Hi, I used finite difference to solve PDES. For the discretized equation, I use ADI to solve it. Now I want to parallelize this ADI solver with OPENMP, but it is hard since the value of one point need the information of his neighbours. I also tried the Guass_sedel point iteration, it was easier to parallelize, but not as fast as ADI. So, can anyone give me some idea? BTW, I did not want to use MPI since the other part of my codes have been parallelized with OPENMP.

The simplest method is to use a couple of arrays to store the values you are building up on the forward sweep. This enables a processor to stop the sweep, handover to the adjacent processor and get on with some other sweeps until the adjacent processor has performed the back substitution and the line can be finished off.

Periodic boundary conditions are slightly more complicated but not much.