d06cbc 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 functions in Chapter F11. More precisely d06cbc 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 functions 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 function from which d06cbc is called.

Constraint: $4 \times nelt + nv \leq nnzmax \leq {nv}^{2}$ .
4: $conn [3 \times nelt]$ – const Integer Input: Note: the $(i, j)$ th element of the matrix is stored in $conn [(j - 1) \times 3 + i - 1]$ .

On entry: the connectivity of the mesh between triangles and vertices. For each triangle $j$ , $conn [(j - 1) \times 3 + i - 1]$ gives the indices of its three vertices (in anticlockwise order), for $i = 1, 2, 3$ and $j = 1, 2, \dots, nelt$ . Note that the mesh vertices are numbered from $1$ to nv.

Constraint: $1 \leq conn [(j - 1) \times 3 + i - 1] \leq nv$ and $conn [(j - 1) \times 3] \neq conn [(j - 1) \times 3 + 1]$ and $conn [(j - 1) \times 3] \neq conn [(j - 1) \times 3 + 2]$ and $conn [(j - 1) \times 3 + 1] \neq conn [(j - 1) \times 3 + 2]$ , 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 Output
7: $icol [nnzmax]$ – Integer 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: $fail$ – NagError * Input/Output: The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM: On entry, argument $⟨ value ⟩$ had an illegal value.
NE_INT: On entry, $nv = ⟨ value ⟩$ .
Constraint: $nv \geq 3$ .
NE_INT_2: On entry, $nelt = ⟨ value ⟩$ and $nv = ⟨ value ⟩$ .
Constraint: $nelt \leq 2 \times nv - 1$ .

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

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 $I = ⟨ value ⟩$ .
NE_INT_3: On entry, $nnzmax = ⟨ value ⟩$ , $nelt = ⟨ value ⟩$ and $nv = ⟨ value ⟩$ .
Constraint: $nnzmax \geq (4 \times nelt + nv)$ .
NE_INT_4: On entry, $conn (I, J) = ⟨ value ⟩$ , $I = ⟨ value ⟩$ , $J = ⟨ value ⟩$ and $nv = ⟨ value ⟩$ .
Constraint: $conn (I, J) \geq 1$ and $conn (I, J) \leq nv$ , where $conn (I, J)$ denotes $conn [(J - 1) \times 3 + I - 1]$ .
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.

A serious error has occurred in an internal call to an auxiliary function. 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.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

d06cbc 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 function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.