Storing method for the coefficient matrix for the Preconditioned GMRES

[elmeliegy__abdelrahm]

Hi All;

Quick Question; How can i use GMRES for a preconditioned very large linear system without storing the entire coefficient matrix?. As i understand; GMRES asks for the RHS vector, the entire coefficient matrix and  the Preconditioner. But for the memory limitation and for the compuational cost i will not be able to assemble and store the entire coefficient matrix. Any thought is very appreciated!.

[Ying_H_Intel]

Hi 

​it seems the MKL GEMRES only support put entire matrix into computing. what is the size for the entire coefficient matrix and your memory? MKL have one parallel sparse solver at  https://software.intel.com/en-us/articles/intel-math-kernel-library-parallel-direct-sparse-solver-for-clusters , which may have distribute requirement about the memory. 

​Best Regards,

​Ying