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Highlighting numerical insights of an efficient SPH method

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  • Francomano, E.
  • Paliaga, M.

Abstract

In this paper we focus on two sources of enhancement in accuracy and computational demanding in approximating a function and its derivatives by means of the Smoothed Particle Hydrodynamics method. The approximating power of the standard method is perceived to be poor and improvements can be gained making use of the Taylor series expansion of the kernel approximation of the function and its derivatives. The modified formulation is appealing providing more accurate results of the function and its derivatives simultaneously without changing the kernel function adopted in the computation. The request for greater accuracy needs kernel function derivatives with order up to the desidered accuracy order in approximating the function or higher for the derivatives. In this paper we discuss on the scheme dealing with the infinitely differentiable Gaussian kernel function. Studies on the accuracy, convergency and computational efforts with various sets of data sites are provided. Moreover, to make large scale problems tractable the improved fast Gaussian transform is considered picking up the computational cost at an acceptable level preserving the accuracy of the computation.

Suggested Citation

  • Francomano, E. & Paliaga, M., 2018. "Highlighting numerical insights of an efficient SPH method," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 899-915.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:899-915
    DOI: 10.1016/j.amc.2018.07.060
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    References listed on IDEAS

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    1. Francomano, Elisa & Hilker, Frank M. & Paliaga, Marta & Venturino, Ezio, 2018. "Separatrix reconstruction to identify tipping points in an eco-epidemiological model," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 80-91.
    2. Ala, Guido & Fasshauer, Gregory E. & Francomano, Elisa & Ganci, Salvatore & McCourt, Michael J., 2017. "An augmented MFS approach for brain activity reconstruction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 3-15.
    3. Ala, Guido & Francomano, Elisa & Ganci, Salvatore, 2015. "Unconditionally stable meshless integration of time-domain Maxwell’s curl equations," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 157-164.
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    Citations

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    Cited by:

    1. Silvia Licciardi & Guido Ala & Elisa Francomano & Fabio Viola & Michele Lo Giudice & Alessandro Salvini & Fausto Sargeni & Vittorio Bertolini & Andrea Di Schino & Antonio Faba, 2024. "Neural Network Architectures and Magnetic Hysteresis: Overview and Comparisons," Mathematics, MDPI, vol. 12(21), pages 1-23, October.
    2. Antonelli, L. & Francomano, E. & Gregoretti, F., 2021. "A CUDA-based implementation of an improved SPH method on GPU," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    3. da Silva, L.P. & Marchi, C.H. & Meneguette, M. & Foltran, A.C., 2022. "Robust RRE technique for increasing the order of accuracy of SPH numerical solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 231-252.
    4. Francomano, Elisa & Paliaga, Marta, 2020. "A normalized iterative Smoothed Particle Hydrodynamics method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 176(C), pages 171-180.

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