NAG Library Routine Document

d06abf (dim2_gen_delaunay)

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: $\mathbf{nvb}\ge 3$.

2:     $\mathbf{nvint}$ – IntegerInput

On entry: the number of fixed interior mesh vertices to which a weight will be applied.

Constraint: $\mathbf{nvint}\ge 0$.

3:     $\mathbf{nvmax}$ – IntegerInput

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

Constraint: $\mathbf{nvmax}\ge \mathbf{nvb}+\mathbf{nvint}$.

4:     $\mathbf{nedge}$ – IntegerInput

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

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

5:     $\mathbf{edge}\left(3,\mathbf{nedge}\right)$ – Integer arrayInput

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 d06abf.

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 $\mathit{j}=1,2,\dots ,\mathbf{nedge}$.

6:     $\mathbf{nv}$ – IntegerOutput

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

7:     $\mathbf{nelt}$ – IntegerOutput

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

8:     $\mathbf{coor}\left(2,\mathbf{nvmax}\right)$ – Real (Kind=nag_wp) arrayInput/Output

On entry: $\mathbf{coor}\left(1,\mathit{i}\right)$ contains the $x$ coordinate of the $\mathit{i}$th input boundary mesh vertex, for $\mathit{i}=1,2,\dots ,\mathbf{nvb}$. $\mathbf{coor}\left(1,\mathit{i}\right)$ contains the $x$ coordinate of the $\left(\mathit{i}-\mathbf{nvb}\right)$th fixed interior vertex, for $\mathit{i}=\mathbf{nvb}+1,\dots ,\mathbf{nvb}+\mathbf{nvint}$. For boundary and interior vertices, $\mathbf{coor}\left(2,\mathit{i}\right)$ contains the corresponding $y$ coordinate, for $\mathit{i}=1,2,\dots ,\mathbf{nvb}+\mathbf{nvint}$.

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

9:     $\mathbf{conn}\left(3,2\times \mathbf{nvmax}+5\right)$ – Integer arrayOutput

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 $\mathit{j}=1,2,\dots ,\mathbf{nelt}$.

10:   $\mathbf{weight}\left(*\right)$ – Real (Kind=nag_wp) arrayInput

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

On entry: the weight of fixed interior vertices. It is the diameter of triangles (length of the longer edge) created around each of the given interior vertices.

Constraint: if $\mathbf{nvint}>0$, $\mathbf{weight}\left(\mathit{i}\right)>0.0$, for $\mathit{i}=1,2,\dots ,\mathbf{nvint}$.

11:   $\mathbf{npropa}$ – IntegerInput

On entry: the propagation type and coefficient, the argument npropa is used when the internal points are created. They are distributed in a geometric manner if npropa is positive and in an arithmetic manner if it is negative. For more details see Section 9.

Constraint: $\mathbf{npropa}\ne 0$.

12:   $\mathbf{itrace}$ – IntegerInput

On entry: the level of trace information required from d06abf.

$\mathbf{itrace}\le 0$

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.

13:   $\mathbf{rwork}\left(\mathbf{lrwork}\right)$ – Real (Kind=nag_wp) arrayWorkspace

14:   $\mathbf{lrwork}$ – IntegerInput

On entry: the dimension of the array rwork as declared in the (sub)program from which d06abf is called.

Constraint: $\mathbf{lrwork}\ge 12\times \mathbf{nvmax}+15$.

15:   $\mathbf{iwork}\left(\mathbf{liwork}\right)$ – Integer arrayWorkspace

16:   $\mathbf{liwork}$ – IntegerInput

On entry: the dimension of the array iwork as declared in the (sub)program from which d06abf is called.

Constraint: $\mathbf{liwork}\ge 6\times \mathbf{nedge}+32\times \mathbf{nvmax}+2\times \mathbf{nvb}+78$.

17:   $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ 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, $\mathbf{edge}\left(\mathit{I},\mathit{J}\right)=〈\mathit{\text{value}}〉$, $\mathit{I}=〈\mathit{\text{value}}〉$, $\mathit{J}=〈\mathit{\text{value}}〉$ 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, $\mathbf{npropa}=0$.

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

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

On entry, $\mathbf{nvint}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nvint}\ge 0$.

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

$\mathbf{ifail}=2$

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.

$\mathbf{ifail}=3$

An error has occurred during the generation of the boundary mesh. It appears that nvmax is not large enough: $\mathbf{nvmax}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=-99$

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

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

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

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (d06abfe.f90)

10.2

Program Data

Program Data (d06abfe.d)

10.3

Program Results

Program Results (d06abfe.r)