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Showing papers on "Discretization published in 2022"


Journal ArticleDOI
03 Feb 2022-Fractals
TL;DR: In this paper , the numerical solution of nonlinear time-fractional Fisher equations via local meshless method combined with explicit difference scheme is presented, which uses radial basis functions to compute space derivatives while Caputo derivative scheme utilizes for time fractional integration to semi-discretize model equations.
Abstract: This paper addresses the numerical solution of nonlinear time-fractional Fisher equations via local meshless method combined with explicit difference scheme. This procedure uses radial basis functions to compute space derivatives while Caputo derivative scheme utilizes for time-fractional integration to semi-discretize the model equations. To assess the accuracy, maximum error norm is used. In order to validate the proposed method, some non-rectangular domains are also considered.

173 citations


Journal ArticleDOI
07 Feb 2022-Fractals
TL;DR: In this article , the authors investigated the consequences of reverse Minkowski and related Hölder-type inequalities via discrete fractional operators having [Formula: see text]-discrete generalized Mittag-Leffler kernels.
Abstract: Discrete fractional calculus ([Formula: see text]) is significant for neural networks, complex dynamic systems and frequency response analysis approaches. In contrast with the continuous-time frameworks, fewer outcomes are accessible for discrete fractional operators. This study investigates some major consequences of two sorts of inequalities by considering discrete Atangana–Baleanu [Formula: see text]-fractional operator having [Formula: see text]-discrete generalized Mittag-Leffler kernels in the sense of Riemann type ([Formula: see text]). Certain novel versions of reverse Minkowski and related Hölder-type inequalities via discrete [Formula: see text]-fractional operators having [Formula: see text]-discrete generalized Mittag-Leffler kernels are given. Moreover, several other generalizations can be generated for nabla [Formula: see text]-fractional sums. The proposing discretization is a novel form of the existing operators that can be provoked by some intriguing features of chaotic systems to design efficient dynamics description in short time domains. Furthermore, by combining two mechanisms, numerous new special cases are introduced.

89 citations


Journal ArticleDOI
TL;DR: In this article , the authors focus on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems and evaluate them in terms of their computational effort and predictive capabilities.
Abstract: Abstract Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized.

42 citations



Journal ArticleDOI
TL;DR: In this paper , a newly disclosed nonstandard finite difference method has been used to discretize a Lotka-Volterra model to investigate the critical normal form coefficients of bifurcations for both one-parameter and twoparameter bifurbation.
Abstract: A newly disclosed nonstandard finite difference method has been used to discretize a Lotka–Volterra model to investigate the critical normal form coefficients of bifurcations for both one-parameter and two-parameter bifurcations. The discrete-time prey–predator model exhibits a variety of local bifurcations such as period-doubling, Neimark–Sacker, and strong resonances. Critical normal form coefficients are determined to reveal dynamical scenarios corresponding to each bifurcation point. We also investigate the complex dynamics of the model numerically by Matlab package using MatcotM based on numerical continuation technique. The numerical continuation validates the theoretical analysis, which is discussed from an ecological perspective.

38 citations


Journal ArticleDOI
TL;DR: In this paper , the authors explore the idea of multiscale modeling with machine learning and employ DeepONet, a neural operator, as an efficient surrogate of the expensive solver.

36 citations


Journal ArticleDOI
TL;DR: In this paper, a finite volume method is used to discretize the mass and energy conservative equations, and all the connections between control volumes including two types of fracture-matrix (f-m), three types of fractures fracture-fracture (f -f), and one type of matrix-matrices (m-m) connections are constructed, and corresponding transmissibility formulas of mass and heat transfer in finite-volume discrete schemes for these connections are given.

34 citations


Journal ArticleDOI
TL;DR: In this paper, the eigenfrequency characteristics of the doubly-curved FG panel are examined considering multi-directional grading influence and geometrical large deformation, and a mathematical model has been established by utilizing HSDT midplane kinematics along with Green Lagrange kind of nonlinear strain terms.

34 citations


Journal ArticleDOI
TL;DR: In this paper , the eigenfrequency characteristics of the doubly-curved FG panel are examined considering multi-directional grading influence and geometrical large deformation, and a mathematical model has been established by utilizing HSDT midplane kinematics along with Green Lagrange kind of nonlinear strain terms.

34 citations


Journal ArticleDOI
TL;DR: In this article , a potential solution to the sign problem is proposed to deformation of the manifold on which the problem is defined, in order to reduce the instabilities of sign problems.
Abstract: A promising path to solving QCD is on a computer by discretizing spacetime, rewriting the QCD Lagrangian to fit in that discretization, and then taking the appropriate continuum and infinite volume limits. A problem with this method is that the calculation of certain quantities of interest is numerically intractable because of a ``sign problem.'' A sign problem appears whenever large cancellations make it impractical to obtain reliable numerical results. This review discusses a potential solution: deformation of the manifold on which the problem is defined in order to reduce these instabilities.

31 citations


Journal ArticleDOI
TL;DR: In this paper , two supervised deep neural networks, i.e., multilayer perceptron (MLP) and deep belief networks (DBN), are compared for missing value imputation, and two differently ordered combinations of data discretization and imputation steps are examined.
Abstract: Often real-world datasets are incomplete and contain some missing attribute values. Furthermore, many data mining and machine learning techniques cannot directly handle incomplete datasets. Missing value imputation is the major solution for constructing a learning model to estimate specific values to replace the missing ones. Deep learning techniques have been employed for missing value imputation and demonstrated their superiority over many other well-known imputation methods. However, very few studies have attempted to assess the imputation performance of deep learning techniques for tabular or structured data with continuous values. Moreover, the effect on the imputation results when the continuous data need to be discretized has never been examined. In this paper, two supervised deep neural networks, i.e., multilayer perceptron (MLP) and deep belief networks (DBN), are compared for missing value imputation. Moreover, two differently ordered combinations of data discretization and imputation steps are examined. The results show that MLP and DBN significantly outperform the baseline imputation methods based on the mean, KNN, CART, and SVM, with DBN performing the best. On the other hand, when considering the discretization of continuous data, the order in which the two steps are combined is not the most important, but rather, the chosen imputation algorithm. That is, the final performance is much better when using DBN for imputation, regardless of whether discretization is performed in the first or second step, than the other imputation methods.

Journal ArticleDOI
TL;DR: In this article , a new kinematically admissible velocity field is proposed to improve the description of the soil movement according to the results of the numerical simulation, and an improved failure mechanism is constructed adopting the spatial discretization technique, which takes into account soil arching effect and plastic deformation within soil mass.
Abstract: Existing mechanism of simulating soil movement at tunnel face is generally based on the translational or rotational velocity field, which is, to some extent, different from the real soil movement in the arching zone. Numerical simulations are carried out first to investigate the characteristics of the velocity distribution at tunnel face and above tunnel vault. Then a new kinematically admissible velocity field is proposed to improve the description of the soil movement according to the results of the numerical simulation. Based on the proposed velocity field, an improved failure mechanism is constructed adopting the spatial discretization technique, which takes into account soil arching effect and plastic deformation within soil mass. Finally, the critical face pressure and the proposed mechanism are compared with the results of the numerical simulation, existing analytical studies and experimental tests to verify the accuracy and improvement of the presented method. The proposed mechanism can serve as an alternative approach for the face stability analysis.

Journal ArticleDOI
TL;DR: A mixed-integer linear programming model of the continuous berth allocation and quay crane assignment problem is established, aiming at minimizing the total stay time and delay penalty of ships, and a large neighborhood search algorithm incorporating the discretization strategy is proposed.
Abstract: The continuous berth allocation and quay crane assignment problem considers the size of berths and ships, the number of quay cranes, the dynamic ships and non-crossing constraints of quay cranes. In this work, a mixed-integer linear programming model of this problem is established, aiming at minimizing the total stay time and delay penalty of ships. To solve the model, the continuous berth is separated into discrete segments via a proposed discretization strategy. Thereafter, a large neighborhood search algorithm composed of the random removal operator and relaxed sorting-based insertion operator and a backtracking comparison-based constraint repair strategy are proposed. The effectiveness of the model and algorithm presented is verified via real-life instances with different characteristics, and the performances of different combinations of removal operators and insertion operators in the large neighborhood search algorithmic framework are analyzed. Numerical results show that the large neighborhood search algorithm can optimally solve the small-scale instances in a reasonable time. Meanwhile, the results of large-scale instances show that the large neighborhood search algorithm incorporating the discretization strategy is more efficient than other genetic algorithms based on continuous optimization. With the proposed approach, high-quality berth and quay crane allocation results can be obtained efficiently.

Journal ArticleDOI
TL;DR: In this article , the Natural Frequencies (NFs) of perfect and imperfect Graphene Nanoplatelet Reinforced Nanocomposite (GNPRN) structures of revolution (conical and cylindrical shells and annular plate structures) resting on elastic foundations under general boundary conditions (BCs).
Abstract: The goal of the present research is to examine the Natural Frequencies (NFs) of perfect and imperfect Graphene Nanoplatelet Reinforced Nanocomposite (GNPRN) structures of revolution (conical and cylindrical shells and annular plate structures) resting on elastic foundations under general boundary conditions (BCs). The graphene nanoplatelet material is implemented to compose the nanocomposite enhanced by a polymeric matrix including porosities. The springs technique is applied to define the general BCs of GNPRN structures of revolution. Elastic foundations are described by two parameters, i.e., Winkler-Pasternak Foundations (WPFs). Additionally, Donnell's hypothesis and first-order shear deformation theory (FSDT) are employed to figure out the primary formulations associated with the GNPRN structures of revolution. In contrast, the equations of motion are found using Hamilton's principle. Then the equations of motion are then discretized using the well-known Generalized Differential Quadrature Method (GDQM). Next, the standard eigenvalue solution is assigned to obtain the NFs of the perfect/imperfect GNPRN structures of revolution. Finally, various benchmarks are addressed to verify the approach suggested for evaluating the NFs of the perfect/imperfect GNPRN structures of revolution. Furthermore, several novel examples highlight the effects of the change in geometrical and material properties, arbitrary boundary conditions, and WPFs on the NFs of the perfect/imperfect GNPRN structures of revolution.

Journal ArticleDOI
TL;DR: In this paper , the authors proposed a mesh-free peridynamics (PD) discretization scheme that employs a simple collocation procedure and is truly mesh free, i.e., it does not depend on any background integration cells.

Journal ArticleDOI
TL;DR: In this paper, a least square space-time control volume scheme is proposed to handle regularity requirements, imposition of boundary conditions, entropy compatibility, and conservation, substantially reducing requisite hyperparameters in the process.

Journal ArticleDOI
TL;DR: A novel meshless technique for solving a class of fractional differential equations based on moving least squares and on the existence of a fractional Taylor series for Caputo derivatives is presented.

Journal ArticleDOI
TL;DR: It is demonstrated using the perturbation analysis that, a system with at least a zero or a non-zero known input can potentially be uniquely identified and allowed for a better understanding of the system compared to classical output-only parameter identification strategies.

Journal ArticleDOI
01 Jan 2022
TL;DR: In this article, a continuous-time algorithm that incorporates network topology changes in discrete jumps is proposed to remove chattering that arises because of the discretization of the underlying CT process, which converges to the SVM classifier over time-varying weight balanced directed graphs by using arguments from matrix perturbation theory.
Abstract: In this letter, we consider the binary classification problem via distributed Support Vector Machines (SVMs), where the idea is to train a network of agents, with limited share of data, to cooperatively learn the SVM classifier for the global database. Agents only share processed information regarding the classifier parameters and the gradient of the local loss functions instead of their raw data. In contrast to the existing work, we propose a continuous-time algorithm that incorporates network topology changes in discrete jumps. This hybrid nature allows us to remove chattering that arises because of the discretization of the underlying CT process. We show that the proposed algorithm converges to the SVM classifier over time-varying weight balanced directed graphs by using arguments from the matrix perturbation theory.

Journal ArticleDOI
26 Apr 2022-Symmetry
TL;DR: This paper presents a new univariate flexible generator of distributions, namely, the odd Perks-G class, a novel discrete distribution class and presents a novel log-location-scale regression model based on the even Perks–Weibull distribution.
Abstract: In this paper, we present a new univariate flexible generator of distributions, namely, the odd Perks-G class. Some special models in this class are introduced. The quantile function (QFUN), ordinary and incomplete moments (MOMs), generating function (GFUN), moments of residual and reversed residual lifetimes (RLT), and four different types of entropy are all structural aspects of the proposed family that hold for any baseline model. Maximum likelihood (ML) and maximum product spacing (MPS) estimates of the model parameters are given. Bayesian estimates of the model parameters are obtained. We also present a novel log-location-scale regression model based on the odd Perks–Weibull distribution. Due to the significance of the odd Perks-G family and the survival discretization method, both are used to introduce the discrete odd Perks-G family, a novel discrete distribution class. Real-world data sets are used to emphasize the importance and applicability of the proposed models.

Journal ArticleDOI
TL;DR: In this paper , the input-parameter-state estimation capabilities of a novel unscented Kalman filter are examined on both linear and nonlinear systems, where the unknown input is estimated in two stages within each time step.

Journal ArticleDOI
TL;DR: In this article , a finite volume method is used to discretize the mass and energy conservative equations, and all the connections between control volumes including two types of fracture-matrix (f-m), three types of fractures fracture-fracture (f -f), and one type of matrix-matrices (m-m) connections are constructed, and corresponding transmissibility formulas of mass and heat transfer in finite-volume discrete schemes for these connections are given.

Journal ArticleDOI
TL;DR: In this paper , an auxiliary physics informed neural network (A-PINN) framework was proposed to solve forward and inverse problems of nonlinear IDEs without the need of label data.

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a fully decoupled structure and second-order time accuracy for highly coupled nonlinear incompressible magnetohydrodynamic (MHD) systems.

Journal ArticleDOI
TL;DR: In this paper , a discrete inverted Kumaraswamy distribution is derived using the general approach of discretization of a continuous distribution, and some important distributional and reliability properties of the Discrete Inverted Kumarasamy Distribution (DIKD) are obtained.
Abstract: In this paper, a discrete inverted Kumaraswamy distribution; which is a discrete version of the continuous inverted Kumaraswamy variable, is derived using the general approach of discretization of a continuous distribution. Some important distributional and reliability properties of the discrete inverted Kumaraswamy distribution are obtained. Maximum likelihood and Bayesian approaches are applied to estimate the model parameters. A simulation study is carried out to illustrate the theoretical results. Finally, a real data set is applied.

Journal ArticleDOI
TL;DR: In this paper , a physics-informed attention-based neural network (PIANN) is proposed to learn the complex behavior of non-linear PDEs with dominant hyperbolic character.
Abstract: Physics-informed neural networks (PINNs) have enabled significant improvements in modelling physical processes described by partial differential equations (PDEs) and are in principle capable of modeling a large variety of differential equations. PINNs are based on simple architectures, and learn the behavior of complex physical systems by optimizing the network parameters to minimize the residual of the underlying PDE. Current network architectures share some of the limitations of classical numerical discretization schemes when applied to non-linear differential equations in continuum mechanics. A paradigmatic example is the solution of hyperbolic conservation laws that develop highly localized nonlinear shock waves. Learning solutions of PDEs with dominant hyperbolic character is a challenge for current PINN approaches, which rely, like most grid-based numerical schemes, on adding artificial dissipation. Here, we address the fundamental question of which network architectures are best suited to learn the complex behavior of non-linear PDEs. We focus on network architecture rather than on residual regularization. Our new methodology, called physics-informed attention-based neural networks (PIANNs), is a combination of recurrent neural networks and attention mechanisms. The attention mechanism adapts the behavior of the deep neural network to the non-linear features of the solution, and break the current limitations of PINNs. We find that PIANNs effectively capture the shock front in a hyperbolic model problem, and are capable of providing high-quality solutions inside the convex hull of the training set.

Journal ArticleDOI
TL;DR: In this article , the authors proposed a fully decoupled structure and second-order time accuracy for highly coupled nonlinear incompressible magnetohydrodynamic (MHD) systems.

Journal ArticleDOI
TL;DR: In this paper , an optimal order uniformly accurate boundary layer adaptive method moving mesh method is proposed, which is able to capture the layer phenomena without using a priori information of the solution.

Journal ArticleDOI
TL;DR: In this article, the unconditional stability and convergence analysis of the Euler implicit/explicit scheme with finite element discretization are studied for the incompressible time-dependent Navier-Stokes equations based on the scalar auxiliary variable approach.
Abstract: The unconditional stability and convergence analysis of the Euler implicit/explicit scheme with finite element discretization are studied for the incompressible time-dependent Navier–Stokes equations based on the scalar auxiliary variable approach. Firstly, a corresponding equivalent system of the Navier–Stokes equations with three variables is formulated, the stable finite element spaces are adopted to approximate these variables and the corresponding theoretical analysis results are provided. Secondly, a fully discrete scheme based on the backward Euler method is developed, the temporal treatment is based on the Euler implicit/explicit scheme, which is implicit for the linear terms and explicit for the nonlinear term. Hence, a constant coefficient algebraic system is formed and it can be solved efficiently. The discrete unconditional energy dissipation and stability of numerical solutions in various norms are established with any restriction on the time step, optimal error estimates are also provided. Finally, some numerical results are provided to illustrate the performances of the considered numerical scheme.

Journal ArticleDOI
TL;DR: In this article , an improved version of the Volume-of-Fluid method (VOF-R) is introduced and utilized for modeling multiphase/multifluid flows and transport processes.