NAG Library Function Document

nag_mesh2d_renum (d06ccc)

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:     nedge – IntegerInput

On entry: the number of the boundary edges in the input mesh.

Constraint: $\mathbf{nedge}\ge 1$.

4:     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_renum (d06ccc) is called.

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

5:     nnz – Integer *Output

On exit: the number of nonzero entries in the matrix based on the input mesh.

6:     coor[$2\times \mathbf{nv}$] – doubleInput/Output

On entry: $\mathbf{coor}\left[\left(\mathit{i}-1\right)\times 2+0\right]$ contains the $x$ coordinate of the $\mathit{i}$th input mesh vertex, for $\mathit{i}=1,2,\dots ,\mathbf{nv}$; while $\mathbf{coor}\left[\left(\mathit{i}-1\right)\times 2+1\right]$ contains the corresponding $y$ coordinate.

On exit: $\mathbf{coor}\left[\left(\mathit{i}-1\right)\times 2+0\right]$ will contain the $x$ coordinate of the $\mathit{i}$th renumbered mesh vertex, for $\mathit{i}=1,2,\dots ,\mathbf{nv}$; while $\mathbf{coor}\left[\left(\mathit{i}-1\right)\times 2+1\right]$ will contain the corresponding $y$ coordinate.

7:     edge[$3\times \mathbf{nedge}$] – IntegerInput/Output

On entry: the specification of the boundary or interface edges. $\mathbf{edge}\left[\left(j-1\right)\times 3+0\right]$ and $\mathbf{edge}\left[\left(j-1\right)\times 3+1\right]$ contain the vertex numbers of the two end points of the $j$th boundary edge. $\mathbf{edge}\left[\left(j-1\right)\times 3+2\right]$ is a user-supplied tag for the $j$th boundary or interface edge: $\mathbf{edge}\left[\left(j-1\right)\times 3+2\right]=0$ for an interior edge and has a nonzero tag otherwise. Note that the edge vertices are numbered from $1$ to nv.

Constraint: $1\le \mathbf{edge}\left[\left(\mathit{j}-1\right)\times 3+\mathit{i}-1\right]\le \mathbf{nv}$ and $\mathbf{edge}\left[\left(\mathit{j}-1\right)\times 3+0\right]\ne \mathbf{edge}\left[\left(\mathit{j}-1\right)\times 3+1\right]$, for $\mathit{i}=1,2$ and $\mathit{j}=1,2,\dots ,\mathbf{nedge}$.

On exit: the renumbered specification of the boundary or interface edges.

8:     conn[$3\times \mathbf{nelt}$] – IntegerInput/Output

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 $\mathbf{conn}\left[\left(\mathit{j}-1\right)\times 3+0\right]\ne \mathbf{conn}\left[\left(\mathit{j}-1\right)\times 3+1\right]$ and $\mathbf{conn}\left[\left(\mathit{j}-1\right)\times 3+0\right]\ne \mathbf{conn}\left[\left(\mathit{j}-1\right)\times 3+2\right]$ 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 $\mathit{j}=1,2,\dots ,\mathbf{nelt}$.

On exit: the renumbered connectivity of the mesh between triangles and vertices.

9:     irow[nnzmax] – IntegerOutput

10:   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 $A$.

11:   itrace – IntegerInput

On entry: the level of trace information required from nag_mesh2d_renum (d06ccc).

$\mathbf{itrace}\le 0$

No output is generated.

$\mathbf{itrace}=1$

Information about the effect of the renumbering on the finite element matrix are output. This information includes the half bandwidth and the sparsity structure of this matrix before and after renumbering.

$\mathbf{itrace}>1$

The output is similar to that produced when $\mathbf{itrace}=1$ but the sparsities (for each row of the matrix, indices of nonzero entries) of the matrix before and after renumbering are also output.

12:   outfile – const char *Input

On entry: the name of a file to which diagnostic output will be directed. If outfile is NULL the diagnostic output will be directed to standard output.

13:   fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_FAIL_SPARSITY

An error has occurred during the computation of the compact sparsity of the finite element matrix. Check the Triangle/Vertices connectivity.

NE_INT

On entry, $\mathbf{nedge}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nedge}\ge 1$.

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, the endpoints of the edge $j$ have the same index $i$: $j=〈\mathit{\text{value}}〉$ and $i=〈\mathit{\text{value}}〉$.

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

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

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

NE_INT_3

On entry, $\mathbf{nnzmax}=〈\mathit{\text{value}}〉$, $\mathbf{nelt}=〈\mathit{\text{value}}〉$ and $\mathbf{nv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nnzmax}\ge \left(4\times \mathbf{nelt}+\mathbf{nv}\right)$ and $\mathbf{nnzmax}\le {\mathbf{nv}}^2$.

NE_INT_4

On entry, $\mathbf{CONN}\left(i,j\right)=〈\mathit{\text{value}}〉$, $i=〈\mathit{\text{value}}〉$, $j=〈\mathit{\text{value}}〉$ and $\mathbf{nv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{CONN}\left(i,j\right)\ge 1$ and $\mathbf{CONN}\left(i,j\right)\le \mathbf{nv}$, where $\mathbf{CONN}\left(i,j\right)$ denotes $\mathbf{conn}\left[\left(j-1\right)\times 3+i-1\right]$.

On entry, $\mathbf{EDGE}\left(i,j\right)=〈\mathit{\text{value}}〉$, $i=〈\mathit{\text{value}}〉$, $j=〈\mathit{\text{value}}〉$ and $\mathbf{nv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{EDGE}\left(i,j\right)\ge 1$ and $\mathbf{EDGE}\left(i,j\right)\le \mathbf{nv}$, where $\mathbf{EDGE}\left(i,j\right)$ denotes $\mathbf{edge}\left[\left(j-1\right)\times 3+i-1\right]$.

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 the renumbering function. Check the input mesh especially the connectivity. Seek expert help.

NE_NOT_CLOSE_FILE

Cannot close file $〈\mathit{\text{value}}〉$.

NE_NOT_WRITE_FILE

Cannot open file $〈\mathit{\text{value}}〉$ for writing.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (d06ccce.c)

9.2  Program Data

Program Data (d06ccce.d)

9.3  Program Results

Program Results (d06ccce.r)

Figure 1: Mesh of the geometry

Figure 2: Sparsity of the matrix before (top) and after (bottom) the renumbering