A nonperiodic Chebyshev spectral method avoiding penalization techniques for a class of nonlinear peridynamic models

Lopez, L.; Pellegrino, Sabrina Francesca

doi:10.1002/nme.7058

Cited by 12 publications

(3 citation statements)

References 38 publications

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“…Other techniques (for instance, see [ 38 ]) for optimizing hyperparameters in hybrid methods could also be investigated. Even more challenging is the idea of combining these techniques with more complex nonlocal models, which is now emerging in unsaturated flow modeling (e.g., [ 39 ]), coupled with sophisticated numerical techniques for nonlocal problems (as in [ 40 , 41 ]).…”

Section: Discussion and Future Workmentioning

confidence: 99%

Soil Moisture Sensor Information Enhanced by Statistical Methods in a Reclaimed Water Irrigation Framework

Giorgio¹,

Buono

Berardi

et al. 2022

Sensors

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Time series modeling and forecasting play important roles in many practical fields. A good understanding of soil water content and salinity variability and the proper prediction of variations in these variables in response to changes in climate conditions are essential to properly plan water resources and appropriately manage irrigation and fertilization tasks. This paper provides a 48-h forecast of soil water content and salinity in the peculiar context of irrigation with reclaimed water in semi-arid environments. The forecasting was performed based on (i) soil water content and salinity data from 50 cm beneath the soil surface with a time resolution of 15 min, (ii) hourly atmospheric data and (iii) daily irrigation amounts. Exploratory data analysis and data pre-processing phases were performed and then statistical models were constructed for time series forecasting based on the set of available data. The obtained prediction models showed good forecasting accuracy and good interpretability of the results.

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Section: Discussion and Future Workmentioning

confidence: 99%

Soil Moisture Sensor Information Enhanced by Statistical Methods in a Reclaimed Water Irrigation Framework

Giorgio¹,

Buono

Berardi

et al. 2022

Sensors

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“…Numerical methods for solving nonlocal wave equations involve temporal discretization of derivatives and numerical integration in the spatial domain. Various numerical algorithms have been adopted into peridynamics, including the meshfree method [6], quadrature methods [7,8], the finite element method [9], the discontinuous Galerkin method [10], and spectral methods [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Iterated Crank–Nicolson Method for Peridynamic Models

Liu,

Appiah-Adjei,

Brio

2024

Dynamics

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In this paper, we explore the iterated Crank–Nicolson (ICN) algorithm for the one-dimensional peridynamic model. The peridynamic equation of motion is an integro-differential equation that governs structural deformations such as fractures. The ICN method was originally developed for hyperbolic advection equations. In peridynamics, we apply the ICN algorithm for temporal discretization and the midpoint quadrature method for spatial integration. Several numerical tests are carried out to evaluate the performance of the ICN method. In general, the ICN method demonstrates second-order accuracy, consistent with the Störmer–Verlet (SV) method. When the weight is 1/3, the ICN method behaves as a third-order Runge–Kutta method and maintains strong stability-preserving (SSP) properties for linear problems. Regarding energy conservation, the ICN algorithm maintains at least second-order accuracy, making it superior to the SV method, which converges linearly. Furthermore, selecting a weight of 0.25 results in fourth-order superconvergent energy variation for the ICN method. In this case, the ICN method exhibits energy variation similar to that of the fourth-order Runge–Kutta method but operates approximately 20% faster. Higher-order convergence for energy can also be achieved by increasing the number of iterations in the ICN method.

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“…Such a division is solely for summarizing purposes, and a plethora of subdivisions, parallelisms, and couplings can be found in the literature. Moreover, further numerical methods, like spectral methods [43][44][45], considering or neglecting the volume penalization step [46,47], boundary element methods (BEMs) [48] have been developed recently in the context of peridynamics, enlarging the range of available PD numerical tools. In [49] a mesh-free method has been developed to numerically solve the PD equation for so-called prototype microelastic brittle (PMB) materials, showing that the stability criterion for the proposed numerical scheme weakly depends on space discretization, but the results are principally dictated by the peridynamic horizon size.…”

Section: Introductionmentioning

confidence: 99%

Bond-based peridynamics, a survey prospecting nonlocal theories of fluid-dynamics

et al. 2022

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Peridynamic (PD) theories have become widespread in various research areas due to the ability of modeling discontinuity formation and evolution in materials. Bond-based peridynamics (BB-PD), notwithstanding some modeling limitations, is widely employed in numerical simulations due to its easy implementation combined with physical intuitiveness and stability. In this paper, we review and investigate several aspects of bond-based peridynamic models. We present a detailed description of peridynamics theory, applications, and numerical models. We display the employed BB-PD integral kernels together with their differences and commonalities; then we discuss some consequences of their mathematical structure. We critically analyze and comment on the kinematic role of nonlocality, the relation between kernel structure and material impenetrability, and the role of PD kernel nonlinearity in crack formation prediction. Finally, we propose and present the idea of extending BB-PD to fluids in the framework of fading memory material, drawing some perspectives for a deeper and more comprehensive understanding of the peridynamics in fluids.

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A nonperiodic Chebyshev spectral method avoiding penalization techniques for a class of nonlinear peridynamic models

Cited by 12 publications

References 38 publications

Soil Moisture Sensor Information Enhanced by Statistical Methods in a Reclaimed Water Irrigation Framework

Soil Moisture Sensor Information Enhanced by Statistical Methods in a Reclaimed Water Irrigation Framework

Iterated Crank–Nicolson Method for Peridynamic Models

Bond-based peridynamics, a survey prospecting nonlocal theories of fluid-dynamics

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