Colouring in symmetric and non symmetric block jacobi precond

NGSolve
1

Hello there,

I was inspecting the source code of BlockJacobiPrecond and BlockJacobiPrecondSymmetric and I think I have noticed a different strategy for colouring their blocks.

In the first version, the procedure is along the lines of

for b in blocks
 can_colour = true
 for eq in b
   if has_color[eq]
     can_colour = false

//do some stuff
 for eq in b
   for eeq in mat.GetRowIndices(eq):
     has_color[eq] = true

while on the symmetric version,

for b in blocks
 can_colour = true
 for eq in b
   for eeq in mat.GetRowIndices(eq):
     if has_color[eeq]
       can_colour = false

//do some stuff
 for eq in b
   for eeq in mat.GetRowIndices(eq):
     has_color[eq] = true

Assuming that we have an equation x in block a and an equation y in block b and that the dof corresponding to x does not affect the residual of y (and vice-versa), but they would both affect the residual of a given equation z (that does not belong to blocks a nor b).
If I understood correctly, on the non symmetric version, a and b could be assigned the same colour. For the symmetric version, this does not hold.

If I may ask, is there a reasoning for this difference?

2

Hi Francisco,
I am not sure whether this answers the question exactly, but one difference between the non-symmetric and the symmetric one is the following:
In the symmetric one, the row-indices are stored only for the lower triangular matrix. So, in terms of row-indices, it must be more restrictive in comparison to the non-symmetric one.
best, Joachim