This paper investigates the interaction between layered saturated soft rock–soil mass and pile groups considering free‐standing length and rock‐socketed depth. The modeling of the identical pile is on the basis of one‐dimensional compression bar with a three‐node bar element. The global force balance equation for the pile group is then derived using the finite element method (FEM). Taking the existence

Sand‐rubber mixture (SRM), a composite material made of recycled rubber and sand, is gaining increasing attention in construction engineering due to its lightweight nature, cost‐effectiveness, ease of processing, and other advantages. However, the mechanical behavior of SRM remains a complex issue as the addition of rubber not only increases the types of contacts between grains, but also changes the

SIAM Journal on Numerical Analysis, Volume 63, Issue 3, Page 1209-1231, June 2025. Abstract. Transparent (or exact or nonreflecting) boundary conditions are essential to truncate infinite computational domains. Since transparent boundary conditions are usually nonlocal and expensive, they must be approximated. In this paper, we study such an approximation for the Helmholtz equation on an infinite strip

SIAM Journal on Numerical Analysis, Volume 63, Issue 3, Page 1183-1208, June 2025. Abstract. We study a high order absorbing boundary condition, the so-called complete radiation boundary condition (CRBC), for a time-harmonic electromagnetic wave propagation problem in a waveguide in [math]. The CRBC has been designed for an absorbing boundary condition for simulating wave propagations governed by the

Heat exchanger (HEX) design is an optimization process that seeks to maximize heat transfer between two fluids while minimizing pressure drops. There are several conceptual design methods based on integral equations that only work with specific temperature values at the inlet and outlet of the HEX. However, it is very interesting to obtain approximate temperature distributions in these early stages

This study proposes an optimization methodology to find optimal heat source paths for point-melting in Electron Beam Melting (EBM) Powder Bed Fusion (PBF) processes, aiming to reduce the need for support structures and improve print quality. The building process is simulated using a time-dependent, one-way coupled, non-linear thermo-mechanical model, assuming negligible molten flow, with elastoplastic

Concrete materials consist of multiple phases with distinct mechanical properties, making it essential to accurately identify the mechanical behavior of both constituent phases and their interfaces for effective multiscale modeling. This study estimates the elastic properties of the interfacial transition zone using a machine learning (ML) approach. A dataset is generated from numerical simulations

We consider a stable unique continuation problem for the wave equation that has been discretized so far using fairly sophisticated space-time methods. Here, we propose to solve this problem using a standard discontinuous Galerkin method for the temporal discretization. Error estimates are established under a geometric control condition. We also investigate two preconditioning strategies that can be

Unlike traditional finite element analysis, isogeometric analysis (IGA) employs the Non-Uniform Rational B-Splines (NURBS) basis functions in computer aided design (CAD) as the interpolation functions. Many researchers have shown great interest in applying isogeometric analysis to nonlinear Kirchhoff rod problems. However, most existing studies have overlooked the objectivity of isogeometric elements

We determine spatially varying discontinuous material properties using a domain-decomposition based physics-informed neural networks (PINNs) framework named the Adaptive Interface-PINNs or AdaI-PINNs (Roy et al., 2024). We propose the use of distinct neural networks for the field variables and material properties within each material, utilizing adaptive activation functions. While the neural networks

This study conducts a comprehensive numerical analysis to examine how the interphase zone influences the mechanical behavior of multiphase metal matrix composites at the microscale. A unit-cell model is developed within a finite element framework to capture the mechanical response of (a) interphase and particle deformation and damage, (b) a porous metal matrix, and (c) surface separation at two distinct

In this paper we propose and analyse a second-order accurate (in both time and space) numerical scheme for the Poisson–Nernst–Planck–Navier–Stokes system, which describes the ion electro-diffusion in fluids. In particular, the Poisson–Nernst–Planck (PNP) equation is reformulated as a nonconstant mobility gradient flow in the energetic variational approach. The marker and cell finite difference method

Miura surfaces are the solutions of a constrained nonlinear elliptic system of equations. This system is derived by homogenization from the Miura fold, which is a type of origami fold with multiple applications in engineering. A previous inquiry gave suboptimal conditions for existence of solutions and proposed an $H^{2}$-conformal finite element method to approximate them. In this paper the existence

An optimal design scheme is developed for treating collapsible loess foundation by the super down‐hole dynamic compaction method (SDDC) in terms of the loess foundation treatment project. This method involves the application of high‐energy impacts to the soil to achieve a compacting effect (CE), which is defined as the measurable improvement in soil density and reduction in its collapsibility. The

Owing to their dual role in utilizing geothermal energy and supporting structural loads, energy piles are affected by thermomechanical loads. Moreover, the heating/cooling of energy piles also causes non‐negligible thermal stresses in the soil around the piles. The load transfer method is commonly used to address the thermomechanical response of energy piles. However, this method has problems such

The effective stresses are found to continually increase for undrained cavity expansion in Mohr–Coulomb soils with unlimited dilation. This paper revisits this problem and presents a new solution with further consideration of limited soil dilation. The soil is modelled as a non‐associated Mohr–Coulomb model, and the limited dilation is controlled by the limited plastic volumetric strain, beyond which

This study proposes a three‐dimensional transformed differential quadrature solution for the thermo‐mechanical (TM) and thermo‐hydro‐mechanical (THM) coupling of transversely isotropic soils considering groundwater. Initially, the governing equations for TH coupling above the water table and THM coupling below the water table are introduced. Subsequently, two‐dimensional Fourier integral transform

This study presents a predictive method for process-induced deformation (PID) and residual stress in a V-shaped carbon fiber reinforced thermoplastic composite (CFRTP) using sequential thermoforming simulations within integrated thermo-mechanical simulation framework implemented in ABAQUS with user-defined materials subroutine (UMAT). The FE-based thermoforming simulation incorporates theoretical models

Concrete can show an increased material strength under dynamic loading conditions, which is related to the heterogeneity at the mesoscale, as well as the rate of loading. The ability to capture this phenomenon and predict behaviour under dynamic fracture propagation is of interest to different applications. High aspect ratio interface elements are developed here for mesoscale modelling of concrete

In recent years, a new class of mixed finite elements—compatible-strain mixed finite elements (CSMFEs)—has emerged that uses the differential complex of nonlinear elasticity. Their excellent performance in benchmark problems, such as numerical stability for modeling large deformations in near-incompressible solids, makes them a promising choice for solving engineering problems. Explicit forms exist

We establish the existence and uniqueness of a renormalized solution to an evolution equation featuring the non-local fractional p(x, y)-Laplacian and nonnegative \(L^1\)-data. The definition of renormalized solutions is adapted to the non-local nature to bypass the use of chain rules which is unavailable. The fractional p(x, y)-Laplacian well encapsulates the fractional p-Laplacian with a constant

Coupled nonlinear thermo‐hydro‐mechanical finite element simulations were carried out to investigate the behavior of energy micropiles subjected to thermal loading cycles. Two kinds of problems were analyzed: The case of an isolated micropile, for which comparison with previous research on medium‐size isolated energy pile is provided, and the case of large groups of micropiles, with the aim of investigating

Translatory bumps are becoming a major challenge in the excavation of coal seams. This study presents closed‐form solutions of stress and plastic zone width for translatory coal seam bumps within the framework of the Lippmann theory. The strength of coal seam taken as an elastic−perfectly plastic material and the friction force at the coal−rock interface are evaluated by the generalized effective stress

Geological applications of phase‐field methods for fracture are notably scarce. This work conducts a numerical examination of the applicability of standard phase‐field models in reproducing jointing within sedimentary layers. We explore how the volumetric‐deviatoric split alongside the AT1 and AT2 phase‐field formulations has several advantages in simulating jointing, but also has intrinsic limitations

The current study discusses the approximate solutions for a class of fractional stochastic integro-differential equation with short memory driven by non-instantaneous impulses (NIIs) defined on a separable Hilbert space. The approximation to the nonlinear functions is obtained using orthogonal projection operator. The existence and convergence of the sequence of approximate solutions is proved using

Over‐break and under‐break excavation is very common in practical tunnel engineering with asymmetrical cavity contour, while existing conformal mapping schemes of complex variable method generally focus on tunnelling with theoretical and symmetrical cavity contour. Besides, the solution strategies of existing conformal mapping schemes for non‐circular tunnel generally apply optimization theory and

The generalization capability of Graph Convolutional Networks (GCNs) has been researched recently. The generalization error bound based on algorithmic stability is obtained for various structures of GCN. However, the generalization error bound computed by this method increases rapidly during the iteration since the algorithmic stability exponential depends on the number of iterations, which is not

In this paper, we consider the long time behavior of solutions of the three dimensional (3D) generalized Navier-Stokes equations with damping. This family of 3D generalized Navier-Stokes equations with damping can be viewed as an interpolation model between subcritical (if \(\alpha >\frac{5}{4}\)), critical (if \(\alpha =\frac{5}{4}\)), and supercritical dissipations (if \(\alpha <\frac{5}{4}\)) and

In this study, the virtual element method (VEM) is utilized to address fine-to-coarse mesh transitions in phase-field fracture simulations for brittle, homogeneous media. The VEM discretization of the phase-field brittle damage equation is proposed, where the consistency and stability matrices of the damage sub-problem are derived by treating it as a general second-order linear elliptic equation. A

Geotextile‐encased stone columns (GESCs) for improving weak foundations commonly experience static and dynamic loads. However, the effectiveness of GESCs in resisting dynamic loading remains a concern. Three‐dimensional numerical models using a continuum‐discrete coupled method are developed to investigate the dynamic response of GESC groups in sand under sinusoidal loading. The models capture the

Bioinspired composite materials, such as nacre, achieve exceptional mechanical performance through the strategic arrangement of stiff and soft components. Inspired by this natural architecture, this study presents a novel finite element modeling framework for simulating staggered composites with finite-thickness interfaces. Combining continuum and cohesive elements, the model accurately captures tension-compression

SIAM Journal on Numerical Analysis, Volume 63, Issue 3, Page 1160-1182, June 2025. Abstract. We construct a structure preserving nonconforming finite element approximation scheme for the biharmonic wave maps into spheres equations. It satisfies a discrete energy law and preserves the nonconvex sphere constraint of the continuous problem. The discrete sphere constraint is enforced at the mesh-points

SIAM Journal on Numerical Analysis, Volume 63, Issue 3, Page 1128-1159, June 2025. Abstract. A long-standing and formidable challenge faced by all conservative numerical schemes for relativistic magnetohydrodynamics (RMHD) equations is the recovery of primitive variables from conservative ones. This process involves solving highly nonlinear equations subject to physical constraints. An ideal solver

The effects of surrounding soil degradation on the performance of piles during their operational phase remain inadequately understood within dynamic context. This study presents an energy‐based methodology for estimating the dynamic impedance of a single pile situated in radially weakened soil. To achieve this, the surrounding soil is segmented into discrete annular zones, wherein soil deformation

The present study develops a finite element‐based numerical method for simulation of frictional rotational sliding induced damage and heating effects on rock. The method is applied to the Sievers’ J‐ miniature drill test, which is widely used for estimating the rock drillability and predicting the cutter life. A continuum approach based on a damage‐viscoplastic model for rock failure is adopted. The

The application of stabilizing piles to increase slope stability is a common practice in slope engineering. Most related studies primarily focus on single‐row stabilizing piles; however, for large‐scale slopes, single‐row stabilizing piles may fail to meet the stability requirement, necessitating the use of double‐row or even multiple‐row stabilizing piles. Specifically, for large‐scale earth slopes

In this paper we devise and analyze a Banach-spaced mixed virtual element scheme for the steady motion of $\rho $-type Brinkman–Forchheimer equation with strongly symmetric stress. Our approach introduces stress and vorticity as additional variables, enabling the elimination of pressure from the original unknowns, which can later be recovered using a postprocessing formula based solely on the stress

This paper considers robust solutions to a class of nonlinear least squares problems using a min-max optimization approach. We give an explicit formula for the value function of the inner maximization problem and show the existence of global minimax points. We establish error bounds from any solution of the nonlinear least squares problem to the solution set of the robust nonlinear least squares problem

Inspired by the idea of ‘walk-on-sphere’ algorithm, we propose a novel finite-difference framework for solving the fractional Poisson equation under the help of the Feynman-Kac representation of its solution, i.e., walk-on-sphere-motivated finite-difference scheme. By choosing suitable basis functions in interpolatory quadrature and using graded meshes, the convergence rates can achieve up to $O(h^{2})$

Consider the interaction of biharmonic waves with a periodic array of cavities, characterized by the Kirchhoff–Love model. This paper investigates the perfectly matched layer (PML) formulation and its numerical solution to the governing biharmonic wave equation. The study establishes the well-posedness of the associated variational problem employing the Fredholm alternative theorem. Based on the examination

SIAM Journal on Numerical Analysis, Volume 63, Issue 3, Page 1105-1127, June 2025. Abstract. We propose a new stabilized finite element method for the classical Kolmogorov equation. The latter serves as a basic model problem for large classes of kinetic-type equations and, crucially, is characterized by degenerate diffusion. The stabilization is constructed so that the resulting method admits a numerical

SIAM Journal on Numerical Analysis, Volume 63, Issue 3, Page 1078-1104, June 2025. Abstract. This paper addresses the challenge of constructing finite element [math] complexes in three dimensions. Tangential-normal continuity is introduced in order to develop distributional finite element [math] complexes. The spaces constructed are applied to discretize the quad curl problem, demonstrating optimal

The dynamic characterization of structures using discrete models, as well as the application of modal superposition to compute their dynamic response, has been rarely explored in the literature. This is at odds with the international relevance of discrete models in structural assessment, and the multiple fields of application of modal analysis and superposition, from structural health monitoring to

Gradient-enhanced regularization is a frequently utilized method for addressing numerical issues in material modeling. As a consequence of the regularization scheme, Laplacian terms will emerge in the strong form of evolution equations for additional field variables, also called internal variables. In a series of previous works, the Neighbored Element Method (NEM) was presented as a combination of

This paper investigates the thermo‐mechanical effects of Euler–Bernoulli beams on layered transversely isotropic (TI) saturated subgrade due to moving loads. Firstly, the governing equations for the beam and subgrade are derived using Euler–Bernoulli beam theory, poroelastic mechanics, and thermoelasticity. Then, by adopting the extended precise integration solution for the layered TI saturated subgrade

This study introduces a novel family of exponential sampling type neural network Kantorovich operators, leveraging Hadamard fractional integrals to significantly enhance function approximation capabilities. By incorporating a flexible parameter \(\alpha \), derived from fractional Hadamard integrals, and utilizing exponential sampling, introduced to tackle exponentially sampled data, our operators

A novel computational cost-effective approach is presented for 2D elastic dynamic analysis by utilizing rotationally periodic symmetry. The proposed algorithm is developed on the platform of TPAA-SBFEM, integrating all its advantages. By recourse of TPAA, an elastic dynamic problem is converted into a series of recursive spatial problems which are solved by SBFEM. The block-circulant SBFEM global stiffness

SIAM Journal on Numerical Analysis, Volume 63, Issue 3, Page 1055-1077, June 2025. Abstract. We consider finite element methods of multiscale type to approximate solutions for two-dimensional symmetric elliptic partial differential equations with heterogeneous [math] coefficients. The methods are of Galerkin type and follow the Variational Multiscale and Localized Orthogonal Decomposition (LOD) approaches

Graph neural networks have achieved champions in wide applications. Neural message passing is a typical key module for feature propagation by aggregating neighboring features. In this work, we propose a new message passing based on multiscale framelet transforms, called Framelet Message Passing. Different from traditional spatial methods, it integrates framelet representation of neighbor nodes from

CO2 injection in the subsurface is considered an option to improve oil and gas production and, more recently, to store CO2. Consequently, there is a need to better understand the interactions between CO2 and rock deposits. Among the primary deposit candidates are carbonate rocks. During CO2 injection in the subsurface, the formation's pore structure and mechanical properties are altered by the interaction

This paper is devoted to exploring a new class of Hilfer fractional stochastic switched dynamical systems with the Rosenblatt process and abrupt changes, where the abrupt changes occur suddenly at specific points and extend over finite time intervals. Initially, we established solvability outcomes for the proposed switched dynamical systems by employing the fractional calculus, fixed point method,

In this paper, we study a multivariate version of the generalized counting process (GCP) and discuss its various time-changed variants. The time is changed using random processes such as the stable subordinator, inverse stable subordinator, and their composition, tempered stable subordinator, gamma subordinator etc. Several distributional properties that include the probability generating function

Recovering an unknown signal from quadratic measurements has gained popularity due to its wide range of applications, including phase retrieval, fusion frame phase retrieval, and positive operator-valued measures. In this paper, we employ a least squares approach to reconstruct the signal and establish its non-asymptotic statistical properties. Our analysis shows that the estimator perfectly recovers

SIAM Journal on Numerical Analysis, Volume 63, Issue 3, Page 1025-1054, June 2025. Abstract. In this paper, we apply quasi-Monte Carlo (QMC) methods with an initial preintegration step to estimate cumulative distribution functions and probability density functions in uncertainty quantification (UQ). The distribution and density functions correspond to a quantity of interest involving the solution to

This paper investigates the dynamic response of water‐saturated concrete under high stress levels, with a particular emphasis on the role of pore pressure. An enhanced elastoplastic damage model, incorporating dual plastic mechanisms, is proposed to capture the coupled hydromechanical behavior of concrete under combined high stress and high strain rate loading. Key improvements include the refinement

This paper aims to study the eigenvalue problems of a mixed local and nonlocal operator in the exterior of a nonempty, bounded, simply connected domain \(\varOmega \subset {\mathbb {R}}^N\) with Lipschitz boundary \(\partial \varOmega \ne \emptyset \). By employing the variational methods combined with the Ljusternik-Schnirelmann principle, we prove the existence of a non-decreasing sequence of eigenvalues

In this paper, we focus on a type of fractional nonlinear Schrödinger equation with odd periodic boundary conditions, where the nonlinearity periodically depending on spatial variable x. By an abstract KAM (Kolmogorov-Arnold-Moser) theorem for infinite dimensional reversible systems with unbounded perturbation, we obtain that there exists a lot of smooth quasi-periodic solutions with small amplitude

We deal with the boundary value problem $$\begin{aligned} {\left\{ \begin{array}{ll} (-\Delta )^s u(x)= \lambda f(u(x)), & x\in \Omega ,\\ u(x)=0, & x\in \mathbb {R}^N \setminus \Omega , \end{array}\right. } \end{aligned}$$ where \(\Omega \) is an open and bounded subset of \(\mathbb {R}^N\) with smooth boundary, \((-\Delta )^s\), \(s\in (0,1)\) denotes the fractional Laplacian, \(\lambda \ge 0\) and

The hypoplastic theory has gained significant attraction in the geomechanics community for constitutive modeling and numerical simulation. However, the absence of an analytical benchmark for numerical simulations incorporating the hypoplastic model remains a notable gap. This study revisits the basic hypoplastic model for normally consolidated soil, as proposed by Wu et al., by providing explicit formulations