A fast numerical scheme for fractional viscoelastic models of wave propagation
<|reference_start|>A fast numerical scheme for fractional viscoelastic models of wave propagation: We propose a fast scheme for approximating the Mittag-Leffler function by an efficient sum-of-exponentials (SOE), and apply the scheme to the viscoelastic model of wave propagation with mixed finite element methods for the spatial discretization and the Newmark-beta scheme for the second-order temporal derivative. Compared with traditional L1 scheme for fractional derivative, our fast scheme reduces the memory complexity from $\mathcal O(N_sN) $ to $\mathcal O(N_sN_{exp})$ and the computation complexity from $\mathcal O(N_sN^2)$ to $\mathcal O(N_sN_{exp}N)$, where $N$ denotes the total number of temporal grid points, $N_{exp}$ is the number of exponentials in SOE, and $N_s$ represents the complexity of memory and computation related to the spatial discretization. Numerical experiments are provided to verify the theoretical results.<|reference_end|>
@article{yuan2024a,
    title={A fast numerical scheme for fractional viscoelastic models of wave
  propagation},
    author={Hao Yuan and Xiaoping Xie},
    journal={arXiv preprint arXiv:2410.01467},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.01467},
    primaryClass={math.NA cs.NA}
}