# ParMooN - a modernized program package based on mapped finite elements

## TL;DR

ParMooN is a modernized software package for solving elliptic and parabolic PDEs, featuring advanced finite element methods, geometric multigrid preconditioning, and parallelization for distributed computing environments.

## Contribution

The paper introduces parallelization of ParMooN, enhancing its efficiency and scalability for distributed memory systems, which is a significant advancement over its predecessor MooNMD.

## Key findings

- Parallel geometric multigrid preconditioner shows promising efficiency.
- Comparison with PETSc solvers indicates competitive performance.
- Parallelization improves scalability and computational speed.

## Abstract

{\sc ParMooN} is a program package for the numerical solution of elliptic and parabolic partial differential equations. It inherits the distinct features of its predecessor {\sc MooNMD} \cite{JM04}: strict decoupling of geometry and finite element spaces, implementation of mapped finite elements as their definition can be found in textbooks, and a geometric multigrid preconditioner with the option to use different finite element spaces on different levels of the multigrid hierarchy. After having presented some thoughts about in-house research codes, this paper focuses on aspects of the parallelization for a distributed memory environment, which is the main novelty of {\sc ParMooN}. Numerical studies, performed on compute servers, assess the efficiency of the parallelized geometric multigrid preconditioner in comparison with some parallel solvers that are available in the library {\sc PETSc}. The results of these studies give a first indication whether the cumbersome implementation of the parallelized geometric multigrid method was worthwhile or not.