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On variable-order fractional linear viscoelasticity Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-05-13 Andrea Giusti, Ivano Colombaro, Roberto Garra, Roberto Garrappa, Andrea Mentrelli
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Efficient function approximation in enriched approximation spaces IMA J. Numer. Anal. (IF 2.1) Pub Date : 2024-05-12 Astrid Herremans, Daan Huybrechs
An enriched approximation space is the span of a conventional basis with a few extra functions included, for example to capture known features of the solution to a computational problem. Adding functions to a basis makes it overcomplete and, consequently, the corresponding discretized approximation problem may require solving an ill-conditioned system. Recent research indicates that these systems can
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Well-posedness and stability of a fractional heat-conductor with fading memory Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-05-10 Sebti Kerbal, Nasser-eddine Tatar, Nasser Al-Salti
We consider a problem which describes the heat diffusion in a complex media with fading memory. The model involves a fractional time derivative of order between zero and one instead of the classical first order derivative. The model takes into account also the effect of a neutral delay. We discuss the existence and uniqueness of a mild solution as well as a classical solution. Then, we prove a Mittag-Leffler
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Generalized fractional derivatives generated by Dickman subordinator and related stochastic processes Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-05-10 Neha Gupta, Arun Kumar, Nikolai Leonenko, Jayme Vaz
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Error analysis for local discontinuous Galerkin semidiscretization of Richards’ equation IMA J. Numer. Anal. (IF 2.1) Pub Date : 2024-05-11 Scott Congreve, Vít Dolejší, Sunčica Sakić
This paper concerns an error analysis of the space semidiscrete scheme for the Richards’ equation modeling flows in variably saturated porous media. This nonlinear parabolic partial differential equation can degenerate; namely, we consider the case where the time derivative term can vanish, i.e., the fast-diffusion type of degeneracy. We discretize the Richards’ equation by the local discontinuous
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Variational data assimilation with finite-element discretization for second-order parabolic interface equation IMA J. Numer. Anal. (IF 2.1) Pub Date : 2024-05-11 Xuejian Li, Xiaoming He, Wei Gong, Craig C Douglas
In this paper, we propose and analyze a finite-element method of variational data assimilation for a second-order parabolic interface equation on a two-dimensional bounded domain. The Tikhonov regularization plays a key role in translating the data assimilation problem into an optimization problem. Then the existence, uniqueness and stability are analyzed for the solution of the optimization problem
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Implicit and Fully Discrete Approximation of the Supercooled Stefan Problem in the Presence of Blow-Ups SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-05-09 Christa Cuchiero, Christoph Reisinger, Stefan Rigger
SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1145-1170, June 2024. Abstract.We consider two approximation schemes of the one-dimensional supercooled Stefan problem and prove their convergence, even in the presence of finite time blow-ups. All proofs are based on a probabilistic reformulation recently considered in the literature. The first scheme is a version of the time-stepping scheme
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Existence and regularity of mild solutions to backward problem for nonlinear fractional super-diffusion equations in Banach spaces Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-05-06 Xuan X. Xi, Yong Zhou, Mimi Hou
In this paper, we study a class of backward problems for nonlinear fractional super-diffusion equations in Banach spaces. We consider the time fractional derivative in the sense of Caputo type. First, we establish some results for the existence of the mild solutions. Moreover, we obtain regularity results of the first order and fractional derivatives of mild solutions. These conclusions are mainly
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On the convergence of the Galerkin method for random fractional differential equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-05-06 Marc Jornet
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Asymptotic Compatibility of a Class of Numerical Schemes for a Nonlocal Traffic Flow Model SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-05-07 Kuang Huang, Qiang Du
SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1119-1144, June 2024. Abstract. This paper considers numerical discretization of a nonlocal conservation law modeling vehicular traffic flows involving nonlocal intervehicle interactions. The nonlocal model involves an integral over the range measured by a horizon parameter and it recovers the local Lighthill–Richards–Whitham model as the
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A linearly implicit finite element full-discretization scheme for SPDEs with nonglobally Lipschitz coefficients IMA J. Numer. Anal. (IF 2.1) Pub Date : 2024-05-08 Mengchao Wang, Xiaojie Wang
The present article deals with strong approximations of additive noise driven stochastic partial differential equations (SPDEs) with nonglobally Lipschitz nonlinearity in a bounded domain $ \mathcal{D} \in{\mathbb{R}}^{d}$, $ d \leq 3$. As the first contribution, we establish the well-posedness and regularity of the considered SPDEs in space dimension $d \le 3$, under more relaxed assumptions on the
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Stability of convergence rates: kernel interpolation on non-Lipschitz domains IMA J. Numer. Anal. (IF 2.1) Pub Date : 2024-05-08 Tizian Wenzel, Gabriele Santin, Bernard Haasdonk
Error estimates for kernel interpolation in Reproducing Kernel Hilbert Spaces usually assume quite restrictive properties on the shape of the domain, especially in the case of infinitely smooth kernels like the popular Gaussian kernel. In this paper we prove that it is possible to obtain convergence results (in the number of interpolation points) for kernel interpolation for arbitrary domains $\varOmega
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Kernel Interpolation of High Dimensional Scattered Data SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-05-06 Shao-Bo Lin, Xiangyu Chang, Xingping Sun
SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1098-1118, June 2024. Abstract. Data sites selected from modeling high-dimensional problems often appear scattered in nonpaternalistic ways. Except for sporadic-clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These features defy any theoretical treatment that requires local or global
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An Asymptotic Preserving Discontinuous Galerkin Method for a Linear Boltzmann Semiconductor Model SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-05-06 Victor P. DeCaria, Cory D. Hauck, Stefan R. Schnake
SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1067-1097, June 2024. Abstract. A key property of the linear Boltzmann semiconductor model is that as the collision frequency tends to infinity, the phase space density [math] converges to an isotropic function [math], called the drift-diffusion limit, where [math] is a Maxwellian and the physical density [math] satisfies a second-order parabolic
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A semi‐analytical model for coupled THM consolidation of saturated clays improved by PVTD considering thermal contraction Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-05-07 Yi Tian, Guosheng Jiang, Yue Gui, Minjie Wen, Guoxiong Mei, Wenbing Wu, Yi Zhang
Previous studies have demonstrated that saturated normally consolidated and lightly over‐consolidated clays undergo contraction when heated due to a reduction in preconsolidation pressure. A linear constitutive model is proposed to describe the thermal contraction, with this model, governing equations are developed for the coupled thermo‐hydro‐mechanical (THM) consolidation induced by a prefabricated
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Effect of soil layering and interface resistance on electro‐osmotic consolidation of layered soils: A Green's function approach Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-05-06 Zhang‐Long Chen, Jian‐Ping Li, Yun‐Shan Xu, Jun Liu, Shun Wang
During electro‐osmotic consolidation, effective voltage attenuation induced by the increasing interface resistance is an important phenomenon, which significantly decreases consolidation effectiveness. This paper presents an analytical model for one‐dimensional electro‐osmotic consolidation in layered soils with horizontal graphite electrodes considering effective voltage attenuation. The mathematical
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A certified wavelet-based physics-informed neural network for the solution of parameterized partial differential equations IMA J. Numer. Anal. (IF 2.1) Pub Date : 2024-05-05 Lewin Ernst, Karsten Urban
Physics Informed Neural Networks (PINNs) have frequently been used for the numerical approximation of Partial Differential Equations (PDEs). The goal of this paper is to construct PINNs along with a computable upper bound of the error, which is particularly relevant for model reduction of Parameterized PDEs (PPDEs). To this end, we suggest to use a weighted sum of expansion coefficients of the residual
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Strong convergence of adaptive time-stepping schemes for the stochastic Allen–Cahn equation IMA J. Numer. Anal. (IF 2.1) Pub Date : 2024-05-05 Chuchu Chen, Tonghe Dang, Jialin Hong
It is known from Beccari et al. (2019) that the standard explicit Euler-type scheme (such as the exponential Euler and the linear-implicit Euler schemes) with a uniform timestep, though computationally efficient, may diverge for the stochastic Allen–Cahn equation. To overcome the divergence, this paper proposes and analyzes adaptive time-stepping schemes, which adapt the timestep at each iteration
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A Novel Mixed Spectral Method and Error Estimates for Maxwell Transmission Eigenvalue Problems SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-05-03 Jing An, Waixiang Cao, Zhimin Zhang
SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1039-1066, June 2024. Abstract. In this paper, a novel mixed spectral-Galerkin method is proposed and studied for a Maxwell transmission eigenvalue problem in a spherical domain. The method utilizes vector spherical harmonics to achieve dimension reduction. By introducing an auxiliary vector function, the original problem is rewritten as
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Gain Coefficients for Scrambled Halton Points SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-05-02 Art B. Owen, Zexin Pan
SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1021-1038, June 2024. Abstract. Randomized quasi-Monte Carlo, via certain scramblings of digital nets, produces unbiased estimates of [math] with a variance that is [math] for any [math]. It also satisfies some nonasymptotic bounds where the variance is no larger than some [math] times the ordinary Monte Carlo variance. For scrambled Sobol’
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Modeling dynamic crack branching in unsaturated porous media through multi‐phase micro‐periporomechanics Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-05-03 Hossein Pashazad, Xiaoyu Song
Dynamic crack branching in unsaturated porous media holds significant relevance in various fields, including geotechnical engineering, geosciences, and petroleum engineering. This article presents a numerical investigation into dynamic crack branching in unsaturated porous media using a recently developed coupled micro‐periporomechanics (PPM) paradigm. This paradigm extends the PPM model by incorporating
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A framework for estimating the matric suction in unsaturated soils using multiple artificial intelligence techniques Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-05-03 Junjie Wang, Sai Vanapalli
Implementation of the state‐of‐the‐art understanding of the mechanics of unsaturated soils into geotechnical engineering practice is partly limited due to the lack of quick, reliable, and economical techniques for matric suction measurement. Matric suction is one of the key stress state variables that significantly influences the hydro‐mechanical behavior of unsaturated soils. In this paper, to address
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Hopf’s lemma and radial symmetry for the Logarithmic Laplacian problem Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-05-03 Lihong Zhang, Xiaofeng Nie
In this paper, we prove Hopf’s lemma for the Logarithmic Laplacian. At first, we introduce the strong minimum principle. Then Hopf’s lemma for the Logarithmic Laplacian in the ball is proved. On this basis, Hopf’s lemma of the Logarithmic Laplacian is extended to any open set with the property of the interior ball. Finally, an example is given to explain Hopf’s lemma can be applied to the study of
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Non-confluence of fractional stochastic differential equations driven by Lévy process Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-05-03 Zhi Li, Tianquan Feng, Liping Xu
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Modified SANISAND‐F model for simple shear path Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-30 Xingbo Huang, Yifei Sun, Chenglong Gu
Simple shear behavior of sand is representative in geotechnical engineering with potential failure occurred along a thin shear zone. The strength and deformation of sand under simple shear are accompanied with principal stress rotation (PSR). This study proposes a modified SANISAND‐F model to capture the simple shear behavior of sand with PSR. A new plastic flow rule along with a kinematic hardening
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The mechanism of granite breaking by electric pulse under high temperature and high pressure environment Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-29 Weiji Liu, Xin Zhou, Xiaohua Zhu
High‐voltage electric pulse drilling technology has the advantages of high rock‐breaking efficiency, and low rock‐breaking energy consumption, which is one of the most promising rock‐breaking methods in geothermal drilling. However, there is insufficient understanding of the mechanism of high‐voltage electric pulse breaking of HDR under high‐temperature and high‐pressure environments (HTHP). In this
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Application of subordination principle to coefficient inverse problem for multi-term time-fractional wave equation Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-04-29 Emilia Bazhlekova
An initial-boundary value problem for the multi-term time-fractional wave equation on a bounded domain is considered. For the largest and smallest orders of the involved Caputo fractional time-derivatives, \(\alpha \) and \(\alpha _m\), it is assumed \(1<\alpha <2\) and \(\alpha -\alpha _m\le 1\). Subordination principle with respect to the corresponding single-term time-fractional wave equation of
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Finite element methods for multicomponent convection-diffusion IMA J. Numer. Anal. (IF 2.1) Pub Date : 2024-04-28 Francis R A Aznaran, Patrick E Farrell, Charles W Monroe, Alexander J Van-Brunt
We develop finite element methods for coupling the steady-state Onsager–Stefan–Maxwell (OSM) equations to compressible Stokes flow. These equations describe multicomponent flow at low Reynolds number, where a mixture of different chemical species within a common thermodynamic phase is transported by convection and molecular diffusion. Developing a variational formulation for discretizing these equations
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m‐AGC tangent visco‐plastic operator with hardening/softening, and application to the visco‐plastic relaxation analysis of stable and unstable problems using fracture‐based geomechanical interfaces Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-27 Irene Jaqués, Ignacio Carol
A previous perfect visco‐plastic constitutive formulation of the Perzyna type incorporating the concepts of prescribed stress increments and m‐AGC tangent operator (m‐Assumed algorithmic generalized compliance tangent operator) is extended to the case of Hardening/Softening (H/S). This extension is possible thanks to the closed‐form solution developed for the evolution of the loading function during
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A fractional Darcian model‐based analytical solution for non‐Darcian flow toward a fully penetrating well in a confined aquifer Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-25 Kun Tu, Qiang Wu, Hongwei Zhang, Xiang Li
The Forchheimer and Izbash equations have been long employed to investigate the behavior of non‐Darcian flow toward a well in various aquifer systems, but both two equations inevitably introduce problems such as more or less empirical nature, and dimensional unbalance. Therefore, this work makes the attempt to introduce the fractional Darcian model for characterizing the non‐Darcian behavior flow toward
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Performance analysis of multilayered transversely isotropic saturated media under temperature and horizontally circular loads Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-24 Wei Yong Feng, Zhi Yong Ai
This study constructs a multilayered transversely isotropic saturated model under thermal and horizontally circular loads, and further investigates the model's thermo‐hydro‐mechanical coupling response. Firstly, the ordinary differential matrix equations of thermoelastic saturated media in the integral transformed domain are derived. Secondly, the solution for multilayered thermoelastic saturated media
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Transversely isotropic effects on the coupled thermo‐hydro‐mechanical performance for layered saturated media Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-24 Yong Zhi Zhao, Zhenming Shi, Zhi Yong Ai
In this manuscript, a novel transformed differential quadrature solution to the coupled thermo‐hydro‐mechanical (THM) problem of layered transversely isotropic (TI) saturated media is proposed, accompanied by a sensitivity analysis of pertinent parameters. Initially, the THM governing equations that encompass the transverse isotropy characteristics of thermal, permeable, and mechanical properties are
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Numerical investigation on the influence of secondary flaw lengths on the mechanical characteristics and cracking behaviour of red sandstone containing orthogonal cross flaws Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-24 Rongchao Xu, Baoyang Dou, Ying Zhao, Wenbin Peng, Zhen Li
Flaw length has a significant effect on the cracking behaviour of fractured rock. PFC2D was used to simulate the uniaxial compression of red sandstone samples with secondary flaw lengths L2 of 0 mm, 5 mm, 10 mm, 15 and 20 mm under different primary flaw angles α(α = 0°, 15°, 30°, 45°, 60°, 75°, and 90°). Based on the simulation results, the effects of the secondary flaw length on the mechanical parameters
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Semi‐implicit material point method for simulating infiltration‐induced failure of unsaturated soil structures Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-24 Soma Hidano, Yuya Yamaguchi, Shinsuke Takase, Shuji Moriguchi, Kenji Kaneko, Kenjiro Terada
This study presents a semi‐implicit MPM to adequately characterize the mechanical behavior of unsaturated soil based on Biot's mixture theory. To represent the dependency of the degree of saturation on the suction, we employ the VG model along with a soil‐water characteristic curve, which determines a functional form of permeability called the Mualem model. Hencky's hyperelastic model and the Drucker‐Prager
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Analysis of laterally loaded floating piles using a refined Tajimi model Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-24 Changjie Zheng, George Kouretzis, Xuanming Ding
This paper presents a novel mathematical model for the analysis of laterally loaded floating piles embedded in a homogeneous soil layer of finite thickness. The governing equations of the soil surrounding the pile are established by treating soil as a Tajimi‐type continuum, and their solution yields a closed‐form expression that provides the lateral force developing to resist pile deflection. Accordingly
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A coupled finite difference‐spectral boundary integral method with applications to fluid diffusion in fault structures Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-24 Yuhan Wang, Elías Rafn Heimisson
Fluid migration in geological materials, a subject of great interest in various geophysical applications, has been interpreted through multiple numerical methods. Taking advantage of both a volume‐based method and a boundary integral method, we innovate a hybrid spectral‐boundary‐integral and finite‐difference method (SBI‐FDM) to describe the fluid injection and propagation in the fault structure.
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Numerical modelling of thermal jet assisted rock cutting with double PDC cutters Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-24 Timo Saksala
Preconditioning of rock for drilling operations is a potential method to facilitate the mechanical breakage and mitigate the tool wear. This paper numerically investigates one such preconditioning technique, namely, the thermal jet assisted rock cutting. For this end, a numerical method for solving the governing thermo‐mechanical problem is developed and validated. The continuum approach is chosen
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A Two-Level Block Preconditioned Jacobi–Davidson Method for Multiple and Clustered Eigenvalues of Elliptic Operators SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-04-22 Qigang Liang, Wei Wang, Xuejun Xu
SIAM Journal on Numerical Analysis, Volume 62, Issue 2, Page 998-1019, April 2024. Abstract. In this paper, we propose a two-level block preconditioned Jacobi–Davidson (BPJD) method for efficiently solving discrete eigenvalue problems resulting from finite element approximations of [math]th ([math]) order symmetric elliptic eigenvalue problems. Our method works effectively to compute the first several
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A general analytical solution for axisymmetric electro‐osmotic consolidation of unsaturated soil with semi‐permeable boundary Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-18 Xudong Zhao, Junjun Ni, Yang Liu, Wenhui Gong
This study proposes a closed‐form solution for axisymmetric electro‐osmotic consolidation of unsaturated soil under semi‐permeable boundary conditions. The governing equations are formulated to allow for vertical and radial flows of liquid and air phases. The techniques of eigenfunction expansion and Laplace transformation are employed to develop the exact solution for excess pore‐air (EPAP) and pore‐water
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Monotone iterative technique for multi-term time fractional measure differential equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-04-17 Haide Gou, Min Shi
In this paper, we investigate the existence and uniqueness of the S-asymptotically \(\omega \)-periodic mild solutions to a class of multi-term time-fractional measure differential equations with nonlocal conditions in an ordered Banach spaces. Firstly, we look for suitable concept of S-asymptotically \(\omega \)-periodic mild solution to our concern problem, by means of Laplace transform and \((\beta
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The mystery of Carleson frames Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 2024-04-17 Ole Christensen, Marzieh Hasannasab, Friedrich M. Philipp, Diana Stoeva
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Effectiveness of the tail-atomic norm in gridless spectrum estimation Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 2024-04-16 Wei Li, Shidong Li, Jun Xian
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An integrated EOS, pore‐crush, strength and damage model framework for near‐field ground‐shock Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-15 Kane C. Bennett, Alyson M. Stahl, Thomas R. Canfield, Garrett G. Euler
An integrated Equation of State (EOS) and strength/pore‐crush/damage model framework is provided for modeling near to source (near‐field) ground‐shock response, where large deformations and pressures necessitate coupling EOS with pressure‐dependent plastic yield and damage. Nonlinear pressure‐dependence of strength up to high‐pressures is combined with a Modified Cam‐Clay‐like cap‐plasticity model
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Probabilistic assessment of existing shield tunnel longitudinal responses to tunnelling Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-12 Rongzhu Liang, Zhiwei Zhang, Jin Wu, Zhongchao Li, Shian Cao, Wenbing Wu
This paper proposes a probabilistic‐based framework to assess the failure probability of the existing shield tunnel owing to undercrossing tunnelling. A novel deterministic model using the two‐phase analysis method is presented to evaluate the longitudinal behaviours of the in‐service shield tunnel. First, the tunnelling‐induced settlement is estimated using the Loganathan and Poulos’ method; second
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Large‐strain consolidation of vacuum preloading combined with partially penetrating prefabricated vertical drains Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-12 Wei Guo, You Zhou, Liqiang Sun, Huihuang Jiang, Ruiqing Lang, Hao Chen, Yuxiao Ren
A system of vacuum preloading combined with partially penetrating prefabricated vertical drains (PP‐PVDs) is an effective solution for promoting the consolidation of the dredged marine clay. However, a significant and traditionally challenging‐to‐predict amount of deformation or settlement occurs. Therefore, it is necessary to introduce a three‐dimensional large‐strain consolidation model to consider
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A bi‐fidelity inverse analysis method for deep excavations considering three‐dimensional effects Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-12 Yuanqin Tao, Sunjuexu Pan, Honglei Sun, Yuanqiang Cai, Ge Zhang, Miaojun Sun
Inverse analysis methods are commonly used in braced excavations for improved deformation predictions. This paper proposes a bi‐fidelity ensemble randomized maximum likelihood (BF‐EnRML) method for efficient inverse analyses of deep excavations considering the three‐dimensional effects. The bi‐fidelity (BF) model is developed by the low‐fidelity model (i.e., two‐dimensional finite element model, 2D
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An explicit spectral Fletcher–Reeves conjugate gradient method for bi-criteria optimization IMA J. Numer. Anal. (IF 2.1) Pub Date : 2024-04-12 Y Elboulqe, M El Maghri
In this paper, we propose a spectral Fletcher–Reeves conjugate gradient-like method for solving unconstrained bi-criteria minimization problems without using any technique of scalarization. We suggest an explicit formulae for computing a descent direction common to both criteria. The latter further verifies a sufficient descent property that does not depend on the line search nor on any convexity assumption
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A novel stability equation for the estimation of the factor of safety for homogeneous dry finite slopes Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-11 Naloan Coutinho Sampa, Joshua Schorr
This paper introduces a novel closed‐form equation (surrogate model) for approximating the Morgenstern–Price estimate of the factor of safety of homogeneous dry finite slopes with circular failure surfaces. Unlike typically used methods, the proposed equation does not require the definition of a critical failure surface, splitting the soil mass into slices, or the iterative reduction of soil resistance
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Study on the formation mechanism and preventive measure of pot cover effect for subgrade in seasonal frozen soil area under freeze–thaw cycles Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-10 Ruiling Zhang, Yaling Chou, Mingli Zhang, Hongbo Liu
The presence of an impervious cover layer inhibits the free evaporation of moisture in the soil during seasonal freeze–thaw cycles, leading to a phenomenon known as the pot cover effect. This can result in severe frost heave issues in airport runways, highway subgrades, railway subgrades, and other similar infrastructure. In this study, a disease investigation was conducted at a gas transmission station
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Variability and loss of uniqueness of numerical solutions in FEM×DEM modeling with second gradient enhancement Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-10 Trung‐Kien Nguyen, Thanh‐Trung Vo, Nhu H. T. Nguyen, Gaël Combe
In the last decade, a new multi‐scale FEM×DEM approach has been developed using Finite Element Method (FEM) coupled with Discrete Element Method (DEM) as a constitutive law to account for the specificities of the mechanical behavior of granular materials. In FEM×DEM model, a DEM calculation is performed on a particle assembly (volume element—VE) at each Gauss point. Recent publications have demonstrated
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On the rate of convergence of Yosida approximation for the nonlocal Cahn–Hilliard equation IMA J. Numer. Anal. (IF 2.1) Pub Date : 2024-04-10 Piotr Gwiazda, Jakub Skrzeczkowski, Lara Trussardi
It is well-known that one can construct solutions to the nonlocal Cahn–Hilliard equation with singular potentials via Yosida approximation with parameter $\lambda \to 0$. The usual method is based on compactness arguments and does not provide any rate of convergence. Here, we fill the gap and we obtain an explicit convergence rate $\sqrt{\lambda }$. The proof is based on the theory of maximal monotone
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Singularity Swapping Method for Nearly Singular Integrals Based on Trapezoidal Rule SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-04-08 Gang Bao, Wenmao Hua, Jun Lai, Jinrui Zhang
SIAM Journal on Numerical Analysis, Volume 62, Issue 2, Page 974-997, April 2024. Abstract. Accurate evaluation of nearly singular integrals plays an important role in many boundary integral equation based numerical methods. In this paper, we propose a variant of singularity swapping method to accurately evaluate the layer potentials for arbitrarily close targets. Our method is based on the global
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Sequential Discretization Schemes for a Class of Stochastic Differential Equations and their Application to Bayesian Filtering SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-04-08 Ö. Deniz Akyildiz, Dan Crisan, Joaquin Miguez
SIAM Journal on Numerical Analysis, Volume 62, Issue 2, Page 946-973, April 2024. Abstract. We introduce a predictor-corrector discretization scheme for the numerical integration of a class of stochastic differential equations and prove that it converges with weak order 1.0. The key feature of the new scheme is that it builds up sequentially (and recursively) in the dimension of the state space of
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A tempered subdiffusive Black–Scholes model Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-04-09 Grzegorz Krzyżanowski, Marcin Magdziarz
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Nonnegative solutions of a coupled k-Hessian system involving different fractional Laplacians Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-04-09 Lihong Zhang, Qi Liu, Bashir Ahmad, Guotao Wang
This paper studies the following coupled k-Hessian system with different order fractional Laplacian operators: $$\begin{aligned} {\left\{ \begin{array}{ll} {S_k}({D^2}w(x))-A(x)(-\varDelta )^{\alpha /2}w(x)=f(z(x)),\\ {S_k}({D^2}z(x))-B(x)(-\varDelta )^{\beta /2}z(x)=g(w(x)). \end{array}\right. } \end{aligned}$$ Firstly, we discuss decay at infinity principle and narrow region principle for the k-Hessian
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Numerical modelling of diaphragm wall construction Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-08 Maria Kmeid, Géraldine Casaux‐Ginestet, Gilles Escadeillas, Julie Armengaud
Diaphragm walls are rectangular shaped cast in place deep foundations. There are two critical phenomena occurring, according to which the final quality can be affected: bentonite suspension exfiltration and concrete placement. Some imperfections seem to appear recurrently on the surface of the final wall. The defects are known as shadowing pathologies. The main reasons can be attributed to the dual
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Mapped material point method for large deformation problems with sharp gradients and its application to soil‐structure interactions Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-08 Yidong Zhao, Minchen Li, Chenfanfu Jiang, Jinhyun Choo
The material point method (MPM) is often applied to large deformation problems that involve sharp gradients in the solution field. Representative examples in geomechanics are interactions between soils and various “structures” such as foundations, penetrometers, and machines, where the displacement fields exhibit sharp gradients around the soil‐structure interfaces. Such sharp gradients should be captured