NAG Library Routine Document

D06CBF

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:     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 D06CBF is called.

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

4:     CONN($3$,NELT) – INTEGER arrayInput

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

5:     NNZ – INTEGEROutput

On exit: the number of nonzero entries in the matrix associated with the input mesh.

6:     IROW(NNZMAX) – INTEGER arrayOutput

7:     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 $A$.

8:     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	$\mathbf{NNZMAX}<4\times \mathbf{NELT}+\mathbf{NV}$ 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 $i=1,3$ and $j$, $1\le j\le \mathbf{NELT}$,
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 $j=1,2,\dots ,\mathbf{NELT}$.

$\mathbf{IFAIL}=2$

A serious error has occurred in an internal call to an auxiliary routine. Check the input mesh, especially the connectivity between triangles and vertices (the parameter CONN). Array dimensions should be checked as well. If the problem persists, contact NAG.

7  Accuracy

8  Further Comments

9  Example