  A parallel and nested version of a frequency filtering preconditioner is
proposed for linear systems corresponding to diffusion equation on a structured
grid. The proposed preconditioner is found to be robust with respect to jumps
in the diffusion coefficients. The storage requirement for the preconditioner
is O(N),where N is number of rows of matrix, hence, a fairly large problem of
size more than 42 million unknowns has been solved on a quad core machine with
64GB RAM. The parallelism is achieved using twisted factorization and SIMD
operations. The preconditioner achieves a speedup of 3.3 times on a quad core
processor clocked at 4.2 GHz, and compared to a well known algebraic multigrid
method, it is significantly faster in both setup and solve times for diffusion
equations with jumps.
