including both boundary and interior vertices). If $\mathbf{nvb}=\mathbf{nvmax}$, no interior vertices will be generated and $\mathbf{nv}=\mathbf{nvb}$.

6:    $\mathbf{nelt}$ – Integer *Output

On exit: the number of triangular elements in the mesh.

7:    $\mathbf{coor}\left[2\times \mathbf{nvmax}\right]$ – 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 boundary mesh vertex; while $\mathbf{coor}\left[\left(\mathit{i}-1\right)\times 2+1\right]$ contains the corresponding $y$ coordinate, for $\mathit{i}=1,2,\dots ,\mathbf{nvb}$.

On exit: $\mathbf{coor}\left[\left(\mathit{i}-1\right)\times 2\right]$ will contain the $x$ coordinate of the $\left(\mathit{i}-\mathbf{nvb}\right)$th generated interior mesh vertex; while $\mathbf{coor}\left[\left(\mathit{i}-1\right)\times 2+1\right]$ will contain the corresponding $y$ coordinate, for $\mathit{i}=\mathbf{nvb}+1,\dots ,\mathbf{nv}$. The remaining elements are unchanged.

8:    $\mathbf{conn}\left[3\times 2\times \left(\mathbf{nvmax}-1\right)\right]$ – IntegerOutput

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 exit: 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.

9:    $\mathbf{bspace}\left[\mathbf{nvb}\right]$ – const doubleInput

On entry: the desired mesh spacing (triangle diameter, which is the length of the longer edge of the triangle) near the boundary vertices.

Constraint: $\mathbf{bspace}\left[\mathit{i}-1\right]>0.0$, for $\mathit{i}=1,2,\dots ,\mathbf{nvb}$.

10:  $\mathbf{smooth}$ – Nag_BooleanInput

On entry: indicates whether or not mesh smoothing should be performed.

If $\mathbf{smooth}=\mathrm{Nag\_TRUE}$, the smoothing is performed; otherwise no smoothing is performed.

11:  $\mathbf{coef}$ – doubleInput

On entry: the coefficient in the stopping criteria for the generation of interior vertices. This argument controls the triangle density and the number of triangles generated is in $\mathit{O}\left({\mathbf{coef}}^2\right)$. The mesh will be finer if coef is greater than $0.7165$ and $0.75$ is a good value.

Suggested value: $0.75$.

12:  $\mathbf{power}$ – doubleInput

On entry: controls the rate of change of the mesh size during the generation of interior vertices. The smaller the value of power, the faster the decrease in element size away from the boundary.

Suggested value: $0.25$.

Constraint: $0.1\le \mathbf{power}\le 10.0$.

13:  $\mathbf{itrace}$ – IntegerInput

On entry: the level of trace information required from nag_mesh2d_inc (d06aac).

$\mathbf{itrace}\le 0$

No output is generated.

$\mathbf{itrace}\ge 1$

Output from the meshing solver is printed. This output contains details of the vertices and triangles generated by the process.

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

14:  $\mathbf{outfile}$ – 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.

15:  $\mathbf{fail}$ – 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: $\mathbf{nedge}\ge 1$.

NE_INT_2

On entry, $\mathbf{nvb}=〈\mathit{\text{value}}〉$ and $\mathbf{nvmax}=〈\mathit{\text{value}}〉$.
Constraint: $3\le \mathbf{nvb}\le \mathbf{nvmax}$.

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

NE_INT_4

On entry, $\mathbf{edge}\left(\mathit{I},\mathit{J}\right)=〈\mathit{\text{value}}〉$, $\mathit{I}=〈\mathit{\text{value}}〉$, $\mathit{J}=〈\mathit{\text{value}}〉$ and $\mathbf{nvb}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{edge}\left(\mathit{I},\mathit{J}\right)\ge 1$ and $\mathbf{edge}\left(\mathit{I},\mathit{J}\right)\le \mathbf{nvb}$, 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.

NE_MESH_ERROR

An error has occurred during the generation of the interior mesh. Check the inputs of the boundary.

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.

NE_REAL

On entry, $\mathbf{power}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{power}\le 10.0$.

On entry, $\mathbf{power}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{power}\ge 0.1$.

NE_REAL_ARRAY_INPUT

On entry, $\mathbf{bspace}\left[\mathit{I}-1\right]=〈\mathit{\text{value}}〉$ and $\mathit{I}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{bspace}\left[\mathit{I}-1\right]>0.0$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (d06aace.c)

10.2

Program Data

Program Data (d06aace.d)

10.3

Program Results

Program Results (d06aace.r)