problems to allocate memory for GRM per chromosome

I am trying to calculate GRM per chromosome to run mixed models for GWAS. I am having trouble to get the matrix for large chromosomes. Could you please any one give an estimate of how much RAM will I need to calculate for example GRM for 11000 individuals and 2Million SNPs?
Is there any alternative to run such analysis?
Please mind that I run the analysis in a linux server 64bits on 4 nodes.
Regards,
Luba