Advances in Applied Mathematics and Mechanics

(The TQCC of Advances in Applied Mathematics and Mechanics is 2. 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 2020-07-01 to 2024-07-01.)
Integrating Krylov Deferred Correction and Generalized Finite Difference Methods for Dynamic Simulations of Wave Propagation Phenomena in Long-Time Intervals37
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 Acoustics32
Error Estimate of a Second Order Accurate Scalar Auxiliary Variable (SAV) Numerical Method for the Epitaxial Thin Film Equation27
An Analytical Solution for Nonlinear Vibration Analysis of Functionally Graded Rectangular Plate in Contact with Fluid23
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 Equation13
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-Constraint12
Singularity of Navier-Stokes Equations Leading to Turbulence11
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 Terms9
Ultra-Chaos: An Insurmountable Objective Obstacle of Reproducibility and Replication9
Electroelastic Analysis of Two-Dimensional Piezoelectric Structures by the Localized Method of Fundamental Solutions9
A Two-Grid Finite-Volume Method for the Schrodinger Equation7
A New Explicit Immersed Boundary Method for Simulation of Fluid-Solid Interactions7
Arbitrarily High-Order Energy-Preserving Schemes for the Camassa-Holm Equation Based on the Quadratic Auxiliary Variable Approach7
A New Conservative Allen-Cahn Type Ohta-Kawaski Phase-Field Model for Diblock Copolymers and Its Numerical Approximations7
An Energy-Stable Finite Element Method for Incompressible Magnetohydrodynamic-Cahn-Hilliard Coupled Model6
A Patch-Based Low-Rank Minimization Approach for Speckle Noise Reduction in Ultrasound Images6
Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay6
Numerical Schemes for Time-Space Fractional Vibration Equations5
Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation4
Fast Prediction of Immiscible Two-Phase Displacements in Heterogeneous Porous Media with Convolutional Neural Network4
An Analytical Approach for Nonlinear Buckling Analysis of Torsionally Loaded Sandwich Carbon Nanotube Reinforced Cylindrical Shells with Auxetic Core4
A Fifth Order Alternative Mapped WENO Scheme for Nonlinear Hyperbolic Conservation Laws4
Lattice Boltzmann Model for Time-Fractional Nonlinear Wave Equations4
Reconstructing the Absorption Function in a Quasi-Linear Sorption Dynamic Model via an Iterative Regularizing Algorithm4
A Stabilizer-Free Weak Galerkin Finite Element Method for the Stokes Equations4
Unconditional Stability and Error Estimates of the Modified Characteristics FEM for the Time-Dependent Viscoelastic Oldroyd Flows4
High-Order Well-Balanced Finite Volume WENO Schemes with Conservative Variables Decomposition for Shallow Water Equations4
A Second-Order Energy Stable BDF Numerical Scheme for the Viscous Cahn-Hilliard Equation with Logarithmic Flory-Huggins Potential4
An Energy-Preserving Scheme for the Coupled Gross-Pitaevskii Equations3
Finite Element Method Coupling Penalty Method for Flexural Shell Model3
Bifurcation and Chaos of Functionally Graded Carbon Nanotube Reinforced Composite Beam with Piezoelectric Layer3
A Well-Balanced Runge-Kutta Discontinuous Galerkin Method for Multilayer Shallow Water Equations with Non-Flat Bottom Topography3
Inverse Scattering Transform and Soliton Solutions for the Hirota Equation with $N$ Distinct Arbitrary Order Poles3
A Novel B-Spline Method for Modeling Transport Problems in Anisotropic Inhomogeneous Media3
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
An SAV Method for Imaginary Time Gradient Flow Model in Density Functional Theory3
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
Legendre Neural Network for Solving Linear Variable Coefficients Delay Differential-Algebraic Equations with Weak Discontinuities3
Unconditional Optimal Error Estimates for the Transient Navier-Stokes Equations with Damping3
Buckling Analysis of FG Porous Truncated Conical Shells Resting on Elastic Foundations in the Framework of the Shear Deformation Theory3
A Coercivity Result of Quadratic Finite Volume Element Schemes over Triangular Meshes3
Broad Learning System with Preprocessing to Recover the Scattering Obstacles with Far–Field Data3
Image Segmentation via Fischer-Burmeister Total Variation and Thresholding3
Anisotropic Yield Criterion for Metals Exhibiting Tension–Compression Asymmetry3
A Symplectic Conservative Perturbation Series Expansion Method for Linear Hamiltonian Systems with Perturbations and Its Applications3
A New Fifth-Order Finite Difference WENO Scheme for Dam-Break Simulations3
Domain-Decomposition Localized Method of Fundamental Solutions for Large-Scale Heat Conduction in Anisotropic Layered Materials3
A Kernel-Independent Sum-of-Gaussians Method by de la Vallee-Poussin Sums3
Coiflet Wavelet-Homotopy Solutions to Bio-Thermal Convection in a Square Cavity3
Exponential Time Differencing Schemes for the Peng-Robinson Equation of State with Preservation of Maximum Bound Principle3
Semi-Discrete and Fully Discrete Mixed Finite Element Methods for Maxwell Viscoelastic Model of Wave Propagation2
Extremum-Preserving Correction of the Nine-Point Scheme for Diffusion Equation on Distorted Meshes2
High Order Efficient Algorithm for Computation of MHD Flow Ensembles2
WENO Interpolation-Based and Upwind-Biased Free-Stream Preserving Nonlinear Schemes2
A Combination of High-OrdCompact Finite Difference Schemes and a Splitting Method that Preserves Accuracy for the Multi-Dimensional Burgers' Equation2
Direct Numerical Simulations of Self-Sustained Oscillations in Two-Dimensional Open Cavity for Subsonic and Supersonic Flow2
An Extension of the Order-Preserving Mapping to the WENO-Z-Type Schemes2
New Energy Analysis of Yee Scheme for Metamaterial Maxwell's Equations on Non-Uniform Rectangular Meshes2
A Self-Adaptive Algorithm of the Clean Numerical Simulation (CNS) for Chaos2
Finite-Time Stability and Instability of Nonlinear Impulsive Systems2
Characterising Mechanical Properties of Flowing Microcapsules Using a Deep Convolutional Neural Network2
Free Vibration of Stiffened Plate with Cracked Stiffeners2
Construction of Non-Equilibrium Gas Distribution Functions through Expansions in Peculiar Velocity Space2
A Radial Basis Function Meshless Numerical Method for Solving Interface Problems in Irregular Domains2
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
A Non-Singular Boundary Element Method for Interactions between Acoustical Field Sources and Structures2
Numerical Solution for Neutral Delay Differential Equation of Constant or Proportional Type Using Hybrid Block Method2
A Class of Robust Low Dissipation Nested Multi-Resolution WENO Schemes for Solving Hyperbolic Conservation Laws2
Interacting Stress Intensity Factors of Multiple Elliptical-Holes and Cracks Under Far-Field and Arbitrary Surface Stresses2
Avoiding Small Denominator Problems by Means of the Homotopy Analysis Method2
Optimal Convergence Rate of $\theta$--Maruyama Method for Stochastic Volterra Integro-Differential Equations with Riemann--Liouville Fractional Brownian Motion2
Optimization of Identifying Point Pollution Sources for the Convection-Diffusion-Reaction Equations2
A Novel Immersed Boundary Method Implemented by Imposing Reconstructed Velocity on Virtual Boundary2
Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations2
$(1+s)$-Order Convergence Analysis of Weak Galerkin Finite Element Methods for Second Order Elliptic Equations2
Dynamic Loadings Induced Vibration of Third Order Shear Deformable FG-CNTRC Beams: Gram-Schmidt-Ritz Method2
An Efficient Second-Order Finite Volume ADI Method for Nonlinear Three-Dimensional Space-Fractional Reaction-Diffusion Equations2