[petsc-users] Estimate memory needs for large grids

[Sajid Ali]

Hi,

I've solving a simple linear equation [ u_t = A*u_xx + A*u_yy + F_t*u ] on
a grid size of 55296x55296. I'm reading a vector of that size from an hdf5
file and have the jacobian matrix as a modified 5-point stencil which is
preallocated with the following
```
  ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
  ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,M,M);CHKERRQ(ierr);
  ierr = MatSetType(A,MATMPIAIJ);CHKERRQ(ierr);
  ierr = MatSetFromOptions(A);CHKERRQ(ierr);
  ierr = MatMPIAIJSetPreallocation(A,5,NULL,5,NULL);CHKERRQ(ierr);
  ierr = MatSeqAIJSetPreallocation(A,5,NULL);CHKERRQ(ierr);
```
Total number of elements is ~3e9 and the matrix size is ~9e9 (but only 5
diagonals are non zeros). I'm reading F_t which has ~3e9 elements. I'm
using double complex numbers and I've compiled with int64 indices.

Thus, for the vector I need, 55296x55296x2x8 bytes ~ 50Gb and for the F
vector, another 50 Gb. For the matrix I need ~250 Gb and some overhead for
the solver.

How do I estimate this overhead (and estimate how many nodes I would need
to run this given the maximum memory per node (as specified by slurm's
--mem option)) ?

Thanks in advance for the help!

-- 
Sajid Ali
Applied Physics
Northwestern University
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