NAG FL Interface
d06aaf (dim2_​gen_​inc)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{nvb}$ – Integer Input

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

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

2: $\mathbf{nvmax}$ – Integer Input

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

3: $\mathbf{nedge}$ – Integer Input

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

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

4: $\mathbf{edge}\left(3,\mathbf{nedge}\right)$ – Integer array Input

On entry: the specification of the boundary edges. $\mathbf{edge}\left(1,j\right)$ and $\mathbf{edge}\left(2,j\right)$ contain the vertex numbers of the two end points of the $j$th boundary edge. $\mathbf{edge}\left(3,j\right)$ is a user-supplied tag for the $j$th boundary edge and is not used by d06aaf.

Constraint: $1\le \mathbf{edge}\left(\mathit{i},\mathit{j}\right)\le \mathbf{nvb}$ and $\mathbf{edge}\left(1,\mathit{j}\right)\ne \mathbf{edge}\left(2,\mathit{j}\right)$, 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: $\mathbf{coor}\left(2,\mathbf{nvmax}\right)$ – Real (Kind=nag_wp) array Input/Output

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

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

8: $\mathbf{conn}\left(3,2\times \left(\mathbf{nvmax}-1\right)\right)$ – Integer array Output

On exit: the connectivity of the mesh between triangles and vertices. For each triangle $\mathit{j}$, $\mathbf{conn}\left(\mathit{i},\mathit{j}\right)$ gives the indices of its three vertices (in anticlockwise order), for $\mathit{i}=1,2,3$ and $\mathit{j}=1,2,\dots ,\mathbf{nelt}$.

9: $\mathbf{bspace}\left(\mathbf{nvb}\right)$ – Real (Kind=nag_wp) array Input

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

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

10: $\mathbf{smooth}$ – Logical Input

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

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

11: $\mathbf{coef}$ – Real (Kind=nag_wp) Input

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: $\mathbf{power}$ – Real (Kind=nag_wp) Input

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: $\mathbf{itrace}$ – Integer Input

On entry: the level of trace information required from d06aaf.

$\mathbf{itrace}\le 0$

No output is generated.

$\mathbf{itrace}\ge 1$

Output from the meshing solver is printed on the current advisory message unit (see x04abf). 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: $\mathbf{rwork}\left(\mathbf{lrwork}\right)$ – Real (Kind=nag_wp) array Workspace

15: $\mathbf{lrwork}$ – Integer Input

On entry: the dimension of the array rwork as declared in the (sub)program from which d06aaf is called.

Constraint: $\mathbf{lrwork}\ge \mathbf{nvmax}$.

16: $\mathbf{iwork}\left(\mathbf{liwork}\right)$ – Integer array Workspace

17: $\mathbf{liwork}$ – Integer Input

On entry: the dimension of the array iwork as declared in the (sub)program from which d06aaf is called.

Constraint: $\mathbf{liwork}\ge 16\times \mathbf{nvmax}+2\times \mathbf{nedge}+\max \left(4\times \mathbf{nvmax}+2,\mathbf{nedge}\right)-14$.

18: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ or $\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

$\mathbf{ifail}=1$

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

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 $\mathbf{edge}\left(\mathit{I},\mathit{J}\right)\le \mathbf{nvb}$.

On entry, $\mathbf{liwork}=〈\mathit{\text{value}}〉$ and $\mathrm{LIWKMN}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{liwork}\ge \mathrm{LIWKMN}$.

On entry, $\mathbf{lrwork}=〈\mathit{\text{value}}〉$ and $\mathrm{LRWKMN}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lrwork}\ge \mathrm{LRWKMN}$.

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

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

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

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

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

$\mathbf{ifail}=2$

An error has occurred during the generation of the interior mesh. Check the definition of the boundary (arguments coor and edge) as well as the orientation of the boundary (especially in the case of a multiple connected component boundary). Setting $\mathbf{itrace}>0$ may provide more details.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results