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Communication Dans Un Congrès Année : 2024

FEMS – Designing a finite element code with computational homogenization in mind

Modesar Shakoor

Résumé

It might seem quite surprising that there are so many different Finite Element (FE) codes: commercial, open-source, explicit, implicit, parallel, GPU-accelerated, etc. When one looks closer at the applications that were in the minds of the people who developed these codes, however, the reason for the existence of each of them becomes more apparent. The open-source FE software FEMS [1] was first developed with mesh adaption in mind [2], and then redesigned for computational homogenization of FExFE or FE² type [3]. In this presentation, the (re-)design of an FE code for FE²-type computational homogenization will be detailed. FE² schemes consist in attaching separate FE meshes of so-called fine scale domains at each integration point of a main FE mesh that is called coarse scale domain. The assembly of the coarse scale FE problem depends on terms that are computed by solving the fine scale problems. On the one hand, without a distributed-memory parallel implementation at the coarse scale, the applications that can be targeted with FE² schemes are quite limited. On the other hand, since all fine scale problems are independent and can easily be run in parallel once the coarse scale mesh is partitioned, it is irrelevant to partition each fine scale mesh. The main issue is the following: how can the same FE code be used to assemble a partitioned problem at the coarse scale, and also sequential problems at the fine scale? The strategy and software design deployed in FEMS in order to deal with this issue will be detailed in this presentation. The first ingredient is to separate the parts of the code that can be factored (e.g., basis functions, quadrature, physical models, numerical techniques) from those that cannot (e.g., matrix assembly, linear solve). The second ingredient is to ensure that, even in the factored parts, functions that make local element-wise or node-wise operations are separated from those that may access the whole mesh. This presentation will describe those ingredients and try to identify some good practices for designing FE² codes. [1] M. Shakoor, FEMS – Finite Element Modeling Software, 2022, https://hal.science/hal-03781711 [2] M. Shakoor, FEMS – A Mechanics-oriented Finite Element Modeling Software, Computer Physics Communications, 260, 107729, 2021. [3] M. Shakoor and C.H. Park, Computational homogenization of unsteady flows with obstacles, International Journal for Numerical Methods in Fluids, 95(4), 499–527, 2023.
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Dates et versions

hal-04494015 , version 1 (07-03-2024)

Identifiants

  • HAL Id : hal-04494015 , version 1

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Modesar Shakoor. FEMS – Designing a finite element code with computational homogenization in mind. 9th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS), Jun 2024, Lisbon, Portugal. ⟨hal-04494015⟩
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