OpenFOAM guide/LduMatrix;;negSumDiag

Subtracts the off-diagonal entries from the diagonal.

for (register label face=0; face<l.size(); face++)
{
    Diag[l[face]] -= Lower[face];
    Diag[u[face]] -= Upper[face];
}

Where:

• Diag is the diagonal coefficient;
• l is the lduAddressing for the lower triangle;
• u is the lduAddressing for the upper triangle;
• Lower is the lower triangle; and
• Upper is the upper triangle.

In terms of discretization coefficients, this is equivalent to:

$A_p = \sum\limits_r A_r$

and in terms of matrix coefficients, this is:

$A_{ii} = -\sum\limits_o A_{o,i} -\sum\limits_n A_{n,i}$

Where:

• A are matrix coefficients; and
• o and n are the owner and neighbour indices.