SIAM Journal on Numerical Analysis, Volume 62, Issue 5, Page 2172-2195, October 2024. Abstract. A novel evolving surface finite element method, based on a novel equivalent formulation of the continuous problem, is proposed for computing the evolution of a closed hypersurface moving under a prescribed velocity field in two- and three-dimensional spaces. The method improves the mesh quality of the approximate

Adsorption characteristics play a crucial role in solute transport processes, serving as a fundamental factor for evaluating the performance of clay liners. Nonlinear adsorption isotherms are commonly found with metal ions and organic compounds, which introduce challenges in obtaining analytical solutions for solute transport models. In this study, analytical solutions are proposed for a fully coupled

Residual stresses and shakedown have been successfully presented by two‐dimensional numerical experiments based on the discrete element method (DEM), wherein a cohesionless‐frictional material under moving surface loads was replicated through irregular‐shaped particles. With surface loads below the shakedown limit, both permanent deformations and residual stresses cease to accumulate and the numerical

This paper proposes a simplified analytical solution for longitudinal seismic responses of a circular tunnel crossing a fault zone under longitudinally propagating shear waves. The transmissions and reflections of shear waves at two geological interfaces between the fault zone and intact rock are considered when calculating the free‐field displacement. An improved elastic foundation beam model considering

Sand columns have been widely used to accelerate drainage and then improving the mechanical properties of soft soil foundations. The sand column has also been introduced into the triaxial test by researchers, in the center of the cylindrical specimen, to greatly accelerate drainage and consolidation process. The objective of this paper is to evaluate the consolidation properties of the triaxial cylindrical

Expansive soils are widespread in the world and coincide with areas of high human activity. The main cause of deep instability of expansive soil slopes is due to their softening caused by excavation and seepage. By developing a comprehensive numerical model based on the theory of unsaturated soil, this study examines the characteristics of stress and displacement distribution of expansive soil slopes

In this paper, we study a class of non-autonomous lower critical fractional Choquard equation with a pure-power nonlinear perturbation. Under some reasonable assumptions on the potential function h, we prove the existence and discuss asymptotic behavior of ground state solutions for our problem. Meanwhile, we also prove that the number of normalized solutions is at least the number of global maximum

In this paper, we consider the following Schrödinger system involving the tempered fractional p-Laplacian $$\begin{aligned} {\left\{ \begin{array}{ll} \begin{aligned} & (-\varDelta -\lambda )^s_p u(x)+au^{p-1}(x)=f(u(x),v(x)),\\ & (-\varDelta -\lambda )^t_p v(x)+bv^{p-1}(x)=g(u(x),v(x)), \end{aligned} \end{array}\right. } \end{aligned}$$ where \(n \ge 2\), \(a, b>0\), \(2

We study a nonlinear, nonlocal Dirichlet problem driven by the fractional p-Laplacian, involving a \((p-1)\)-sublinear reaction. By means of a weak comparison principle we prove uniqueness of the solution. Also, comparing the problem to ’asymptotic’ weighted eigenvalue problems for the same operator, we prove a necessary and sufficient condition for the existence of a solution. Our work extends classical

This work comprehensively investigates key parameters associated with a recently proposed non-intrusive coupling strategy for multiscale structural problems. The IGL-GFEM combines the Iterative Global Local Method and the Generalized Finite Element Method with global–local enrichment, GFEM. Different scales of the problem are solved using distinct finite element codes: the commercial software Abaqus

A filtered Lie splitting scheme is proposed for the time integration of the cubic nonlinear Schrödinger equation on the two-dimensional torus $\mathbb{T}^{2}$. The scheme is analysed in a framework of discrete Bourgain spaces, which allows us to consider initial data with low regularity; more precisely initial data in $H^{s}(\mathbb{T}^{2})$ with $s>0$. In this way, the usual stability restriction

This survey aims to present various approaches to non-integer integrals and derivatives and their practical implementation within Wolfram Mathematica. It begins by short discussion of historical moments and applications related to fractional calculus. Different methods for handling non-integer powers of differentiation operators are presented, along with generalizations of fractional integrals and

SIAM Journal on Numerical Analysis, Volume 62, Issue 5, Page 2143-2171, October 2024. Abstract. The coupling of nonconservative hyperbolic systems at a static interface has been a delicate issue as common approaches rely on the Lax-curves of the systems, which are not always available. To address this a new linear relaxation system is introduced, in which a nonlocal source term accounts for the nonconservative

SIAM Journal on Numerical Analysis, Volume 62, Issue 5, Page 2121-2142, October 2024. Abstract. This paper studies the discretization of a homogenization and dimension reduction model for the elastic deformation of microstructured thin plates proposed by Hornung, Neukamm, and Velčić [Calc. Var. Partial Differential Equations, 51 (2014), pp. 677–699]. Thereby, a nonlinear bending energy is based on

Several methods have been developed to model the dynamic behavior of saturated porous media. However, most of them are suitable only for small strain and small displacement problems and are built in a monolithic way, so that individual improvements in the solution of the solid or fluid phases can be difficult. This study shows a macroscopic approach through a partitioned fluid–solid coupling, in which

Deep energy method (DEM) has shown its successes to solve several problems in solid mechanics recently. It is known that determining proper integration scheme to precisely calculate total potential energy (TPE) value is crucial to achieve high-quality training performance of DEM but it has not been discovered satisfactorily in previous related works. To shed light on this matter, this study focuses

In this paper, we investigate the non-confluence property of a class of stochastic differential equations with Markovian switching driven by fractional Brownian motion with Hurst parameter \(H\in (1/2,1)\). By using the generalized Itô formula and stopping time techniques, we obtain some sufficient conditions ensuring the non-confluence property for the considered equations. Additionally, we present

This paper presents a mini immersed finite element (IFE) method for solving two- and three-dimensional two-phase Stokes problems on Cartesian meshes. The IFE space is constructed from the conventional mini element, with shape functions modified on interface elements according to interface jump conditions while keeping the degrees of freedom unchanged. Both discontinuous viscosity coefficients and surface

In this paper, we introduce the concept of Stepanov-like (weighted) pseudo S-asymptotically Bloch type periodic processes in the square mean sense, and establish some basic results on the function space of such processes like completeness, convolution and composition theorems. Under the situation that the functions forcing are Stepanov-like (weighted) pseudo S-asymptotically Bloch type periodic and

The generalized translation invariant (GTI) systems unify the discrete frame theory of generalized shift-invariant systems with its continuous version, such as wavelets, shearlets, Gabor transforms, and others. This article provides sufficient conditions to construct pairwise orthogonal Parseval GTI frames in satisfying the local integrability condition (LIC) and having the Calderón sum one, where

SIAM Journal on Numerical Analysis, Volume 62, Issue 5, Page 2087-2120, October 2024. Abstract. Along with the practical success of the discovery of dynamics using deep learning, the theoretical analysis of this approach has attracted increasing attention. Prior works have established the grid error estimation with auxiliary conditions for the discovery of dynamics using linear multistep methods and

In this paper, we introduce and analyze a Banach spaces-based approach yielding a fully-mixed finite element method for numerically solving the coupled poroelasticity and heat equations, which describe the interaction between the fields of deformation and temperature. A nonsymmetric pseudostress tensor is utilized to redefine the constitutive equation for the total stress, which is an extension of

SIAM Journal on Numerical Analysis, Volume 62, Issue 5, Page 2071-2086, October 2024. Abstract. For the numerical solution of the cubic nonlinear Schrödinger equation with periodic boundary conditions, a pseudospectral method in space combined with a filtered Lie splitting scheme in time is considered. This scheme is shown to converge even for initial data with very low regularity. In particular, for

This paper presents a Chimera approach for the thermal problems in welding and metallic Additive Manufacturing (AM). In particular, a moving mesh is attached to the moving heat source while a fixed background mesh covers the rest of the computational domain. The thermal field of the moving mesh is solved in the heat source reference frame. The chosen framework to couple the solutions on both meshes

The large deformation and fluidization process of a solid–fluid mixture includes significant changes to the temporal scale of the phenomena and the shape and properties of the mixed material. This paper presents an extended B‐spline (EBS)‐based implicit material point method (EBS‐MPM) for the coupled hydromechanical analysis of saturated porous media to enhance the overall versatility of MPM in addressing

The effect of cyclic loading is an essential factor leading to progressive soil strength degradation. Therefore, a comprehensive analysis of the pile‐soil system behavior under cyclic loading is required to ensure the stability of pile group. There is room for improvement in the inherent constraint of the conventional numerical model in terms of approximating the soil resistance distribution along

A novel approach for the solution of linear elasticity problems is introduced in this communication, which uses a hybrid chimera-type technique based on both finite element and improved element-free Galerkin methods. The proposed overset improved element-free Galerkin-finite element method (Ov-IEFG-FEM) for linear elasticity uses the finite element method (FEM) throughout the entire problem geometry

Metal-ceramic composites by their nature have thermal residual stresses at the micro-level, which can compromise the integrity of structural elements made from these materials. The evaluation of thermal residual stresses is therefore of continuing research interest both experimentally and by modeling. In this study, two functionally graded aluminum alloy matrix composites, AlSi12/AlO and AlSi12/SiC

An intrusive Reduced Order Model (ROM) is developed for nonlinear porous media flow problems with transient and time-discontinuous fluid injection rates. The proposed ROM is significantly more computationally efficient than the Full Order Model (FOM). The training regime is generated using the FOM with constant injection rates during the offline stage. The trained ROM exhibits high accuracy for complex

A wide range of applications of unsaturated hydraulic conductivity is well known in geotechnical, hydrological, and agricultural engineering fields. The standard prediction models for hydraulic conductivity function overlook the complexity of soil pore structure and employ a simplistic approach based on the bundle of capillary tubes. This study proposes an alternative approach employing pore network

The contraction or expansion of a cylindrical cavity in an elastoplastic medium is usually analyzed from a continuum based approach with a plasticity constitutive model. However, localized deformations, which are rooted in the post‐failure softening response of geomaterials, are observed in the form of spiral‐shaped fractures in laboratory tests. An alternative approach based on dislocation theory

Loose granular materials may also exhibit instability behaviors similar to liquefaction under drained conditions, commonly referred to as diffuse instability, which can be studied through constant shear drained (CSD) tests. So far, the research on CSD in binary mixtures is still insufficient. Therefore, a series of numerical tests using the discrete element method (DEM) were conducted on binary mixtures

It is shown that discretizations based on variational or weak formulations of the plate bending problem with simple support boundary conditions do not lead to the failure of convergence when polygonal domain approximations are used and the imposed boundary conditions are compatible with the nodal interpolation of the restriction of certain regular functions to approximating domains. It is further shown

Wave propagation in elastodynamic problems in solids often requires fine computational meshes. In this work we propose to combine stabilized finite element methods (FEM) with an artificial neural network (ANN) correction term to solve such problems on coarse meshes. Irreducible and mixed velocity–stress formulations for the linear elasticity problem in the frequency domain are first presented and discretized

Fully grouted rock bolts are widely used in mining, tunneling, and pit support, and thus the study of their anchorage performance is beneficial for optimizing the anchorage system design. In this study, an FDM‐DEM coupled numerical model is established to simulate the whole process of rock bolt pullout test and to investigate the failure mechanism of fully grouted rock bolts. The accuracy of the model

We study the computational complexity of the eigenvalue problem for the Klein–Gordon equation in the framework of the Solvability Complexity Index Hierarchy. We prove that the eigenvalue of the Klein–Gordon equation with linearly decaying potential can be computed in a single limit with guaranteed error bounds from above. The proof is constructive, i.e. we obtain a numerical algorithm that can be implemented

This study establishes a theoretical framework for analyzing the lateral oscillation of marine pipe piles. The additional mass model is introduced herein to consider the inertial fluctuation effect of the soil plug. Analytical mathematical methods are used to determine the complex impedance variation of the pile over a range of frequency effects. An investigation is performed to determine how the presence

SIAM Journal on Numerical Analysis, Volume 62, Issue 4, Page 2048-2070, August 2024. Abstract. We present new Dirichlet–Neumann and Neumann–Dirichlet algorithms with a time domain decomposition applied to unconstrained parabolic optimal control problems. After a spatial semidiscretization, we use the Lagrange multiplier approach to derive a coupled forward-backward optimality system, which can then

SIAM Journal on Numerical Analysis, Volume 62, Issue 4, Page 2025-2047, August 2024. Abstract. Statistical inverse learning aims at recovering an unknown function [math] from randomly scattered and possibly noisy point evaluations of another function [math], connected to [math] via an ill-posed mathematical model. In this paper we blend statistical inverse learning theory with the classical regularization

We establish an a priori error analysis for the lowest-order Raviart–Thomas finite element discretization of the nonlinear Gross-Pitaevskii eigenvalue problem. Optimal convergence rates are obtained for the primal and dual variables as well as for the eigenvalue and energy approximations. In contrast to conforming approaches, which naturally imply upper energy bounds, the proposed mixed discretization

This article aims to investigate the semi-classical analog of the general Caputo-type diffusion equation with time-dependent diffusion coefficient associated with the discrete Schrödinger operator, \(\mathcal {H}_{\hbar ,V}:=-\hbar ^{-2}\mathcal {L}_{\hbar }+V\) on the lattice \(\hbar \mathbb {Z}^{n},\) where V is a positive multiplication operator and \(\mathcal {L}_{\hbar }\) is the discrete Laplacian

SIAM Journal on Numerical Analysis, Volume 62, Issue 4, Page 2004-2024, August 2024. Abstract. We propose and analyze a novel approach to construct structure preserving approximations for the Poisson–Nernst–Planck equations, focusing on the positivity preserving and mass conservation properties. The strategy consists of a standard time marching step with a projection (or correction) step to satisfy

Sparse binary matrices are of great interest in the field of sparse recovery, nonnegative compressed sensing, statistics in networks, and theoretical computer science. This class of matrices makes it possible to perform signal recovery with lower storage costs and faster decoding algorithms. In particular, Bernoulli () matrices formed by independent identically distributed (i.i.d.) Bernoulli () random

A generalized finite element beam with an embedded rotation discontinuity coupled with a 3D macroelement is proposed to assess, till complete failure (no stress transfer), the vulnerability of symmetrically reinforced concrete frame structures subjected to static (monotonic, cyclic) or dynamic loading. The beam follows the Timoshenko beam theory and its sectional behavior is described in terms of generalized

This paper study a class of time-space fractional reaction-diffusion equations with nonlocal initial conditions and construct an abstract theory in fractional power spaces to discuss the results related S-asymptotically \(\omega \)-periodic mild solutions. When the coefficients are sufficiently small, under the condition that the nonlinear term can grow any number of orders, we discuss the existence

In this paper, the averaging principle for stochastic Caputo fractional differential equations with the nonlinear terms satisfying the non-Lipschitz condition is considered. The work in the article is roughly divided into three parts. Firstly, we establish a generalized Gronwall inequality with singular integral kernel which is a key part in our analysis. Secondly, we discuss the existence and uniqueness

In this article we propose two finite-element schemes for the Navier–Stokes equations, based on a reformulation that involves differential operators from the de Rham sequence and an advection operator with explicit skew-symmetry in weak form. Our first scheme is obtained by discretizing this formulation with conforming FEEC (Finite Element Exterior Calculus) spaces: it preserves the point-wise divergence

SIAM Journal on Numerical Analysis, Volume 62, Issue 4, Page 1979-2003, August 2024. Abstract. We introduce a new overlapping domain decomposition method (DDM) to solve fully nonlinear elliptic partial differential equations (PDEs) approximated with monotone schemes. While DDMs have been extensively studied for linear problems, their application to fully nonlinear PDEs remains limited in the literature

The shapes and morphological features of grains in sand assemblies have far‐reaching implications in many engineering applications, such as geotechnical engineering, computer animations, petroleum engineering, and concentrated solar power. Yet, our understanding of the influence of grain geometries on macroscopic response is often only qualitative, due to the limited availability of high‐quality 3D