MFEM Memory Efficiency

[ShaniMW]

Hi all,

I am currently utilizing the MFEM ex2p code to solve a linear elasticity problem with a significant number of degrees of freedom (DOFs). I am keen to understand the processes that contribute to MFEM's memory efficiency, especially when dealing with a large number of unknowns.

From my analysis of the default ex2p code, the linear elastic system's stiffness matrix is stored as a sparse matrix. The system is then solved using the iterative Hyper PCG solver, complemented by the AMG preconditioner, which facilitates a more streamlined solution process.

I have a few specific inquiries:

1. Is the primary source of MFEM's memory efficiency attributed to the storage of the stiffness matrix in sparse format?
2. I noticed an option to enable a specialized version of AMG tailored for elasticity problems. While I understand this might influence the solution time, does it have any implications for memory consumption?
3. I'm aware that static condensation can lead to a reduced system size. However, its efficiency seems to be optimized for problems with an order greater than one. Given that I am employing linear HEX elements, would this approach be beneficial?
4. Additionally, I understand that MPI allows for domain decomposition. How does this feature contribute to MFEM's efficiency in handling large-scale problems?
   I am particularly interested in understanding the factors that make MFEM memory efficienct at solving extensive linear systems with around 1.5M DOFs.

Thanks,
Shani

[jandrej]

Thank you for your interest in MFEM. All your questions are more or less "general" and not solely related to MFEM. I would recommend looking into literature that explain those topics.

Our friends at deal.II offer a comprehensive tutorial that explains the steps for parallel and memory efficiency.

A very compact overview of those techniques can also be reviewed from Jed Browns PETSc tutorial slides

[ShaniMW]

Thanks, I started with deal.II tutorial lectures. I must say they are presented with utmost clarity, making complex concepts easy to grasp.
Thanks for the recommendation
Shani