NAG Library Function Document

nag_mesh2d_sparse (d06cbc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

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 function from which nag_mesh2d_sparse (d06cbc) is called.

Constraint: $4\times \mathbf{nelt}+\mathbf{nv}\le \mathbf{nnzmax}\le {\mathbf{nv}}^2$.

4:     conn[$3\times \mathbf{nelt}$] – const IntegerInput

Note: the $\left(i,j\right)$th element of the matrix is stored in $\mathbf{conn}\left[\left(j-1\right)\times 3+i-1\right]$.

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

Constraint: $1\le \mathbf{conn}\left[\left(\mathit{j}-1\right)\times 3+\mathit{i}-1\right]\le \mathbf{nv}$ and $\mathbf{conn}\left[\left(\mathit{j}-1\right)\times 3\right]\ne \mathbf{conn}\left[\left(\mathit{j}-1\right)\times 3+1\right]$ and $\mathbf{conn}\left[\left(\mathit{j}-1\right)\times 3\right]\ne \mathbf{conn}\left[\left(\mathit{j}-1\right)\times 3+2\right]$ and $\mathbf{conn}\left[\left(\mathit{j}-1\right)\times 3+1\right]\ne \mathbf{conn}\left[\left(\mathit{j}-1\right)\times 3+2\right]$, for $\mathit{i}=1,2,3$ and $\mathit{j}=1,2,\dots ,\mathbf{nelt}$.

5:     nnz – Integer *Output

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

6:     irow[nnzmax] – IntegerOutput

7:     icol[nnzmax] – IntegerOutput

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 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_BAD_PARAM

On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.

NE_INT

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

NE_INT_2

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

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

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 $\mathit{I}=⟨\mathit{\text{value}}⟩$.

NE_INT_3

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

NE_INT_4

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 $\mathbf{CONN}\left(\mathit{I},\mathit{J}\right)\le \mathbf{nv}$, where $\mathbf{CONN}\left(\mathit{I},\mathit{J}\right)$ denotes $\mathbf{conn}\left[\left(\mathit{J}-1\right)\times 3+\mathit{I}-1\right]$.

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.

A serious error has occurred in an internal call to an auxiliary function. Check the input mesh especially the connectivity. Seek expert help.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example