void	d06cbf_ (const Integer nv, const Integer nelt, const Integer nnzmax, const Integer conn[], Integer nnz, Integer irow[], Integer icol[], Integer *ifail)

The routine may be called by the names d06cbf or nagf_mesh_dim2_sparsity.

3 Description

d06cbf generates the sparsity pattern of a finite element matrix associated with a given mesh. The sparsity pattern is returned in a coordinate storage format consistent with the sparse linear algebra routines in Chapter F11. More precisely d06cbf returns the number of nonzero elements in the associated sparse matrix, and their row and column indices. This is designed to assist you in applying finite element discretization to meshes from the D06 Chapter Introduction and in solving the resulting sparse linear system using routines from Chapter F11.

The output sparsity pattern is based on the fact that finite element matrix

A

has elements

a_{i j}

satisfying:

a_{i j} \neq 0 \Rightarrow i ​ and ​ j ​ are vertices belonging to the same triangle.

4 References

None.

5 Arguments

1: $nv$ – Integer Input: On entry: the total number of vertices in the input mesh.

Constraint: $nv \geq 3$ .
2: $nelt$ – Integer Input: On entry: the number of triangles in the input mesh.

Constraint: $nelt \leq 2 \times nv - 1$ .
3: $nnzmax$ – Integer Input: 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: $4 \times nelt + nv \leq nnzmax \leq {nv}^{2}$ .
4: $conn (3, nelt)$ – Integer array Input: On entry: the connectivity of the mesh between triangles and vertices. For each triangle $j$ , $conn (i, j)$ gives the indices of its three vertices (in anticlockwise order), for $i = 1, 2, 3$ and $j = 1, 2, \dots, nelt$ .

Constraint: $1 \leq conn (i, j) \leq nv$ and $conn (1, j) \neq conn (2, j)$ and $conn (1, j) \neq conn (3, j)$ and $conn (2, j) \neq conn (3, j)$ , for $i = 1, 2, 3$ and $j = 1, 2, \dots, nelt$ .
5: $nnz$ – Integer Output: On exit: the number of nonzero entries in the matrix associated with the input mesh.
6: $irow (nnzmax)$ – Integer array Output
7: $icol (nnzmax)$ – Integer array Output: On exit: the first nnz elements contain the row and column indices of the nonzero elements supplied in the finite element matrix $A$ .
8: $ifail$ – 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 $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

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

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: On entry, $conn (I, J) = ⟨ value ⟩$ , $I = ⟨ value ⟩$ , $J = ⟨ value ⟩$ and $nv = ⟨ value ⟩$ .
Constraint: $conn (I, J) \geq 1$ and $conn (I, J) \leq nv$ .

On entry, $nelt = ⟨ value ⟩$ and $nv = ⟨ value ⟩$ .
Constraint: $nelt \leq 2 \times nv - 1$ .

On entry, $nnzmax = ⟨ value ⟩$ , $nelt = ⟨ value ⟩$ and $nv = ⟨ value ⟩$ .
Constraint: $nnzmax \geq (4 \times nelt + nv)$ .

On entry, $nnzmax = ⟨ value ⟩$ and $nv = ⟨ value ⟩$ .
Constraint: $nnzmax \leq {nv}^{2}$ .

On entry, $nv = ⟨ value ⟩$ .
Constraint: $nv \geq 3$ .

On entry, vertices $1$ and $2$ of the triangle $K$ have the same index $I$ : $K = ⟨ value ⟩$ and $I = ⟨ value ⟩$ .

On entry, vertices $1$ and $3$ of the triangle $K$ have the same index $I$ : $K = ⟨ value ⟩$ and $I = ⟨ value ⟩$ .

On entry, vertices $2$ and $3$ of the triangle $K$ have the same index $I$ : $K = ⟨ value ⟩$ and $I = ⟨ value ⟩$ .

$ifail = 2$: 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.

$ifail = - 99$: 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.

$ifail = - 399$: 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.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

d06cbf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.