Institute of Fundamental Technological Research

In this paper, we present the concept of Partial Factorization [1] and discuss its possible applications to the Finite Element method. We consider: (1) reduction of the element tangent matrix, which is particularly important for mixed/enhanced elements and (2) reduction of the sub-domain matrices of the Domain Decomposition (DD) equation solvers run either sequen-tially on a single machine or in parallel on a cluster of computers. We demonstrate that Partial Factorization can be beneficial for these applications.

multi-scale models of multi-layer shells, mixed/enhanced finite elements, parallel computing, domain decomposition, solvers

In this paper, we consider parallelization of the loop over elements using OpenMP in FEAP (Taylor, 2014), which is a research FE code, very popular at universities. Even for a serial version of FEAP (a cluster version also exists) such a parallelization is a non-trivial task due to the existing architecture of this code, which complicates efficient parallelization. First, we compare the serial version of FEAP to the parallel code Warp3D (Dodds et al., 2014), considering the usage of time and memory. As we found, Warp3D is much faster but uses more memory than FEAP. An analysis of Warp3D helps us to devise our method of parallelization of the loop over elements. Next, we describe several changes in FEAP, which were necessary to parallelize the loop over elements using OpenMP. In particular, the subroutine assembling elemental matrices is identified as crucial to good performance, and several directives for the mutual exclusion synchronization of OpenMP are implemented and tested. Finally, we demonstrate the performance of the parallelized FEAP, designated as ompFEAP, on numerical examples involving 3D and shell elements of FEAP as well as user’s elements. We conclude that ompFEAP, using the directive ATOMIC for synchronization of the assembling, provides a very good speedup and efficiency.

Parallelization, OpenMP, Finite element method, FEAP, 3D and shell elements

The paper concerns parallelization of an FE code for machines with shared memory in order to speed up computations of large models.
The loop was parallelized over elements in the research code FEAP using OpenMP, which required several modifications of the code
and a specific method of synchronization for assembling, see [2] for details. The parallel solver was also applied.
Performance of the parallelized FEAP, designated as ’ompFEAP’ is demonstrated in calculations of effective properties of materials
using the RVE method. Two RVE examples are computed, for a heterogenous metal-ceramic composite and for a ceramic foam with a
complicated micro-structure. We conclude that ompFEAP provides a very good speedup and efficiency causing only a small increase
in memory usage.

parallelization, OpenMP, finite element method, FEAP, RVE, shells

finite element methods, solid-shell elements

This paper concerns parallelization of an FE code for machines with shared memory in order to speed up computations of large models. We parallelized the loop over elements in the research code FEAP using OpenMP, which required several modifications of the code and a specific method of synchronization for assembling, for details see [2]. The parallel solver was also applied. We demonstrate performance of the parallelized FEAP, designated as ’ompFEAP’, in calculations of effective properties of materials using the RVE method. Two RVE examples are computed, for a heterogenous metal-ceramic composite and for a ceramic foam with a complicated micro-structure. We conclude that ompFEAP provides a very good speedup and efficiency causing only a small increase in memory usage.

parallelization, OpenMP, finite element method, FEAP, RVE, shells

In this paper, we derived the corrected shape functions for 6-node triangular element using the concept proposed in (Celia & Gray 1984). These shape functions were implemented in the two-dimensional 6-node triangular element for heat conduction as a replacement of the isoparametric ones. The numerical tests indicate that, for distorted meshes, the new element is more accurate than the standard element. Comparisons of the accuracy of a range of triangular and quadrilateral elements also are provided.

Six-node triangular element, heat conduction, corrected shape functions, sensitivity to mesh distortion, patch test