[petsc-users] Number of Blocks in the Block Jacobi preconditionr

[Wenlei Xie]

Hi,

I am using PETSc to solve linear systems with Block Jacobi preconditioner, and I am currently studying the trade off between the number of blocks. 
In my experiments I tried a very sparse 1M*1M matrix and try different number of blocks. I expect the result would be, if I use less blocks (thus each block has larger size), then the convergence rate would increase but the time spend on each iteration would would also increase; while for more blocks (and each block has smaller size), both the convergence rate and the time on each iteration will be decreased. However, the result turns out to that the time on each iteration also decreased as the block size increased. Is it because I misused it?

I am use Richardson method as the Krylov method, and ILU as the solver inside each block matrix. The matrix contains around 3.5M non-zeros entries and I use METIS to partition it into blocks. 

Thank you!


Best,
Wenlei