NAG Library Routine Document

d06cbf (dim2_sparsity)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{nv}$ – IntegerInput

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

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

2:     $\mathbf{nelt}$ – IntegerInput

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

Constraint: $\mathbf{nelt}\le 2\times \mathbf{nv}-1$.

3:     $\mathbf{nnzmax}$ – 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:     $\mathbf{conn}\left(3,\mathbf{nelt}\right)$ – 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:     $\mathbf{nnz}$ – IntegerOutput

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

6:     $\mathbf{irow}\left(\mathbf{nnzmax}\right)$ – Integer arrayOutput

7:     $\mathbf{icol}\left(\mathbf{nnzmax}\right)$ – 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:     $\mathbf{ifail}$ – 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, $\mathbf{conn}\left(\mathit{I},\mathit{J}\right)=〈\mathit{\text{value}}〉$, $\mathit{I}=〈\mathit{\text{value}}〉$, $\mathit{J}=〈\mathit{\text{value}}〉$ and $\mathbf{nv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{conn}\left(\mathit{I},\mathit{J}\right)\ge 1$ and $\mathbf{conn}\left(\mathit{I},\mathit{J}\right)\le \mathbf{nv}$.

On entry, $\mathbf{nelt}=〈\mathit{\text{value}}〉$ and $\mathbf{nv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nelt}\le 2\times \mathbf{nv}-1$.

On entry, $\mathbf{nnzmax}=〈\mathit{\text{value}}〉$, $\mathbf{nelt}=〈\mathit{\text{value}}〉$ and $\mathbf{nv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nnzmax}\ge \left(4\times \mathbf{nelt}+\mathbf{nv}\right)$.

On entry, $\mathbf{nnzmax}=〈\mathit{\text{value}}〉$ and $\mathbf{nv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nnzmax}\le {\mathbf{nv}}^2$.

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

On entry, vertices $1$ and $2$ of the triangle $\mathit{K}$ have the same index $\mathit{I}$: $\mathit{K}=〈\mathit{\text{value}}〉$ and $\mathit{I}=〈\mathit{\text{value}}〉$.

On entry, vertices $1$ and $3$ of the triangle $\mathit{K}$ have the same index $\mathit{I}$: $\mathit{K}=〈\mathit{\text{value}}〉$ and $\mathit{I}=〈\mathit{\text{value}}〉$.

On entry, vertices $2$ and $3$ of the triangle $\mathit{K}$ have the same index $\mathit{I}$: $\mathit{K}=〈\mathit{\text{value}}〉$ and $\mathit{I}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=2$

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 argument conn). Array dimensions should also be checked. If the problem persists, contact NAG.

$\mathbf{ifail}=-99$

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