I am working on a flow physics problem (2D), which ultimately boils down to solving Eigen value problem. Even for a grid size of 60 x 60, the matrix in the Eigen value problem end up with 1260 million elements (This matrix has to be solved iteratively!). Sometimes the matrix is sparse and other times it is not depending on the nature of problem to be solved.
I use ARPACK written in Fortran to solve the problem. Surprisingly, MATLAB solves the same Eigen value problems at least 5 times faster than the Fortran counterpart. (And I wonder how!)
My question is : Are there any techniques that is known in the computation community to speed up the Eigen solver?
Parallel-ized ARPACK is one solution that I tried, but still not up to the level of MATLAB