Advances in Applied Mathematics and Mechanics

Article	Citations
A Localized Space-Time Method of Fundamental Solutions for Diffusion and Convection-Diffusion Problems	52
Integrating Krylov Deferred Correction and Generalized Finite Difference Methods for Dynamic Simulations of Wave Propagation Phenomena in Long-Time Intervals	37
Localized Method of Fundamental Solutions for Three-Dimensional Elasticity Problems: Theory	35
Recent Advances and Emerging Applications of the Singular Boundary Method for Large-Scale and High-Frequency Computational Acoustics	31
Error Estimate of a Second Order Accurate Scalar Auxiliary Variable (SAV) Numerical Method for the Epitaxial Thin Film Equation	22
An Analytical Solution for Nonlinear Vibration Analysis of Functionally Graded Rectangular Plate in Contact with Fluid	19
High-Order Accurate Entropy Stable Finite Difference Schemes for One- and Two-Dimensional Special Relativistic Hydrodynamics	18
Multiple-Relaxation-Time Lattice Boltzmann Simulation of Magnetic Field Effect on Natural Convection of Non-Newtonian Nanofluid in Rectangular Enclosure	14
Singularity of Navier-Stokes Equations Leading to Turbulence	11
Convergence Analysis and Error Estimate for Distributed Optimal Control Problems Governed by Stokes Equations with Velocity-Constraint	10
Localized Method of Fundamental Solutions for Acoustic Analysis Inside a Car Cavity with Sound-Absorbing Material	10
Efficient Preconditioned Iterative Linear Solvers for 3-D Magnetostatic Problems Using Edge Elements	9
A Two-Level Factored Crank-Nicolson Method for Two-Dimensional Nonstationary Advection-Diffusion Equation With Time Dependent Dispersion Coefficients and Source Terms	8
Two-Grid Finite Volume Element Method Combined with Crank-Nicolson Scheme for Semilinear Parabolic Equations	8
A Second Order Accurate in Time, Energy Stable Finite Element Scheme for the Flory-Huggins-Cahn-Hilliard Equation	8
A New Conservative Allen-Cahn Type Ohta-Kawaski Phase-Field Model for Diblock Copolymers and Its Numerical Approximations	7
Ultra-Chaos: An Insurmountable Objective Obstacle of Reproducibility and Replication	7
A Compact Difference Scheme for the Time-Fractional Partial Integro-Differential Equation with a Weakly Singular Kernel	7
A New Explicit Immersed Boundary Method for Simulation of Fluid-Solid Interactions	7
A Two-Grid Finite-Volume Method for the Schrodinger Equation	6
Arbitrarily High-Order Energy-Preserving Schemes for the Camassa-Holm Equation Based on the Quadratic Auxiliary Variable Approach	6
Transient Response of High Dimensional Nonlinear Dynamic System for a Rotating Cantilever Twisted Plate	6
An Energy-Stable Finite Element Method for Incompressible Magnetohydrodynamic-Cahn-Hilliard Coupled Model	6
Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay	5
Electroelastic Analysis of Two-Dimensional Piezoelectric Structures by the Localized Method of Fundamental Solutions	5

Numerical Schemes for Time-Space Fractional Vibration Equations	5
Non-Convex and Convex Coupling Image Segmentation via TGpV Regularization and Thresholding	5
A Jacobi Collocation Method for the Fractional Ginzburg-Landau Differential Equation	4
High-Order Well-Balanced Finite Volume WENO Schemes with Conservative Variables Decomposition for Shallow Water Equations	4
A Posteriori Error Estimates of the Galerkin Spectral Methods for Space-Time Fractional Diffusion Equations	4
A Variable Correction-Based Immersed Boundary Method for Compressible Flows over Stationary and Moving Bodies	4
Unconditional Stability and Error Estimates of the Modified Characteristics FEM for the Time-Dependent Viscoelastic Oldroyd Flows	4
A Robust Riemann Solver for Multiple Hydro-Elastoplastic Solid Mediums	4
The Weak Galerkin Finite Element Method for Solving the Time-Dependent Integro-Differential Equations	4
An Analytical Approach for Nonlinear Buckling Analysis of Torsionally Loaded Sandwich Carbon Nanotube Reinforced Cylindrical Shells with Auxetic Core	4
Two-Grid Stabilized FEMs Based on Newton Type Linearization for the Steady-State Natural Convection Problem	4
A Patch-Based Low-Rank Minimization Approach for Speckle Noise Reduction in Ultrasound Images	4
Fast Prediction of Immiscible Two-Phase Displacements in Heterogeneous Porous Media with Convolutional Neural Network	4
Performance Comparison on Parallel CPU and GPU Algorithms for Two Dimensional Unified Gas-Kinetic Scheme	4
A Second-Order Energy Stable BDF Numerical Scheme for the Viscous Cahn-Hilliard Equation with Logarithmic Flory-Huggins Potential	3
Unconditional Optimal Error Estimates for the Transient Navier-Stokes Equations with Damping	3
A Fifth Order Alternative Mapped WENO Scheme for Nonlinear Hyperbolic Conservation Laws	3
Anisotropic Yield Criterion for Metals Exhibiting Tension–Compression Asymmetry	3
The Crank-Nicolson/Explicit Scheme for the Natural Convection Equations with Nonsmooth Initial Data	3
Impacts of Down-Up Hill Segment on the Threshold of Shock Formation of Ring Road Vehicular Flow	3
A New Fifth-Order Finite Difference WENO Scheme for Dam-Break Simulations	3
Inverse Scattering Transform and Soliton Solutions for the Hirota Equation with $N$ Distinct Arbitrary Order Poles	3
Lattice Boltzmann Model for Time-Fractional Nonlinear Wave Equations	3
Image Segmentation via Fischer-Burmeister Total Variation and Thresholding	3
Finite Element Methods for Nonlinear Backward Stochastic Partial Differential Equations and Their Error Estimates	3
A Symplectic Conservative Perturbation Series Expansion Method for Linear Hamiltonian Systems with Perturbations and Its Applications	3
A Fully Discrete Explicit Multistep Scheme for Solving Coupled Forward Backward Stochastic Differential Equations	3
Domain-Decomposition Localized Method of Fundamental Solutions for Large-Scale Heat Conduction in Anisotropic Layered Materials	3
A Novel B-Spline Method for Modeling Transport Problems in Anisotropic Inhomogeneous Media	3
An Energy-Preserving Scheme for the Coupled Gross-Pitaevskii Equations	3
An Energy Stable SPH Method for Incompressible Fluid Flow	3
A Discontinuous Galerkin Method by Patch Reconstruction for Convection-Diffusion Problems	3
A Stabilizer-Free Weak Galerkin Finite Element Method for the Stokes Equations	3
Complex Pattern Formations by Spatial Varying Parameters	2
A Kernel-Independent Sum-of-Gaussians Method by de la Vallee-Poussin Sums	2
Construction of Non-Equilibrium Gas Distribution Functions through Expansions in Peculiar Velocity Space	2
Solving Fourth-Order PDEs using the LMAPS	2
Optimization of Identifying Point Pollution Sources for the Convection-Diffusion-Reaction Equations	2
Finite-Time Stability and Instability of Nonlinear Impulsive Systems	2
A Generalization of a Troubled-Cell Indicator to $h$-Adaptive Meshes for Discontinuous Galerkin Methods	2
Direct Numerical Simulations of Self-Sustained Oscillations in Two-Dimensional Open Cavity for Subsonic and Supersonic Flow	2
$(1+s)$-Order Convergence Analysis of Weak Galerkin Finite Element Methods for Second Order Elliptic Equations	2
Extremum-Preserving Correction of the Nine-Point Scheme for Diffusion Equation on Distorted Meshes	2
Interacting Stress Intensity Factors of Multiple Elliptical-Holes and Cracks Under Far-Field and Arbitrary Surface Stresses	2
High Order Efficient Algorithm for Computation of MHD Flow Ensembles	2
Constructing Separable Non-$2\pi$-Periodic Solutions to the Navier-Lame Equation in Cylindrical Coordinates Using the Buchwald Representation: Theory and Applications	2
Dynamic Loadings Induced Vibration of Third Order Shear Deformable FG-CNTRC Beams: Gram-Schmidt-Ritz Method	2
An Efficient Numerical Method for the Valuation of American Better-of Options Based on the Front-Fixing Transform and the Far Field Truncation	2
Temperature Effect on the Fundamental Breakdown Mechanism of Mack Mode Disturbances in Hypersonic Boundary Layers	2
Spectral Collocation Methods for Second-Order Volterra Integro-Differential Equations with Weakly Singular Kernels	2

Coiflet Wavelet-Homotopy Solutions to Bio-Thermal Convection in a Square Cavity	2
A Combination of High-OrdCompact Finite Difference Schemes and a Splitting Method that Preserves Accuracy for the Multi-Dimensional Burgers' Equation	2
Legendre Neural Network for Solving Linear Variable Coefficients Delay Differential-Algebraic Equations with Weak Discontinuities	2
A Well-Balanced Runge-Kutta Discontinuous Galerkin Method for Multilayer Shallow Water Equations with Non-Flat Bottom Topography	2
An Extension of the Order-Preserving Mapping to the WENO-Z-Type Schemes	2
A Class of Robust Low Dissipation Nested Multi-Resolution WENO Schemes for Solving Hyperbolic Conservation Laws	2
Characterising Mechanical Properties of Flowing Microcapsules Using a Deep Convolutional Neural Network	2
Fitted Finite Volume Method for Pricing American Options under Regime-Switching Jump-Diffusion Models Based on Penalty Method	2
Optimal Convergence Rate of $\theta$--Maruyama Method for Stochastic Volterra Integro-Differential Equations with Riemann--Liouville Fractional Brownian Motion	2
A Coercivity Result of Quadratic Finite Volume Element Schemes over Triangular Meshes	2
WENO Interpolation-Based and Upwind-Biased Free-Stream Preserving Nonlinear Schemes	2
Buckling Analysis of FG Porous Truncated Conical Shells Resting on Elastic Foundations in the Framework of the Shear Deformation Theory	2
Discontinuous Galerkin Methods for Multi-Pantograph Delay Differential Equations	2
New Energy Analysis of Yee Scheme for Metamaterial Maxwell's Equations on Non-Uniform Rectangular Meshes	2
Bifurcation and Chaos of Functionally Graded Carbon Nanotube Reinforced Composite Beam with Piezoelectric Layer	2
Semi-Discrete and Fully Discrete Mixed Finite Element Methods for Maxwell Viscoelastic Model of Wave Propagation	2
A Radial Basis Function Meshless Numerical Method for Solving Interface Problems in Irregular Domains	2
A Novel Immersed Boundary Method Implemented by Imposing Reconstructed Velocity on Virtual Boundary	2
A Parallel Pressure Projection Stabilized Finite Element Method for Stokes Equation with Nonlinear Slip Boundary Conditions	2
Exponential Time Differencing Schemes for the Peng-Robinson Equation of State with Preservation of Maximum Bound Principle	2
Avoiding Small Denominator Problems by Means of the Homotopy Analysis Method	2
A High-Order Well-Balanced Discontinuous Galerkin Method Based on the Hydrostatic Reconstruction for the Ripa Model	2
Finite Element Method Coupling Penalty Method for Flexural Shell Model	2
A Non-Singular Boundary Element Method for Interactions between Acoustical Field Sources and Structures	2
Numerical Analysis of Crack-Tip Fields Using a Meshless Method in Linear Elastic Materials	1
A Well-Balanced FVC Scheme for 2D Shallow Water Flows on Unstructured Triangular Meshes	1
Vibration Behavior of a Sandwich Porous Elliptical Micro-Shell with a Magneto-Rheological Core Based on the Modified Couple Stress Theory	1
Nonconforming Mixed FEM Analysis for Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation with Time-Space Coupled Derivative	1
The Modified Localized Method of Approximated Particular Solutions for Linear and Nonlinear Convection-Diffusion-Reaction PDEs	1
A Nonconforming Nitsche's Extended Finite Element Method for Elliptic Interface Problems	1
Multi-Modes Multiscale Approach of Heat Transfer Problems in Heterogeneous Solids with Uncertain Thermal Conductivity	1
The Formulation of Finite Difference RBFWENO Schemes for Hyperbolic Conservation Laws: An Alternative Technique	1
An Efficient and Unconditionally Convergent Galerkin Finite Element Method for the Nonlinear Schrodinger Equation in High Dimensions	1
An Efficient Second-Order Finite Volume ADI Method for Nonlinear Three-Dimensional Space-Fractional Reaction-Diffusion Equations	1
Radially Symmetrical Problems for Compressible Fluids with a High-Resolution Boundary Condition	1
Error Analysis of Two-Level Finite Element Method for the Nonlinear Conductivity Problem in Maxwell's System	1
Vibration Control for Flexible Spacecraft using Multi Impulse Robust Input Shaper and Optimal Control Method	1
A New Mixed Finite Element Method for Biot Consolidation Equations	1
Waves Induced by the Appearance of Single-Point Heat Source in Constant Flow	1
A Conservative SAV-RRK Finite Element Method for the Nonlinear Schrödinger Equation	1
A Multi-Dimensional Shock-Capturing Limiter for High-Order Least Square-Based Finite Difference-Finite Volume Method on Unstructured Grids	1
Two-Grid Immersed Finite Volume Element Methods for Semi-Linear Elliptic Interface Problems with Non-Homogeneous Jump Conditions	1
Superconvergence Analysis for the Maxwell's Equations in Debye Medium with a Thermal Effect	1
Uncertainty Quantification of Store-Separation Simulation Due to Ejector Modeling Using a Monte Carlo Approach with Kriging Model	1
Large Eddy Simulation of the Vortex-Induced Vibration of a Circular Cylinder by Using the Local Domain-Free Discretization Method	1
Analytical Solution for Vibration of Continuously Varying-Thickness Beams Resting on Pasternak Elastic Foundations	1
An Implicit-Explicit Scheme for the Radiation Hydrodynamics	1
Numerical Assessment of Criteria for Mesh Adaptation in the Finite Volume Solution of Shallow Water Equations	1
Positive and Conservative Characteristic Block-Centered Finite Difference Methods for Convection Dominated Diffusion Equations	1
Stability and Convergence of the Canonical Euler Splitting Method for Nonlinear Composite Stiff Functional Differential-Algebraic Equations	1
A Numerical-Analytical Method for Time-Fractional Dual-Phase-Lag Models of Heat Transfer	1
A Mixed Formulation of Stabilized Nonconforming Finite Element Method for Linear Elasticity	1
A Weak Galerkin Mixed Finite Element Method for Acoustic Wave Equation	1
A Kernel-Independent Treecode for General Rotne-Prager-Yamakawa Tensor	1
FEA Versus IGA in a Two-Node Beam Element Based on Unified and Integrated Method	1
A Note on the Generating Function Method	1
High-Order Finite Difference Schemes Based on Symmetric Conservative Metric Method: Decomposition, Geometric Meaning and Connection with Finite Volume Schemes	1
A Highly Efficient Reduced-Order Extrapolating Model for the 2D Viscoelastic Wave Equation	1
Solving PDEs with a Hybrid Radial Basis Function: Power-Generalized Multiquadric Kernel	1
Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation	1
A Discontinuous Galerkin Finite Element Method Without Interior Penalty Terms	1
Jacobi Spectral Galerkin Methods for a Class of Nonlinear Weakly Singular Volterra Integral Equations	1
Entropy Generation Analysis around Airfoil Using Multi-Block Lattice Boltzmann Method	1
An SAV Method for Imaginary Time Gradient Flow Model in Density Functional Theory	1
Upwind Strategy for Localized Method of Approximate Particular Solutions with Applications to Convection Dominated Diffusion Problems	1
Explicit High Order One-Step Methods for Decoupled Forward Backward Stochastic Differential Equations	1
A Posteriori Error Estimates for $hp$ Spectral Element Approximation of Elliptic Control Problems with Integral Control and State Constraints	1
A Modified Characteristics Finite Element Method for the Electroneutral Micro-Fluids	1
Numerical Solution for Neutral Delay Differential Equation of Constant or Proportional Type Using Hybrid Block Method	1
A Conservative Gradient Discretization Method for Parabolic Equations	1
An Improved Single-Relaxation-Time Multiphase Lattice Boltzmann Model for Multiphase Flows with Large Density Ratios and High Reynolds Numbers	1
Stochastic Runge-Kutta–Munthe-Kaas Methods in the Modelling of Perturbed Rigid Bodies	1
An Upwind Mixed Finite Element Method on Changing Meshes for Positive Semi-Definite Oil-Water Displacement of Darcy-Forchheimer Flow in Porous Media	1
Harmonic Standing-Wave Excitations of Simply-Supported Thick-Walled Hollow Elastic Circular Cylinders: Exact 3D Linear Elastodynamic Response	1
A Self-Adaptive Algorithm of the Clean Numerical Simulation (CNS) for Chaos	1
Broad Learning System with Preprocessing to Recover the Scattering Obstacles with Far–Field Data	1
A Fourth Order WENO Scheme for Hyperbolic Conservation Laws	1
Anderson Acceleration of Nonlinear Solvers for the Stationary Gross-Pitaevskii Equation	1
A Symmetric Inertial Alternating Direction Method of Multipliers for Elliptic Equation Constrained Optimization Problem	1
A Galerkin-Characteristic Finite Element Method for Three-Dimensional Convection-Dominated Problems	1

Accelerated Gradient Descent Methods for the Uniaxially Constrained Landau-de Gennes Model	1
Perfectly Matched Layer Method for Acoustic Scattering Problem by a Locally Perturbed Line with Impedance Boundary Condition	1
A Fully Discrete Explicit Multistep Scheme for Solving Coupled Forward Backward Stochastic Differential Equations	1
Discontinuous Galerkin Methods for Semilinear Elliptic Boundary Value Problem	1