FEMPAR: An Object-Oriented Parallel Finite Element Framework

Abstract

FEMPAR is an open source object oriented Fortran200X scientific software library for the high-performance scalable simulation of complex multiphysics problems governed by partial differential equations at large scales, by exploiting state-of-the-art supercomputing resources. It is a highly modularized, flexible, and extensible library, that provides a set of modules that can be combined to carry out the different steps of the simulation pipeline. FEMPAR includes a rich set of algorithms for the discretization step, namely (arbitrary-order) grad, div, and curl-conforming finite element methods, discontinuous Galerkin methods, B-splines, and unfitted finite element techniques on cut cells, combined with h-adaptivity. The linear solver module relies on state-of-the-art bulk-asynchronous implementations of multilevel domain decomposition solvers for the different discretization alternatives and block-preconditioning techniques for multiphysics problems. FEMPAR is a framework that provides users with out-of-the-box state-of-the-art discretization techniques and highly scalable solvers for the simulation of complex applications, hiding the dramatic complexity of the underlying algorithms. But it is also a framework for researchers that want to experience with new algorithms and solvers, by providing a highly extensible framework. In this work, the first one in a series of articles about FEMPAR, we provide a detailed introduction to the software abstractions used in the discretization module and the related geometrical module. We also provide some ingredients about the assembly of linear systems arising from finite element discretizations, but the software design of complex scalable multilevel solvers is postponed to a subsequent work.

Balancing Domain Decomposition by Constraints and Perturbation

“…The perturbed formulation is built on top of the BDDC preconditioner in the scientific computing software package FEMPAR (FE Multiphysics massively PARallel) [4], a parallel hybrid MPI+OpenMP, object-oriented framework for the massively parallel FE simulation of multiscale multiphysics problems governed by PDEs [6,7]. All our experiments were run on MareNostrum III at BSC (Barcelona) and HLRN-III at RRZN (Hannover).…”

“…Based on our experience, the implementation of this type of algorithm is an involved and timeconsuming task which depends on the physical problem to be solved and also the type of FE formulation being used. For example, the implementation of the corner selection algorithm from [48] in the scientific software FEMPAR [4] has more than 1,500 lines of code. Furthermore, the situation becomes far more complicated when subdomains are disconnected, or connected only by corners or edges.…”

A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing

“…This section describes the software design of a parallel FE framework for growing domains, the so‐called FEMPAR‐AM module, atop the services provided by FEMPAR . FEMPAR is an open‐source general‐purpose object‐oriented scientific software framework for the massively parallel FE simulation of problems governed by PDEs.…”

“…Each abstraction takes charge of a different step in a typical FE simulation, including, amongst others, mesh generation, adaptation, and partitioning, construction of a global FE space and DOF numbering, numerical evaluation of cell and facet integrals and linear system assembly, linear system solution, or generation of simulation output data for later visualisation. The reader is referred to the works of Badia et al for a detailed exposition of the main software abstractions in FEMPAR. Although FEMPAR‐AM exploits most of the software abstractions provided by FEMPAR, the discussion in this section mainly focuses on those that had to be particularly set up and/or customised to support growing domains.…”

“…As FEMPAR‐AM relies on the EBM (Section 3.1), the first software requirement that has to be fulfilled by the underlying FE framework is the ability to build global FE spaces that only carry out DOFs for cells that are active at the current simulation step. In FEMPAR, a global FE space is built from two main ingredients: (1) triangulation_t (see section 7 in the work of Badia et al), which represents the geometrical discretisation of the computational domain into cells; and (2) reference_fe_t (see section 6 in the work of Badia et al), which represents an abstract local FE on top of each of the triangulation cells. A particular type extension of reference_fe_t, referred to as void_reference_fe_t (see section 6.5 in the work of Badia et al), implements a local FE with no DOFs.…”