Two-Dimensional Adaptive Finite Element Using GPGPU

Document Type : Research Article

Authors

1 Civil Engineering Department, K. N. Toosi University of Technology

2 Structure Div/Civil Eng. Faculty/K.N. Toosi University of Technology/Tehran/Iran

Abstract

The discretization error is one of the most common errors in the finite element method. One way to reduce this error is by using adaptive methods. Adaptive methods generally involve a large computational load; a technique for reducing this load is the use of data transfer operators. Even with data transfer operators, adaptive methods still require significant time from users. Given the new capabilities provided by graphics processing units (GPUs) for general-purpose computing under the CUDA platform, and the economic efficiency of GPUs compared to standard processors, this paper aims to present an algorithm that can reduce computation time through general-purpose GPU processing. The proposed algorithm begins with an initial finite element analysis using a nearly uniform mesh and refines the mesh intelligently at each step based on the displacement gradient. The conventional algorithm has been improved at several points. The patch formation stage is implemented using the K-nearest neighbor method to facilitate more efficient parallelization. In the data transfer stage, a dynamic method is employed to select the optimal curve from a set of the best curves. The results show that the acceleration of this algorithm increases proportionally with the number of elements. For instance, for a problem with 908 elements, the processing speed for stages one through three increased by factors of 6.6, 9.1, and 12.7, respectively. The total time required for all three stages in serial processing was 96 seconds, which was reduced to 8 seconds using this algorithm.

Keywords

Main Subjects

References

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Amirkabir Journal of Civil Engineering
Volume 57, Issue 4
2025
Pages 589-610

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