# Accelerating Computation of a Reduced Order Model of a Structural System Resulting from Craig–Bampton Reduction Using GPU Programming

### Abstract

The Craig–Bampton (CB) method is a well-known substructuring technique that reduces the size of a finite element model (FEM) using a set of vibration modes. For large FEA models, the reduction process could be computationally expensive since it requires algebra operations on FEM mode shapes and FEM system sparse matrices. In this paper, we investigate the potential of usage of GPU parallel processing to speed up solving the system of linear equations that results from the CB reduction process made for a model of cyclic structures. A Python based high-level approach, employing the CuPy, GinkGo and STRUMPACK libraries on the GPU, is compared with an optimized Fortran code. In side-to-side comparisons, employing the same inputs, the Python-GPU code is run on a single GPU device and the Fortran code is run on a multi-core compute node. The CB reduction process was split into several parts, each dealing with different kind of algebraic formulation of the problem. Performance comparisons were focused on the sparse system linear solver, since it turned out to be the most time-consuming part. The results suggest that the current GPU-based linear sparse solvers do not surpass the state-of-the-art CPU-based MKL PARDISO solver (at least up to 1M DOFs).

### Keywords

GPU, CPU, reduced order model, structural model, CuPy,### References

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**Computer Assisted Methods in Engineering and Science**, [S.l.], v. 31, n. 1, p. 51–66, feb. 2024. ISSN 2956-5839. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/1011>. Date accessed: 17 apr. 2024. doi: http://dx.doi.org/10.24423/cames.2024.1011.

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