Parallel Thread Processing for Performance Optimization in a Multilevel Finite Element Method (FE2) Analysis

Heterogeneous materials are widely used in civil engineering, and studying these materials is essential to ensure the safety and reliability of structures. One approach to analyzing these complex materials is multiscale analysis, which involves dividing the problem into two distinct observation scales: the macro scale and the micro scale. At the macro scale, the material behaves as if it were homogeneous, while at the micro scale, it is possible to identify and analyze the interactions between the material's different constituents. From these interactions arise the formation of microcracks and other failure mechanisms. This paper employs the Multilevel Finite Element Method (FE2) to perform multiscale analysis on quasi-brittle materials. This strategy consists of using a finite element model to represent the macro scale and others finite element models to represent the micro scale, enabling the capture of the complexities at both scales. Each integration point at the macro scale is associated with a micro scale model, and the macro scale parameters are obtained from a homogenization process based on the micro scale information. However, one of the main challenges of this approach is the high computational cost, as micro scale models typically require significant refinement to correctly describe the different constituents of the medium. This is particularly relevant in phase-field models, the constitutive model adopted at the micro scale. Given the complexity of processing all microscale models, the multiscale analysis becomes computationally expensive. Therefore, the objective of this article is to investigate the potential performance gains achieved through parallel processing, utilizing threads to optimize execution time. Preliminary results will be presented. All implementations were carried out in INSANE (Interactive Structural Analysis Environment), an open-source software developed by the Department of Structural Engineering at UFMG.