PyAdMesh: A novel high-performance software for adaptive finite element analysis

This study introduces PyAdMesh, an open-source software for reducing discretization errors in finite element analysis using an h-adaptive method. Adaptive approaches iteratively refine meshes to minimize errors but require substantial computational resources due to repeated analyses. PyAdMesh addresses this challenge by employing efficient data transfer operators for displacement, stress, and strain, avoiding full reanalysis. The software achieves performance gains through parallel processing on CPU and GPU, leveraging CuPy, Numba, and Python's multiprocessing library. GPU parallelization achieves speed-ups of 30 times compared to serial execution, while CPU parallelization yields an 8-fold improvement. PyAdMesh reduces discretization error from 5.5% to 0.07% using a recovery-based error estimation method. Despite low-end hardware, including an Intel Xeon 6148 CPU and NVIDIA Quadro P4000 GPU, the software demonstrates significant potential for adaptive finite element analysis. Future studies should explore its performance on high-end hardware. This work highlights PyAdMesh's potential for large-scale engineering simulations, balancing computational efficiency and accuracy.