Advances in Applied Mathematics and Mechanics

Papers
(The median citation count of Advances in Applied Mathematics and Mechanics is 1. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2020-11-01 to 2024-11-01.)
ArticleCitations
Integrating Krylov Deferred Correction and Generalized Finite Difference Methods for Dynamic Simulations of Wave Propagation Phenomena in Long-Time Intervals39
Localized Method of Fundamental Solutions for Three-Dimensional Elasticity Problems: Theory36
Recent Advances and Emerging Applications of the Singular Boundary Method for Large-Scale and High-Frequency Computational Acoustics33
Error Estimate of a Second Order Accurate Scalar Auxiliary Variable (SAV) Numerical Method for the Epitaxial Thin Film Equation30
An Analytical Solution for Nonlinear Vibration Analysis of Functionally Graded Rectangular Plate in Contact with Fluid24
Multiple-Relaxation-Time Lattice Boltzmann Simulation of Magnetic Field Effect on Natural Convection of Non-Newtonian Nanofluid in Rectangular Enclosure15
A Second Order Accurate in Time, Energy Stable Finite Element Scheme for the Flory-Huggins-Cahn-Hilliard Equation14
Localized Method of Fundamental Solutions for Acoustic Analysis Inside a Car Cavity with Sound-Absorbing Material13
Convergence Analysis and Error Estimate for Distributed Optimal Control Problems Governed by Stokes Equations with Velocity-Constraint13
Singularity of Navier-Stokes Equations Leading to Turbulence12
Electroelastic Analysis of Two-Dimensional Piezoelectric Structures by the Localized Method of Fundamental Solutions12
Two-Grid Finite Volume Element Method Combined with Crank-Nicolson Scheme for Semilinear Parabolic Equations10
A Two-Level Factored Crank-Nicolson Method for Two-Dimensional Nonstationary Advection-Diffusion Equation with Time Dependent Dispersion Coefficients and Source Terms10
Ultra-Chaos: An Insurmountable Objective Obstacle of Reproducibility and Replication9
An Energy-Stable Finite Element Method for Incompressible Magnetohydrodynamic-Cahn-Hilliard Coupled Model9
Arbitrarily High-Order Energy-Preserving Schemes for the Camassa-Holm Equation Based on the Quadratic Auxiliary Variable Approach7
A Two-Grid Finite-Volume Method for the Schrödinger Equation7
A Stabilizer-Free Weak Galerkin Finite Element Method for the Stokes Equations7
A New Conservative Allen-Cahn Type Ohta-Kawaski Phase-Field Model for Diblock Copolymers and Its Numerical Approximations7
Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation6
Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay6
A Patch-Based Low-Rank Minimization Approach for Speckle Noise Reduction in Ultrasound Images6
Lattice Boltzmann Model for Time-Fractional Nonlinear Wave Equations6
A New Explicit Immersed Boundary Method for Simulation of Fluid-Solid Interactions6
Finite Element Method Coupling Penalty Method for Flexural Shell Model5
Numerical Schemes for Time-Space Fractional Vibration Equations5
A Fifth Order Alternative Mapped WENO Scheme for Nonlinear Hyperbolic Conservation Laws5
An Energy-Preserving Scheme for the Coupled Gross-Pitaevskii Equations4
Fast Prediction of Immiscible Two-Phase Displacements in Heterogeneous Porous Media with Convolutional Neural Network4
A Second-Order Energy Stable BDF Numerical Scheme for the Viscous Cahn-Hilliard Equation with Logarithmic Flory-Huggins Potential4
A Coercivity Result of Quadratic Finite Volume Element Schemes over Triangular Meshes4
High-Order Well-Balanced Finite Volume WENO Schemes with Conservative Variables Decomposition for Shallow Water Equations4
An Analytical Approach for Nonlinear Buckling Analysis of Torsionally Loaded Sandwich Carbon Nanotube Reinforced Cylindrical Shells with Auxetic Core4
Unconditional Optimal Error Estimates for the Transient Navier-Stokes Equations with Damping4
Buckling Analysis of FG Porous Truncated Conical Shells Resting on Elastic Foundations in the Framework of the Shear Deformation Theory4
Exponential Time Differencing Schemes for the Peng-Robinson Equation of State with Preservation of Maximum Bound Principle4
High Order Efficient Algorithm for Computation of MHD Flow Ensembles4
Reconstructing the Absorption Function in a Quasi-Linear Sorption Dynamic Model via an Iterative Regularizing Algorithm4
Unconditional Stability and Error Estimates of the Modified Characteristics FEM for the Time-Dependent Viscoelastic Oldroyd Flows4
A Kernel-Independent Sum-of-Gaussians Method by de la Vallée-Poussin Sums3
Broad Learning System with Preprocessing to Recover the Scattering Obstacles with Far–Field Data3
Anisotropic Yield Criterion for Metals Exhibiting Tension–Compression Asymmetry3
An SAV Method for Imaginary Time Gradient Flow Model in Density Functional Theory3
A New Fifth-Order Finite Difference WENO Scheme for Dam-Break Simulations3
Inverse Scattering Transform and Soliton Solutions for the Hirota Equation with $N$ Distinct Arbitrary Order Poles3
Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations3
A Novel B-Spline Method for Modeling Transport Problems in Anisotropic Inhomogeneous Media3
Coiflet Wavelet-Homotopy Solutions to Bio-Thermal Convection in a Square Cavity3
An Energy Stable SPH Method for Incompressible Fluid Flow3
Impacts of Down-Up Hill Segment on the Threshold of Shock Formation of Ring Road Vehicular Flow3
Bifurcation and Chaos of Functionally Graded Carbon Nanotube Reinforced Composite Beam with Piezoelectric Layer3
Domain-Decomposition Localized Method of Fundamental Solutions for Large-Scale Heat Conduction in Anisotropic Layered Materials3
Temperature Effect on the Fundamental Breakdown Mechanism of Mack Mode Disturbances in Hypersonic Boundary Layers3
Waves Induced by the Appearance of Single-Point Heat Source in Constant Flow3
Avoiding Small Denominator Problems by Means of the Homotopy Analysis Method3
Image Segmentation via Fischer-Burmeister Total Variation and Thresholding3
A Symplectic Conservative Perturbation Series Expansion Method for Linear Hamiltonian Systems with Perturbations and Its Applications3
Legendre Neural Network for Solving Linear Variable Coefficients Delay Differential-Algebraic Equations with Weak Discontinuities3
A Well-Balanced Runge-Kutta Discontinuous Galerkin Method for Multilayer Shallow Water Equations with Non-Flat Bottom Topography3
A Simplified Lattice Boltzmann Method for Turbulent Flow Simulation2
Direct Numerical Simulations of Self-Sustained Oscillations in Two-Dimensional Open Cavity for Subsonic and Supersonic Flow2
A Discontinuous Galerkin Finite Element Method Without Interior Penalty Terms2
Calculation of Four-Dimensional Unsteady Gas Flow via Different Quadrature Schemes and Runge-Kutta 4th Order Method2
Dynamic Loadings Induced Vibration of Third Order Shear Deformable FG-CNTRC Beams: Gram-Schmidt-Ritz Method2
A Class of Robust Low Dissipation Nested Multi-Resolution WENO Schemes for Solving Hyperbolic Conservation Laws2
Finite-Time Stability and Instability of Nonlinear Impulsive Systems2
Interacting Stress Intensity Factors of Multiple Elliptical-Holes and Cracks Under Far-Field and Arbitrary Surface Stresses2
WENO Interpolation-Based and Upwind-Biased Free-Stream Preserving Nonlinear Schemes2
Free Vibration of Stiffened Plate with Cracked Stiffeners2
A Non-Singular Boundary Element Method for Interactions Between Acoustical Field Sources and Structures2
Construction of Non-Equilibrium Gas Distribution Functions Through Expansions in Peculiar Velocity Space2
A Combination of High-Order Compact Finite Difference Schemes and a Splitting Method that Preserves Accuracy for the Multi-Dimensional Burgers' Equation2
An Extension of the Order-Preserving Mapping to the WENO-Z-Type Schemes2
$(1+s)$-Order Convergence Analysis of Weak Galerkin Finite Element Methods for Second Order Elliptic Equations2
Numerical Solution for Neutral Delay Differential Equation of Constant or Proportional Type Using Hybrid Block Method2
An Efficient Second-Order Finite Volume ADI Method for Nonlinear Three-Dimensional Space-Fractional Reaction-Diffusion Equations2
Discontinuous Galerkin Methods for Semilinear Elliptic Boundary Value Problem2
A Well-Balanced FVC Scheme for 2D Shallow Water Flows on Unstructured Triangular Meshes2
Vibration Behavior of a Sandwich Porous Elliptical Micro-Shell with a Magneto-Rheological Core Based on the Modified Couple Stress Theory2
Investigating Droplet and Bubble Deformation under Shear Flow Using the Multi-Pseudo-Potential Scheme of Lattice Boltzmann Method2
New Energy Analysis of Yee Scheme for Metamaterial Maxwell's Equations on Non-Uniform Rectangular Meshes2
Optimization of Identifying Point Pollution Sources for the Convection-Diffusion-Reaction Equations2
A Radial Basis Function Meshless Numerical Method for Solving Interface Problems in Irregular Domains2
A Direct-Forcing Immersed Boundary Projection Method for Thermal Fluid-Solid Interaction Problems2
Piecewise Spectral Collocation Method for Second Order Volterra Integro-Differential Equations with Nonvanishing Delay2
A Self-Adaptive Algorithm of the Clean Numerical Simulation (CNS) for Chaos2
Semi-Discrete and Fully Discrete Mixed Finite Element Methods for Maxwell Viscoelastic Model of Wave Propagation2
Characterising Mechanical Properties of Flowing Microcapsules Using a Deep Convolutional Neural Network2
Extremum-Preserving Correction of the Nine-Point Scheme for Diffusion Equation on Distorted Meshes2
Optimal Convergence Rate of $\theta$--Maruyama Method for Stochastic Volterra Integro-Differential Equations with Riemann--Liouville Fractional Brownian Motion2
A Novel Immersed Boundary Method Implemented by Imposing Reconstructed Velocity on Virtual Boundary2
A Linear Doubly Stabilized Crank-Nicolson Scheme for the Allen–Cahn Equation with a General Mobility2
Upwind Strategy for Localized Method of Approximate Particular Solutions with Applications to Convection Dominated Diffusion Problems1
Integral Equation Method for Inverse Scattering Problem from the Far-Field Data1
Modified Two-Grid Algorithm for Nonlinear Power-Law Conductivity in Maxwell's Problems with High Accuracy1
Two-Grid Crank-Nicolson Finite Volume Element Method for the Time-Dependent Schrödinger Equation1
Numerical Analysis of Crack-Tip Fields Using a Meshless Method in Linear Elastic Materials1
A Buckley-Leverett Theory Based Lattice Boltzmann Method for Immiscible Two-Phase Flow with Viscous Coupling in Porous Media1
Nonconforming Mixed FEM Analysis for Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation with Time-Space Coupled Derivative1
A Maximum-Principle-Preserving Finite Volume Scheme for Diffusion Problems on Distorted Meshes1
The Formulation of Finite Difference RBFWENO Schemes for Hyperbolic Conservation Laws: An Alternative Technique1
Harmonic Standing-Wave Excitations of Simply-Supported Thick-Walled Hollow Elastic Circular Cylinders: Exact 3D Linear Elastodynamic Response1
A Weak Galerkin Mixed Finite Element Method for Acoustic Wave Equation1
An Efficient and Unconditionally Convergent Galerkin Finite Element Method for the Nonlinear Schrödinger Equation in High Dimensions1
A Note on the Generating Function Method1
A New Fifth-Order Finite Volume Central WENO Scheme for Hyperbolic Conservation Laws on Staggered Meshes1
Radially Symmetrical Problems for Compressible Fluids with a High-Resolution Boundary Condition1
Entropy Generation Analysis around Airfoil Using Multi-Block Lattice Boltzmann Method1
Jacobi Spectral Galerkin Methods for a Class of Nonlinear Weakly Singular Volterra Integral Equations1
Interaction of Radiation and Turbulent Natural Convection: A Pseudo-Direct Numerical Study1
Explicit High Order One-Step Methods for Decoupled Forward Backward Stochastic Differential Equations1
A Priori Error Estimates for Spectral Galerkin Approximations of Integral State-Constrained Fractional Optimal Control Problems1
Nonpolynomial Jacobi Spectral-Collocation Method for Weakly Singular Fredholm Integral Equations of the Second Kind1
Stability and Convergence of the Canonical Euler Splitting Method for Nonlinear Composite Stiff Functional Differential-Algebraic Equations1
Analytical Solution for Vibration of Continuously Varying-Thickness Beams Resting on Pasternak Elastic Foundations1
A Fast Implementation of the Linear Bond-Based Peridynamic Beam Model1
A Posteriori Error Estimates for $hp$ Spectral Element Approximation of Elliptic Control Problems with Integral Control and State Constraints1
A New Well-Balanced Finite Volume CWENO Scheme for Shallow Water Equations over Bottom Topography1
Positive and Conservative Characteristic Block-Centered Finite Difference Methods for Convection Dominated Diffusion Equations1
A Symmetric Inertial Alternating Direction Method of Multipliers for Elliptic Equation Constrained Optimization Problem1
SAV Finite Element Method for the Peng-Robinson Equation of State with Dynamic Boundary Conditions1
Error Analysis of Two-Level Finite Element Method for the Nonlinear Conductivity Problem in Maxwell's System1
A Highly Efficient Reduced-Order Extrapolating Model for the 2D Viscoelastic Wave Equation1
A Two-Dimensional Thermoelastic Analysis of a Cylindrical Shell Made of FGM with Temperature-Dependent Physical Properties1
A Multi-Dimensional Shock-Capturing Limiter for High-Order Least Square-Based Finite Difference-Finite Volume Method on Unstructured Grids1
On the Equilibria of the Planar Equilateral Restricted Four-Body Problem with Radiation Pressure1
Deep Domain Decomposition Methods: Helmholtz Equation1
Accelerated Gradient Descent Methods for the Uniaxially Constrained Landau-de Gennes Model1
An Implicit-Explicit Scheme for the Radiation Hydrodynamics1
Uncertainty Quantification of Store-Separation Simulation Due to Ejector Modeling Using a Monte Carlo Approach with Kriging Model1
Large Eddy Simulation of the Vortex-Induced Vibration of a Circular Cylinder by Using the Local Domain-Free Discretization Method1
A Conservative Gradient Discretization Method for Parabolic Equations1
An Improved Single-Relaxation-Time Multiphase Lattice Boltzmann Model for Multiphase Flows with Large Density Ratios and High Reynolds Numbers1
A Modified Characteristics Finite Element Method for the Electroneutral Micro-Fluids1
Numerical Simulations of the Richtmyer–Meshkov Instability of Solid-Vacuum Interface1
Numerical Analysis of Two-Grid Block-Centered Finite Difference Method for Two-Phase Flow in Porous Medium1
A Numerical-Analytical Method for Time-Fractional Dual-Phase-Lag Models of Heat Transfer1
Multi-Modes Multiscale Approach of Heat Transfer Problems in Heterogeneous Solids with Uncertain Thermal Conductivity1
A Coiflet Wavelet Homotopy Technique for Nonlinear PDEs: Application to the Extreme Bending of Orthotropic Plate with Forced Boundary Constraints1
Solving PDEs with a Hybrid Radial Basis Function: Power-Generalized Multiquadric Kernel1
A Mass-Preserving Characteristic Finite Difference Method for Miscible Displacement Problem1
A Kernel-Independent Treecode for General Rotne-Prager-Yamakawa Tensor1
A Galerkin-Characteristic Finite Element Method for Three-Dimensional Convection-Dominated Problems1
Stochastic Runge-Kutta–Munthe-Kaas Methods in the Modelling of Perturbed Rigid Bodies1
Anderson Acceleration of Nonlinear Solvers for the Stationary Gross-Pitaevskii Equation1
Two-Grid Immersed Finite Volume Element Methods for Semi-Linear Elliptic Interface Problems with Non-Homogeneous Jump Conditions1
A Hessian Recovery Based Linear Finite Element Method for Molecular Beam Epitaxy Growth Model with Slope Selection1
A Conservative SAV-RRK Finite Element Method for the Nonlinear Schrödinger Equation1
Chebyshev-Lagrange Multipliers Technique for Vibration Analysis of Functionally Graded Material Beams Using Various Beam Theories1
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