I'm trying to solve SLE of form Ax=b with matrix A being large, sparse, symmetric, positive defined and block-tridiagonal. With exactly the same structure as one arising from five-point finite difference approximation, used for solving Poisson equation. I.e.:
L2 D2 L3
L3 D3 L4
L4 D4 L5 ...
where Di is symmetric tridiagonal and Li is diagonal. When solving Poisson equation, Li = -I with I denoting unit matrix and Di is of form
-1 4 -1
-1 4 -1 ...
I tried direct solver (DSS) and iterative solver (PCG) with different preconditioners. I was able to compute solution, but I'm looking for possible speed-ups. I've solved Poisson eqation of the same size and solution was found much faster. E.g., 0.1 seconds against 15 seconds for PCG and 325 seconds for DSS.
The question is, are there some special routines for dealing with matrices of such a structure in MKL? I understand, that Poisson-case is optimised for matrix with given values, while I have arbitrary values in A. But still, are there some alternatives for PCG?