# A tutorial-driven introduction to the parallel finite element library FEMPAR v1.0.0

## TL;DR

This paper provides a comprehensive tutorial on using the FEMPAR library for finite element simulations of PDEs, demonstrating its capabilities through three progressively complex tutorials on structured, adaptive, and distributed-memory meshes.

## Contribution

It introduces FEMPAR v1.0.0 with detailed tutorials, showcasing its tools for PDE discretization, adaptive refinement, and scalable solvers on distributed-memory platforms.

## Key findings

- Successful simulation of Poisson equation in serial and parallel environments
- Implementation of adaptive mesh refinement on octree meshes
- Distributed-memory PDE simulation with scalable solvers

## Abstract

This work is a user guide to the FEMPAR scientific software library. FEMPAR is an open-source object-oriented framework for the simulation of partial differential equations (PDEs) using finite element methods on distributed-memory platforms. It provides a rich set of tools for numerical discretization and built-in scalable solvers for the resulting linear systems of equations. An application expert that wants to simulate a PDE-governed problem has to extend the framework with a description of the weak form of the PDE at hand (and additional perturbation terms for non-conforming approximations). We show how to use the library by going through three different tutorials. The first tutorial simulates a linear PDE (Poisson equation) in a serial environment for a structured mesh using both continuous and discontinuous Galerkin finite element methods. The second tutorial extends it with adaptive mesh refinement on octree meshes. The third tutorial is a distributed-memory version of the previous one that combines a scalable octree handler and a scalable domain decomposition solver. The exposition is restricted to linear PDEs and simple geometries to keep it concise. The interested user can dive into more tutorials available in the FEMPAR public repository to learn about further capabilities of the library, e.g., nonlinear PDEs and nonlinear solvers, time integration, multi-field PDEs, block preconditioning, or unstructured mesh handling.