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wPINNs: Weak Physics Informed Neural Networks for Approximating Entropy Solutions of Hyperbolic Conservation Laws SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-03-14 Tim De Ryck, Siddhartha Mishra, Roberto Molinaro
SIAM Journal on Numerical Analysis, Volume 62, Issue 2, Page 811-841, April 2024. Abstract. Physics informed neural networks (PINNs) require regularity of solutions of the underlying PDE to guarantee accurate approximation. Consequently, they may fail at approximating discontinuous solutions of PDEs such as nonlinear hyperbolic equations. To ameliorate this, we propose a novel variant of PINNs, termed
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A MPM Lagrangian‐Eulerian hydrocode for simulating buried explosions in transversely isotropic geomaterials Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-03-14 Mian Xiao, WaiChing Sun
Shock waves in geological materials are characterized by a sudden release of rapidly expanding gas, liquid, and solid particles. These shock waves may occur due to explosive volcanic eruptions or be artificially triggered. In fact, underground explosions have often been used as an engineering solution for large‐scale excavation, stimulating oil and gas recovery, creating cavities for underground waste
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Asymptotic analysis of three-parameter Mittag-Leffler function with large parameters, and application to sub-diffusion equation involving Bessel operator Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-11 Hassan Askari, Alireza Ansari
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Global optimization of a nonlinear system of differential equations involving $$\psi $$ -Hilfer fractional derivatives of complex order Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-11
Abstract In this paper, a class of cyclic (noncyclic) operators of condensing nature are defined on Banach spaces via a pair of shifting distance functions. The best proximity point (pair) results are manifested using the concept of measure of noncompactness (MNC) for the said operators. The obtained best proximity point result is used to demonstrate existence of optimum solutions of a system of differential
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Analytical solution for buried pipeline deformation induced by normal and reverse fault considering structural joint influence Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-03-13 Zhiguo Zhang, Jiawei Feng, Zhengguo Zhu, Qihua Zhao, Yutao Pan
Previous studies take less account of analytical solution analysis for buried pipeline under the action of active fault. Furthermore, current theoretical studies of fault‐pipeline interactions generally treat the structure as continuous pipeline, with less attention given to the effect of joints. This paper provides an analytical method to estimate the deformation and internal force of jointed pipelines
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On Optimal Cell Average Decomposition for High-Order Bound-Preserving Schemes of Hyperbolic Conservation Laws SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-03-11 Shumo Cui, Shengrong Ding, Kailiang Wu
SIAM Journal on Numerical Analysis, Volume 62, Issue 2, Page 775-810, April 2024. Abstract. Cell average decomposition (CAD) plays a critical role in constructing bound-preserving (BP) high-order discontinuous Galerkin and finite volume methods for hyperbolic conservation laws. Seeking optimal CAD (OCAD) that attains the mildest BP Courant–Friedrichs–Lewy (CFL) condition is a fundamentally important
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Revisiting the face stability of rock tunnels in the Hoek–Brown strength criterion with tension cutoff Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-03-11 Junhao Zhong, Siau Chen Chian, Hui Chen, Chuantan Hou, Xiaoli Yang
In this work, the three‐dimensional stability of deep tunnel faces is evaluated in rock masses characterized by the generalized Hoek–Brown (H–B) criterion from the perspective of the limit analysis theorem. Considering that underground engineering is gradually developing towards larger burial depths and larger sizes, and the tensile strength of rocks is usually overestimated, the concept of tension
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Cover Image, Volume 48, Issue 5 Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-03-07 Jiujiang Wu, Yi Zhang, Yan Li, Hua Wen, Lijuan Wang
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On the Convergence of Continuous and Discrete Unbalanced Optimal Transport Models for 1-Wasserstein Distance SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-03-05 Zhe Xiong, Lei Li, Ya-Nan Zhu, Xiaoqun Zhang
SIAM Journal on Numerical Analysis, Volume 62, Issue 2, Page 749-774, April 2024. Abstract. We consider a Beckmann formulation of an unbalanced optimal transport (UOT) problem. The [math]-convergence of this formulation of UOT to the corresponding optimal transport (OT) problem is established as the balancing parameter [math] goes to infinity. The discretization of the problem is further shown to be
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Robust DPG Test Spaces and Fortin Operators—The [math] and [math] Cases SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-03-05 Thomas Führer, Norbert Heuer
SIAM Journal on Numerical Analysis, Volume 62, Issue 2, Page 718-748, April 2024. Abstract. At the fully discrete setting, stability of the discontinuous Petrov–Galerkin (DPG) method with optimal test functions requires local test spaces that ensure the existence of Fortin operators. We construct such operators for [math] and [math] on simplices in any space dimension and arbitrary polynomial degree
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Impact of soft minerals on crack propagation in crystalline rocks under uniaxial compression: A grain‐based numerical investigation Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-03-06 Yu Zhou, Wenjun Lv, Bo Li, Qinyuan Liang
Varying external conditions in the metallogenetic process of crystalline rocks contribute to the complex mineral and textural characteristics, rendering the mechanical properties highly heterogeneous at the mineral scale. This research focused on the influences of minerals with relatively low strength and stiffness (soft minerals) in crystalline rocks on their cracking behavior. A particle‐based discrete
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The consolidation behavior of layered fractional viscoelastic soils considering groundwater Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-03-06 Zhi Yong Ai, Zi Kun Ye, Ming Jing Jiang, Qing Song Lu
This paper investigates the consolidation behavior of multi‐layered viscoelastic soils considering groundwater. First, the fractional Merchant viscoelastic model is introduced to describe the behavior of multi‐layered viscoelastic soils considering groundwater. Later, the governing equations are extended to a viscoelastic medium by virtue of the elastic‐viscoelastic corresponding principle in the Laplace–Hankel
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Nehari manifold approach for fractional Kirchhoff problems with extremal value of the parameter Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-05
Abstract In this work we study the following nonlocal problem $$\begin{aligned} \left\{ \begin{aligned} M(\Vert u\Vert ^2_X)(-\varDelta )^s u&= \lambda {f(x)}|u|^{\gamma -2}u+{g(x)}|u|^{p-2}u{} & {} \text{ in }\ \ \varOmega , \\ u&=0{} & {} \text{ on }\ \ \mathbb R^N\setminus \varOmega , \end{aligned} \right. \end{aligned}$$ where \(\varOmega \subset \mathbb R^N\) is open and bounded with smooth boundary
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Analysis of BURA and BURA-based approximations of fractional powers of sparse SPD matrices Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-04 Nikola Kosturski, Svetozar Margenov
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Stable Lifting of Polynomial Traces on Triangles SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-03-04 Charles Parker, Endre Süli
SIAM Journal on Numerical Analysis, Volume 62, Issue 2, Page 692-717, April 2024. Abstract. We construct a right inverse of the trace operator [math] on the reference triangle [math] that maps suitable piecewise polynomial data on [math] into polynomials of the same degree and is bounded in all [math] norms with [math] and [math]. The analysis relies on new stability estimates for three classes of
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On the Convergence of Sobolev Gradient Flow for the Gross–Pitaevskii Eigenvalue Problem SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-03-04 Ziang Chen, Jianfeng Lu, Yulong Lu, Xiangxiong Zhang
SIAM Journal on Numerical Analysis, Volume 62, Issue 2, Page 667-691, April 2024. Abstract. We study the convergences of three projected Sobolev gradient flows to the ground state of the Gross–Pitaevskii eigenvalue problem. They are constructed as the gradient flows of the Gross–Pitaevskii energy functional with respect to the [math]-metric and two other equivalent metrics on [math], including the
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Homogenization of Nondivergence-Form Elliptic Equations with Discontinuous Coefficients and Finite Element Approximation of the Homogenized Problem SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-03-01 Timo Sprekeler
SIAM Journal on Numerical Analysis, Volume 62, Issue 2, Page 646-666, April 2024. Abstract. We study the homogenization of the equation [math] posed in a bounded convex domain [math] subject to a Dirichlet boundary condition and the numerical approximation of the corresponding homogenized problem, where the measurable, uniformly elliptic, periodic, and symmetric diffusion matrix [math] is merely assumed
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A Numerical Framework for Nonlinear Peridynamics on Two-Dimensional Manifolds Based on Implicit P-(EC)[math] Schemes SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-03-01 Alessandro Coclite, Giuseppe M. Coclite, Francesco Maddalena, Tiziano Politi
SIAM Journal on Numerical Analysis, Volume 62, Issue 2, Page 622-645, April 2024. Abstract. In this manuscript, an original numerical procedure for the nonlinear peridynamics on arbitrarily shaped two-dimensional (2D) closed manifolds is proposed. When dealing with non-parameterized 2D manifolds at the discrete scale, the problem of computing geodesic distances between two non-adjacent points arise
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Analytical solution for one‐dimensional thaw consolidation model with double moving boundaries Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-03-02 Tao Han, Yang Zhou, Guang‐si Zhao, Meng‐meng Lu
A one‐dimensional thaw consolidation model considering the density change from pore ice to pore water is established, and the model describes a special type of moving boundary problem with double moving boundaries. An analytical solution for the model under a time‐varying external load is developed using certain form of superposition principle and the similarity type of general solution. Some known
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Interpreting correlations in stress‐dependent permeability, porosity, and compressibility of rocks: A viewpoint from finite strain theory Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-03-02 Luyu Wang, Yanjun Zhang
Characteristics of stress‐dependent properties of rocks are commonly described by empirical laws. It is crucial to establish a universal law that connects rock properties with stress. The present study focuses on exploring the correlations among permeability, porosity, and compressibility observed in experiments. To achieve this, we propose a novel finite strain‐based dual‐component (FS‐DC) model,
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Numerical Analysis for Convergence of a Sample-Wise Backpropagation Method for Training Stochastic Neural Networks SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-03-01 Richard Archibald, Feng Bao, Yanzhao Cao, Hui Sun
SIAM Journal on Numerical Analysis, Volume 62, Issue 2, Page 593-621, April 2024. Abstract. The aim of this paper is to carry out convergence analysis and algorithm implementation of a novel sample-wise backpropagation method for training a class of stochastic neural networks (SNNs). The preliminary discussion on such an SNN framework was first introduced in [Archibald et al., Discrete Contin. Dyn
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Improving the performance of destructive interference phononic crystal structure through topology optimization Finite Elem. Anal. Des. (IF 3.1) Pub Date : 2024-03-01 Tam Yee Ha, Gil Ho Yoon
This study examines the phenomenon of intrinsic nature in wave mitigation, specifically focusing on the concept of destructive interference (DI). When waves interact, they can exhibit either destructive interference or constructive interference depending on the phase difference. In the case of mechanical waves propagating through a mechanical structure, their characteristics such as wave speed, wavelength
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Analysis of a class of completely non-local elliptic diffusion operators Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-29
Abstract This work explores the possibility of developing the analog of some classic results from elliptic PDEs for a class of fractional ODEs involving the composition of both left- and right-sided Riemann-Liouville (R-L) fractional derivatives, \({D^\alpha _{a+}}{D^\beta _{b-}}\) , \(1<\alpha +\beta <2\) . Compared to one-sided non-local R-L derivatives, these composite operators are completely non-local
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Discrete convolution operators and equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-27
Abstract In this work we introduce discrete convolution operators and study their most basic properties. We then solve linear difference equations depending on such operators. The theory herein developed generalizes, in particular, the theory of discrete fractional calculus and fractional difference equations. To that matter we make use of the so-called Sonine pairs of kernels.
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Approximate optimal control of fractional stochastic hemivariational inequalities of order (1, 2] driven by Rosenblatt process Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-27 Zuomao Yan
We study the approximate optimal control for a class of fractional stochastic hemivariational inequalities with non-instantaneous impulses driven by Rosenblatt process in a Hilbert space. Firstly, a suitable definition of piecewise continuous mild solution is introduced, and by using stochastic analysis, properties of \(\alpha \)-order sine and cosine family and Picard type approximate sequences, we
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Optimal control of fractional non-autonomous evolution inclusions with Clarke subdifferential Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-27 Xuemei Li, Xinge Liu, Fengzhen Long
In this paper, the non-autonomous fractional evolution inclusions of Clarke subdifferential type in a separable reflexive Banach space are investigated. The mild solution of the non-autonomous fractional evolution inclusions of Clarke subdifferential type is defined by introducing the operators \(\psi (t,\tau )\) and \(\phi (t,\tau )\) and V(t), which are generated by the operator \(-\mathcal {A}(t)\)
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Solving PDEs on unknown manifolds with machine learning Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 2024-02-29 Senwei Liang, Shixiao W. Jiang, John Harlim, Haizhao Yang
This paper proposes a mesh-free computational framework and machine learning theory for solving elliptic PDEs on unknown manifolds, identified with point clouds, based on diffusion maps (DM) and deep learning. The PDE solver is formulated as a supervised learning task to solve a least-squares regression problem that imposes an algebraic equation approximating a PDE (and boundary conditions if applicable)
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Marcinkiewicz–Zygmund inequalities for scattered and random data on the q-sphere Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 2024-02-29 Frank Filbir, Ralf Hielscher, Thomas Jahn, Tino Ullrich
The recovery of multivariate functions and estimating their integrals from finitely many samples is one of the central tasks in modern approximation theory. Marcinkiewicz–Zygmund inequalities provide answers to both the recovery and the quadrature aspect. In this paper, we put ourselves on the -dimensional sphere , and investigate how well continuous -norms of polynomials of maximum degree on the sphere
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Separation-Free Spectral Super-Resolution via Convex Optimization Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 2024-02-29 Zai Yang, Yi-Lin Mo, Gongguo Tang, Zongben Xu
Atomic norm methods have recently been proposed for spectral super-resolution with flexibility in dealing with missing data and miscellaneous noises. A notorious drawback of these convex optimization methods however is their lower resolution in the high signal-to-noise (SNR) regime as compared to conventional methods such as ESPRIT. In this paper, we devise a simple weighting scheme in existing atomic
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A nonlinear optimization method for calibration of large‐scale deep cement mixing in very soft clay deep excavation Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-02-28 Thanh Sang To, Hoang Le Minh, Thien Quoc Huynh, Samir Khatir, Magd Abdel Wahab, Thanh Cuong‐Le
This work proposes a novel technique to conduct back‐analysis of lateral displacement of deep cement mixing (DCM) columns in deep excavation construction. For the first time, we propose a process to investigate both soil and underground structure end‐to‐end automatically. The novel technique is a complex combination of three crucial factors: (1) a nature‐inspired optimization algorithm (O), (2) a three‐dimensional
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Exterior ballistics analysis of shotgun using discrete element method with equivalent aerodynamic forces Finite Elem. Anal. Des. (IF 3.1) Pub Date : 2024-02-28 Shigan Deng, Jason Wang, Sheng-Wei Chi, Chun-Cheng Lin, Jau-Nan Yeh, Chien-Chih Lai
This research continues the research of Deng et al. (2022) [1], using Discrete Element Method (DEM) coupled with Finite Element Analysis to solve shotgun exterior ballistics. The simulation examples in this research are using an Italian-made 24 gm #9½ birdshot with 433 pellets fired from 30” long, 12-gauge cylinder and full choke barrels. The simulations of shotgun exterior ballistics of this research
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A parallel implementation of a mixed multiscale domain decomposition method applied to the magnetostatic simulation of 2D electrical machines Finite Elem. Anal. Des. (IF 3.1) Pub Date : 2024-02-28 A. Ruda, F. Louf, P.-A. Boucard, X. Mininger, T. Verbeke
This article introduces a mixed domain decomposition method (DDM) designed to meet the requirements of advanced numerical optimization in electrical machines. The primary objective is to adapt the multiscale LATIN method, primarily used for mechanical studies, to the magnetostatic context. The proposed method offers an effective iterative scheme that relies on a mixed formulation of the equations on
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Exponential lower bound for the eigenvalues of the time-frequency localization operator before the plunge region Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 2024-02-28 Aleksei Kulikov
For a pair of sets the time-frequency localization operator is defined as , where is the Fourier transform and are projection operators onto and Ω, respectively. We show that in the case when both and Ω are intervals, the eigenvalues of satisfy if , where is arbitrary and , provided that . This improves the result of Bonami, Jaming and Karoui, who proved it for . The proof is based on the properties
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On the necessity of the inf-sup condition for a mixed finite element formulation IMA J. Numer. Anal. (IF 2.1) Pub Date : 2024-02-28 Fleurianne Bertrand, Daniele Boffi
We study a nonstandard mixed formulation of the Poisson problem, sometimes known as dual mixed formulation. For reasons related to the equilibration of the flux, we use finite elements that are conforming in $\textbf{H}(\operatorname{\textrm{div}};\varOmega )$ for the approximation of the gradients, even if the formulation would allow for discontinuous finite elements. The scheme is not uniformly inf-sup
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A time-fractional superdiffusion wave-like equation with subdiffusion possibly damping term: well-posedness and Mittag-Leffler stability Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-26
Abstract In this article, we focus on the application of the recent notion of time-fractional derivative developed in Sobolev spaces to the study of well-posedness and stability for a time-fractional wave-like equation with superdiffusion and subdiffusion terms.
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Schrödinger-Maxwell equations driven by mixed local-nonlocal operators Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-26
Abstract In this paper we prove existence of solutions to Schrödinger-Maxwell type systems involving mixed local-nonlocal operators. Two different models are considered: classical Schrödinger-Maxwell equations and Schrödinger-Maxwell equations with a coercive potential, and the main novelty is that the nonlocal part of the operator is allowed to be nonpositive definite according to a real parameter
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The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces II Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-26
Abstract In this work we study the Riemann-Liouville fractional integral of order \(\alpha \in (0,1/p)\) as an operator from \(L^p(I;X)\) into \(L^{q}(I;X)\) , with \(1\le q\le p/(1-p\alpha )\) , whether \(I=[t_0,t_1]\) or \(I=[t_0,\infty )\) and X is a Banach space. Our main result provides necessary and sufficient conditions to ensure the compactness of the Riemann-Liouville fractional integral from
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Uniform approximation of common Gaussian process kernels using equispaced Fourier grids Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 2024-02-27 Alex Barnett, Philip Greengard, Manas Rachh
The high efficiency of a recently proposed method for computing with Gaussian processes relies on expanding a (translationally invariant) covariance kernel into complex exponentials, with frequencies lying on a Cartesian equispaced grid. Here we provide rigorous error bounds for this approximation for two popular kernels—Matérn and squared exponential—in terms of the grid spacing and size. The kernel
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Orlicz-Lorentz-Karamata Hardy martingale spaces: inequalities and fractional integral operators Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-23 Zhiwei Hao, Libo Li, Long Long, Ferenc Weisz
Let \(0
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Operational matrix based numerical scheme for the solution of time fractional diffusion equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-23 S. Poojitha, Ashish Awasthi
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Time-dependent identification problem for a fractional Telegraph equation with the Caputo derivative Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-22
Abstract This study investigates the inverse problem of determining the right-hand side of a telegraph equation given in a Hilbert space. The main equation under consideration has the form \((D_{t}^{\rho })^{2}u(t)+2\alpha D_{t}^{\rho }u(t)+Au(t)=p( t)q+f(t)\) , where \(0
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Generalized Krätzel functions: an analytic study Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-22 Ashik A. Kabeer, Dilip Kumar
The paper is devoted to the study of generalized Krätzel functions, which are the kernel functions of type-1 and type-2 pathway transforms. Various analytical properties such as Lipschitz continuity, fixed point property and integrability of these functions are investigated. Furthermore, the paper introduces two new inequalities associated with generalized Krätzel functions. The composition formulae
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On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-22 Nabil Chems Eddine, Maria Alessandra Ragusa, Dušan D. Repovš
We obtain critical embeddings and the concentration-compactness principle for the anisotropic variable exponent Sobolev spaces. As an application of these results,we confirm the existence of and find infinitely many nontrivial solutions for a class of nonlinear critical anisotropic elliptic equations involving variable exponents and two real parameters. With the groundwork laid in this work, there
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Existence, uniqueness and regularity for a semilinear stochastic subdiffusion with integrated multiplicative noise Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-21 Ziqiang Li, Yubin Yan
We investigate a semilinear stochastic time-space fractional subdiffusion equation driven by fractionally integrated multiplicative noise. The equation involves the \(\psi \)-Caputo derivative of order \(\alpha \in (0,1)\) and the spectral fractional Laplacian of order \(\beta \in (\frac{1}{2},1]\). The existence and uniqueness of the mild solution are proved in a suitable Banach space by using the
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Topology optimization of stationary fluid–structure interaction problems considering a natural frequency constraint for vortex-induced vibrations attenuation Finite Elem. Anal. Des. (IF 3.1) Pub Date : 2024-02-23 L.O. Siqueira, K.E.S. Silva, E.C.N. Silva, R. Picelli
Topology optimization applied to fluid–structure interaction problems is challenging because the physical phenomenon in real engineering applications is usually transient and strongly coupled. This leads to costly solutions for the forward and adjoint problems, the computational bottleneck of the topology optimization method. Thus, this paper proposes a topology optimization problem formulated in the
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Small time asymptotics of the entropy of the heat kernel on a Riemannian manifold Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 2024-02-22 Vlado Menkovski, Jacobus W. Portegies, Mahefa Ratsisetraina Ravelonanosy
We give an asymptotic expansion of the relative entropy between the heat kernel of a compact Riemannian manifold and the normalized Riemannian volume for small values of and for a fixed element . We prove that coefficients in the expansion can be expressed as universal polynomials in the components of the curvature tensor and its covariant derivatives at , when they are expressed in terms of normal
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Asymptotic behavior for a porous-elastic system with fractional derivative-type internal dissipation Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-21 Wilson Oliveira, Sebastião Cordeiro, Carlos Alberto Raposo da Cunha, Octavio Vera
This work deals with the solution and asymptotic analysis for a porous-elastic system with internal damping of the fractional derivative type. We consider an augmented model. The energy function is presented and establishes the dissipativity property of the system. We use the semigroup theory. The existence and uniqueness of the solution are obtained by applying the well-known Lumer-Phillips Theorem
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Virtual Element Methods Without Extrinsic Stabilization SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-02-20 Chunyu Chen, Xuehai Huang, Huayi Wei
SIAM Journal on Numerical Analysis, Volume 62, Issue 1, Page 567-591, February 2024. Abstract. Virtual element methods (VEMs) without extrinsic stabilization in an arbitrary degree of polynomial are developed for second order elliptic problems, including a nonconforming VEM and a conforming VEM in arbitrary dimension. The key is to construct local [math]-conforming macro finite element spaces such
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The G-invariant graph Laplacian Part I: Convergence rate and eigendecomposition Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 2024-02-21 Eitan Rosen, Paulina Hoyos, Xiuyuan Cheng, Joe Kileel, Yoel Shkolnisky
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Variable bandwidth via Wilson bases Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 2024-02-21 Beatrice Andreolli, Karlheinz Gröchenig
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Existence of positive solutions for fractional delayed evolution equations of order $$\gamma \in (1,2)$$ via measure of non-compactness Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-02-20
Abstract The purpose of this paper is to consider the fractional delayed evolution equation of order \(\gamma \in (1,2)\) in ordered Banach space. In the absence of assumptions about the compactness of cosine families or related sine families, the existence results of positive solutions are studied by using some fixed point theorems and monotone iterative method under the conditions that nonlinear
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Semi-analytical solution for double-layered elliptical cylindrical foundation model improved by prefabricated vertical drains Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-02-15 Xudong Zhao, Nanning Guo, Wenzhao Cao, Wenhui Gong, Yang Liu
This work proposes a semi-analytical solution for a double-layered elliptical cylindrical soft foundation improved by prefabricated vertical drains. The governing equations, continuity conditions are boundary conditions in the elliptical cylindrical system are introduced first. The Laplace transform is employed to convert the time variable t in partial differential equations into the Laplace complex
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Rheological consolidation analysis of saturated clay ground under cyclic loading based on the fractional order Kelvin model Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-02-15 Lian Wang, Hui Chen, Shengwei Liu, Yunyan Yu
Based on Biot porous medium theory, considering the coupled reaction of soil skeleton rheology and pore pressure dissipation, the present work investigates the dynamic consolidation characteristics of saturated clay ground under cyclic loading. First, the rheological behavior of the soil skeleton was described by the fractional order Kelvin model. The dynamic consolidation governing equations for the
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Simplified method for evaluating tunnel response induced by a new tunnel excavation underneath Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-02-15 Guohui Feng, Changjie Xu, Zhi Ding, Luju Liang, Yujie Li, Minliang Chi
To estimate the tunnel response induced by a new tunnel excavation underneath, theoretical solutions are proposed in this study. The overlying tunnel is idealized as an infinite Timoshenko beam resting on the Kerr foundation model, then the vertical force balance equation is established. The unloading stress can be expressed as Fourier cosine series and a theoretical solution can be derived. The effectiveness
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A novel unresolved/semi-resolved CFD-DEM coupling method with dynamic unstructured mesh Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-02-15 Jin-Hui He, Ming-Guang Li, Jin-Jian Chen
The greatest challenge when performing large deformation simulations using the CFD-DEM coupling method lies in the dynamical update of the fluid meshes. To address this problem, a novel CFD-DEM coupling method integrated with the dynamic unstructured grid is proposed in this work. The mesh initialization and reconstruction are performed by the Constrained Delaunay triangulation (CDT) implemented by
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Slope stability analysis with a hypoplastic constitutive model: Investigating a stochastic anisotropy model and a hydro-mechanical coupled simulation Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-02-15 Yang Xue, Fasheng Miao, Shun Wang, Yang Tang, Yiping Wu, Daniel Dias
A reliable constitutive model is essential for accurately predicting slope deformation in numerical analysis, which includes assessing slope stability as an integral component. However, calculating slope stability in numerical models can be challenging due to complex boundary conditions and advanced constitutive models, especially when probabilistic and hydro-mechanical coupled simulations are required
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Block preconditioning strategies for generalized continuum models with micropolar and nonlocal damage formulations Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-02-20 Nasser Alkmim, Peter Gamnitzer, Matthias Neuner, Günter Hofstetter
In this work, preconditioning strategies are developed in the context of generalized continuum formulations used to regularize multifield models for simulating localized failure of quasi‐brittle materials. Specifically, a micropolar continuum extended by a nonlocal damage formulation is considered for regularizing both, shear dominated failure and tensile cracking. For such models, additional microrotation
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Analyzing cyclic shear behavior at the sand–rough concrete interface: An experimental and DEM study across varying displacement amplitudes Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-02-20 Shixun Zhang, Feiyu Liu, Weixiang Zeng, Mengjie Ying
Pile foundations frequently endure dynamic loads, necessitating an in‐depth examination of the cyclic shear properties at the pile–soil interface. This study involved a series of cyclic direct shear (CDS) tests conducted on sand and concrete with irregular surface, utilizing varying displacement amplitudes (1, 3, 6, and 10 mm) and joint roughness coefficients (0.4, 5.8, 9.5, 12.8, and 16.7). Discrete