NAG Library Routine Document

D06CCF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     NV – INTEGERInput

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

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

2:     NELT – INTEGERInput

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

Constraint: $\mathbf{NELT}\le 2\times \mathbf{NV}-1$.

3:     NEDGE – INTEGERInput

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

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

4:     NNZMAX – INTEGERInput

On entry: the maximum number of nonzero entries in the matrix based on the input mesh. It is the dimension of the arrays IROW and ICOL as declared in the subroutine from which D06CCF is called.

Constraint: $4\times \mathbf{NELT}+\mathbf{NV}\le \mathbf{NNZMAX}\le {\mathbf{NV}}^2$.

5:     NNZ – INTEGEROutput

On exit: the number of nonzero entries in the matrix based on the input mesh.

6:     COOR($2$,NV) – 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 mesh vertex, for $\mathit{i}=1,2,\dots ,\mathbf{NV}$; while $\mathbf{COOR}\left(2,\mathit{i}\right)$ contains the corresponding $y$ coordinate.

On exit: $\mathbf{COOR}\left(1,\mathit{i}\right)$ will contain the $x$ coordinate of the $\mathit{i}$th renumbered mesh vertex, for $\mathit{i}=1,2,\dots ,\mathbf{NV}$; while $\mathbf{COOR}\left(2,\mathit{i}\right)$ will contain the corresponding $y$ coordinate.

7:     EDGE($3$,NEDGE) – INTEGER arrayInput/Output

On entry: the specification of the boundary or interface 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 or interface edge: $\mathbf{EDGE}\left(3,j\right)=0$ for an interior edge and has a nonzero tag otherwise.

Constraint: $1\le \mathbf{EDGE}\left(\mathit{i},\mathit{j}\right)\le \mathbf{NV}$ and $\mathbf{EDGE}\left(1,\mathit{j}\right)\ne \mathbf{EDGE}\left(2,\mathit{j}\right)$, for $\mathit{i}=1,2$ and $\mathit{j}=1,2,\dots ,\mathbf{NEDGE}$.

On exit: the renumbered specification of the boundary or interface edges.

8:     CONN($3$,NELT) – INTEGER arrayInput/Output

On entry: 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 $\mathit{j}=1,2,\dots ,\mathbf{NELT}$.

Constraint: $1\le \mathbf{CONN}\left(\mathit{i},\mathit{j}\right)\le \mathbf{NV}$ and $\mathbf{CONN}\left(1,\mathit{j}\right)\ne \mathbf{CONN}\left(2,\mathit{j}\right)$ and $\mathbf{CONN}\left(1,\mathit{j}\right)\ne \mathbf{CONN}\left(3,\mathit{j}\right)$ and $\mathbf{CONN}\left(2,\mathit{j}\right)\ne \mathbf{CONN}\left(3,\mathit{j}\right)$, for $\mathit{i}=1,2,3$ and $\mathit{j}=1,2,\dots ,\mathbf{NELT}$.

On exit: the renumbered connectivity of the mesh between triangles and vertices.

9:     IROW(NNZMAX) – INTEGER arrayOutput

10:   ICOL(NNZMAX) – INTEGER arrayOutput

On exit: the first NNZ elements contain the row and column indices of the nonzero elements supplied in the finite element matrix $A$.

11:   ITRACE – INTEGERInput

On entry: the level of trace information required from D06CCF.

$\mathbf{ITRACE}\le 0$

No output is generated.

$\mathbf{ITRACE}=1$

Information about the effect of the renumbering on the finite element matrix are output. This information includes the half bandwidth and the sparsity structure of this matrix before and after renumbering.

$\mathbf{ITRACE}>1$

The output is similar to that produced when $\mathbf{ITRACE}=1$ but the sparsities (for each row of the matrix, indices of nonzero entries) of the matrix before and after renumbering are also output.

12:   IWORK(LIWORK) – INTEGER arrayWorkspace

13:   LIWORK – INTEGERInput

On entry: the dimension of the array IWORK as declared in the (sub)program from which D06CCF is called.

Constraint: $\mathbf{LIWORK}\ge \max \left(\mathbf{NNZMAX},20\times \mathbf{NV}\right)$.

14:   RWORK(LRWORK) – REAL (KIND=nag_wp) arrayWorkspace

15:   LRWORK – INTEGERInput

On entry: the dimension of the array RWORK as declared in the (sub)program from which D06CCF is called.

Constraint: $\mathbf{LRWORK}\ge \mathbf{NV}$.

16:   IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction 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 parameter, 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,	$\mathbf{NV}<3$,
or	$\mathbf{NELT}>2\times \mathbf{NV}-1$,
or	$\mathbf{NEDGE}<1$,
or	$\mathbf{NNZMAX}<4\times \mathbf{NELT}+\mathbf{NV}$ or $\mathbf{NNZMAX}>{\mathbf{NV}}^2$
or	$\mathbf{CONN}\left(i,j\right)<1$ or $\mathbf{CONN}\left(i,j\right)>\mathbf{NV}$ for some $i=1,2,3$ and $j=1,2,\dots ,\mathbf{NELT}$,
or	$\mathbf{CONN}\left(1,j\right)=\mathbf{CONN}\left(2,j\right)$ or $\mathbf{CONN}\left(1,j\right)=\mathbf{CONN}\left(3,j\right)$ or $\mathbf{CONN}\left(2,j\right)=\mathbf{CONN}\left(3,j\right)$ for some $j=1,2,\dots ,\mathbf{NELT}$,
or	$\mathbf{EDGE}\left(i,j\right)<1$ or $\mathbf{EDGE}\left(i,j\right)>\mathbf{NV}$ for some $i=1,2$ and $j=1,2,\dots ,\mathbf{NEDGE}$,
or	$\mathbf{EDGE}\left(1,j\right)=\mathbf{EDGE}\left(2,j\right)$ for some $j=1,2,\dots ,\mathbf{NEDGE}$,
or	$\mathbf{LIWORK}<\max \left(\mathbf{NNZMAX},20\times \mathbf{NV}\right)$,
or	$\mathbf{LRWORK}<\mathbf{NV}$.

$\mathbf{IFAIL}=2$

A serious error has occurred during the computation of the compact sparsity of the finite element matrix or in an internal call to the renumbering routine. Check the input mesh, especially the connectivity between triangles and vertices (the parameter CONN). If the problem persists, contact NAG.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (d06ccfe.f90)

9.2  Program Data

Program Data (d06ccfe.d)

9.3  Program Results

Program Results (d06ccfe.r)

Figure 1: Mesh of the geometry

Figure 2: Sparsity of the matrix before (top) and after (bottom) the renumbering