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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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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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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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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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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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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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Estimates for $$p$$ -adic fractional integral operators and their commutators on $$p$$ -adic mixed central Morrey spaces and generalized mixed Morrey spaces Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-04-08 Naqash Sarfraz, Muhammad Aslam, Qasim Ali Malik
In this paper, we define the \(p\)-adic mixed Morrey type spaces and study the boundedness of \(p\)-adic fractional integral operators and their commutators on these spaces. More precisely, we first obtain the boundedness of \(p\)-adic fractional integral operators and their commutators on \(p\)-adic mixed central Morrey spaces. Moreover, we further extend these results on \(p\)-adic generalized mixed
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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
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Subordination results for a class of multi-term fractional Jeffreys-type equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-04-04 Emilia Bazhlekova
Jeffreys equation and its fractional generalizations provide extensions of the classical diffusive laws of Fourier and Fick for heat and particle transport. In this work, a class of multi-term time-fractional generalizations of the classical Jeffreys equation is studied. Restrictions on the parameters are derived, which ensure that the fundamental solution to the one-dimensional Cauchy problem is a
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Three‐dimensional stability analysis for a deep‐buried tunnel roof considering soil stratum strength nonlinearity Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-05 Jingshu Xu, Xinrui Wang, Ruotong Wang, Xiuli Du
A three‐dimensional (3D) collapse mechanism was employed in this work to investigate the roof stability of deep‐buried cylindrical tunnels in soil considering strength nonlinearity. Based on the kinematic approach of limit analysis, three tunnel roof stability measures, namely, the stability number, the required support pressure, and the factor of safety solutions were derived to provide quantitative
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Collage theorems, invertibility and fractal functions Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-04-03
Abstract Collage Theorem provides a bound for the distance between an element of a given space and a fixed point of a self-map on that space, in terms of the distance between the point and its image. We give in this paper some results of Collage type for Reich mutual contractions in b-metric and strong b-metric spaces. We give upper and lower bounds for this distance, in terms of the constants of the
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Research on calculation model for ultimate bearing capacity of tensile type anchor cables and the shape of internal fracture surface in anchorage segment Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-04 Qingyang Ren, Xin Meng, Bin Chen, Songqiang Xiao, Honghua Jin, Shan Mou, Zhongyao Li
The generalized model and parameter equation for the internal fracture surface of tensile type anchor cable anchorage section are constructed, and the calculation model of ultimate bearing capacity is derived based on the principle of limit equilibrium. The shape of the internal fracture surface in the anchorage section and the expression of its parameter equation are experimentally studied, and the
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An activation mechanism for cyclic degradation of clays in bounding surface plasticity Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-04 Francesca Palmieri, Mahdi Taiebat
During undrained cyclic loading, clayey soils experience substantial stiffness and strength degradation when subjected to shear amplitudes exceeding a critical threshold. This paper presents an enhanced bounding surface rate‐independent plasticity model, an evolution of the previous SANICLAY model, tailored to capture this specific behavior during cyclic loading. A distinguishing feature of the proposed
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Error bounds for kernel-based approximations of the Koopman operator Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 2024-04-04 Friedrich M. Philipp, Manuel Schaller, Karl Worthmann, Sebastian Peitz, Feliks Nüske
We consider the data-driven approximation of the Koopman operator for stochastic differential equations on reproducing kernel Hilbert spaces (RKHS). Our focus is on the estimation error if the data are collected from long-term ergodic simulations. We derive both an exact expression for the variance of the kernel cross-covariance operator, measured in the Hilbert-Schmidt norm, and probabilistic bounds
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A Posteriori Error Control for Fourth-Order Semilinear Problems with Quadratic Nonlinearity SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-04-03 Carsten Carstensen, Benedikt Gräßle, Neela Nataraj
SIAM Journal on Numerical Analysis, Volume 62, Issue 2, Page 919-945, April 2024. Abstract. A general a posteriori error analysis applies to five lowest-order finite element methods for two fourth-order semilinear problems with trilinear nonlinearity and a general source. A quasi-optimal smoother extends the source term to the discrete trial space and, more important, modifies the trilinear term in
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Monolithic and local time-stepping decoupled algorithms for transport problems in fractured porous media IMA J. Numer. Anal. (IF 2.1) Pub Date : 2024-04-03 Yanzhao Cao, Thi-Thao-Phuong Hoang, Phuoc-Toan Huynh
The objective of this paper is to develop efficient numerical algorithms for the linear advection-diffusion equation in fractured porous media. A reduced fracture model is considered where the fractures are treated as interfaces between subdomains and the interactions between the fractures and the surrounding porous medium are taken into account. The model is discretized by a backward Euler upwind-mixed
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Cut Finite Element Method for Divergence-Free Approximation of Incompressible Flow: A Lagrange Multiplier Approach SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-04-01 Erik Burman, Peter Hansbo, Mats Larson
SIAM Journal on Numerical Analysis, Volume 62, Issue 2, Page 893-918, April 2024. Abstract. In this note, we design a cut finite element method for a low order divergence-free element applied to a boundary value problem subject to Stokes’ equations. For the imposition of Dirichlet boundary conditions, we consider either Nitsche’s method or a stabilized Lagrange multiplier method. In both cases, the
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Stochastic assessment of 3‐D tunnels in near‐fault ground motion using modified domain reduction method Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-01 Bhavesh Banjare, Gauri Ranjan Krishna Chand Avatar
A robust assessment of tunnels due to uncertainties present in soil and ground motion properties can affect the dynamic response of these structures. In this paper, a stochastic analysis considering an aleatory variability in shear velocity Vs by performing Monte Carlo simulations and assessing its influence on underground tunnels. To numerically assess the response of the soil‐tunnel system to near‐fault
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Geotechnical analysis involving strain localization of overconsolidated soils based on unified hardening model with hardening variable updated by a composite scheme Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-04-01 Jianbin Tang, Xi Chen, Liusheng Cui, Zhe Xu, Guoqiang Liu
Strain localization simulation of overconsolidated soils with high overconsolidation ratio (OCR) has been a long‐standing challenge. Some critical state soil models, including the modified Cam‐clay (MCC) model, have been widely applied, but they may not predict the shear dilatancy of overconsolidated soils well in some cases. Hence, the unified hardening (UH) model, which may be viewed as a generalized
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Generalized Dimension Truncation Error Analysis for High-Dimensional Numerical Integration: Lognormal Setting and Beyond SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-03-28 Philipp A. Guth, Vesa Kaarnioja
SIAM Journal on Numerical Analysis, Volume 62, Issue 2, Page 872-892, April 2024. Abstract. Partial differential equations (PDEs) with uncertain or random inputs have been considered in many studies of uncertainty quantification. In forward uncertainty quantification, one is interested in analyzing the stochastic response of the PDE subject to input uncertainty, which usually involves solving high-dimensional
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Global existence for three-dimensional time-fractional Boussinesq-Coriolis equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-26 Jinyi Sun, Chunlan Liu, Minghua Yang
The paper is concerned with the three-dimensional Boussinesq-Coriolis equations with Caputo time-fractional derivatives. Specifically, by striking new balances between the dispersion effects of the Coriolis force and the smoothing effects of the Laplacian dissipation involving with a time-fractional evolution mechanism, we obtain the global existence of mild solutions to Cauchy problem of three-dimensional
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Transformations of the matrices of the fractional linear systems to their canonical stable forms Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-26 Tadeusz Kaczorek, Lukasz Sajewski
A new approach to the transformations of the matrices of the fractional linear systems with desired eigenvalues is proposed. Conditions for the existence of the solution to the transformation problem of the linear system to its asymptotically stable controllable and observable canonical forms with desired eigenvalues are given and illustrated by numerical examples of fractional linear systems.
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Some aspects of the contribution of Mkhitar Djrbashian to fractional calculus Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-26
Abstract This survey shows the way in which the Armenian mathematician Academician M.M. Djrbashian introduced the apparatus of fractional calculus in investigation of weighted classes and spaces of regular functions since his earliest work of 1945 (see [3, 4] or Addendum to [22]). The investigations of M.M. Djrbashian in this topic reached their final point by his exhaustive factorization theory for
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Relative controllability of linear state-delay fractional systems Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-25
Abstract In this paper, our focus is on exploring the relative controllability of systems governed by linear fractional differential equations incorporating state delay. We introduce a novel counterpart to the Cayley-Hamilton theorem. Leveraging a delayed perturbation of the Mittag-Leffler function, along with a determining function and an analog of the Cayley-Hamilton theorem, we establish an algebraic
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Theta-type convolution quadrature OSC method for nonlocal evolution equations arising in heat conduction with memory Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-25 Leijie Qiao, Wenlin Qiu, M. A. Zaky, A. S. Hendy
In this paper, we propose a robust and simple technique with efficient algorithmic implementation for numerically solving the nonlocal evolution problems. A theta-type (\(\theta \)-type) convolution quadrature rule is derived to approximate the nonlocal integral term in the problem under consideration, such that \(\theta \in (\frac{1}{2},1)\), which remains untreated in the literature. The proposed
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Diffusion equations with spatially dependent coefficients and fractal Cauer-type networks Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-22
Abstract In this article, we formulate and solve the representation problem for diffusion equations: giving a discretization of the Laplace transform of a diffusion equation under a space discretization over a space scale determined by an increment \(h>0\) , can we construct a continuous in h family of Cauer ladder networks whose constitutive equations match for all \(h>0\) the discretization. It is
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On the Approximability and Curse of Dimensionality of Certain Classes of High-Dimensional Functions SIAM J. Numer. Anal. (IF 2.9) Pub Date : 2024-03-22 Christian Rieger, Holger Wendland
SIAM Journal on Numerical Analysis, Volume 62, Issue 2, Page 842-871, April 2024. Abstract. In this paper, we study the approximability of high-dimensional functions that appear, for example, in the context of many body expansions and high-dimensional model representation. Such functions, though high-dimensional, can be represented as finite sums of lower-dimensional functions. We will derive sampling
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Peridynamic modeling of seepage in multiscale fractured rigid porous media Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-03-22 Zhuang Cai, Heng Zhang, Zhiyuan Li, Dan Huang
The numerical simulation of seepage in fractured porous media holds significant relevance for subsurface energy development. The presence of fractures at various scales profoundly influences the hydraulic properties of porous media during seepage. A peridynamic (PD)‐based frame is proposed for the seepage problem analysis of multiscale fractured porous media, in which micro‐fractures are implicitly
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Asymptotical stabilization of fuzzy semilinear dynamic systems involving the generalized Caputo fractional derivative for $$q \in (1,2)$$ Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-20 Truong Vinh An, Vasile Lupulescu, Ngo Van Hoa
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Rich phenomenology of the solutions in a fractional Duffing equation Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-20 Sara Hamaizia, Salvador Jiménez, M. Pilar Velasco
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Hydro‐mechanically coupled CEL analyses with effective contact stresses Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-03-20 Patrick Staubach
The coupled Eulerian–Lagrangian (CEL) method implemented in Abaqus is an established tool for modelling large deformations in numerical geomechanics. As shown in previous work, it can be extended to a hydro‐mechanically coupled scheme by exploiting the similarity of the heat balance equation to the mass balance equation of fluids. However, the distinction between effective and total contact stresses
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Sum of series and new relations for Mittag-Leffler functions Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2024-03-19 Sarah A. Deif, E. Capelas de Oliveira
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Multi‐porous extension of anisotropic poroelasticity: Linkage with micromechanics Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-03-19 Filip P. Adamus, David Healy, Philip G. Meredith, Thomas M. Mitchell
We attempt to formalise the relationship between the poroelasticity theory and the effective medium theory of micromechanics. The assumptions of these two approaches vary, but both can be linked by considering the undrained response of a material; and that is the main focus of the paper. To analyse the linkage between poroelasticity and micromechanics, we do not limit ourselves to the original theory
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Multi‐porous extension of anisotropic poroelasticity: Consolidation and related coefficients Int. J. Numer. Anal. Methods Geomech. (IF 4.0) Pub Date : 2024-03-19 Filip P. Adamus, David Healy, Philip G. Meredith, Thomas M. Mitchell, Ashley Stanton‐Yonge
We propose the generalization of the anisotropic poroelasticity theory. At a large scale, a medium is viewed as quasi‐static, which is the original assumption of Biot. At a smaller scale, we distinguish different sets of pores or fractures that are characterized by various fluid pressures, which is the original poroelastic extension of Aifantis. In consequence, both instantaneous and time‐dependent
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Frame set for Gabor systems with Haar window Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 2024-03-18 Xin-Rong Dai, Meng Zhu
We describe the full structure of the frame set for the Gabor system with the window being the Haar function . This is the first compactly supported window function for which the frame set is represented explicitly.
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Frame set for shifted sinc-function Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 2024-03-16 Yurii Belov, Andrei V. Semenov
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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