OOIR: Observatory of International Research

Papers

(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 2020-11-01 to 2024-11-01.)

Article	Citations
Integrating Krylov Deferred Correction and Generalized Finite Difference Methods for Dynamic Simulations of Wave Propagation Phenomena in Long-Time Intervals	39
Localized Method of Fundamental Solutions for Three-Dimensional Elasticity Problems: Theory	36
Recent Advances and Emerging Applications of the Singular Boundary Method for Large-Scale and High-Frequency Computational Acoustics	33
Error Estimate of a Second Order Accurate Scalar Auxiliary Variable (SAV) Numerical Method for the Epitaxial Thin Film Equation	30
An Analytical Solution for Nonlinear Vibration Analysis of Functionally Graded Rectangular Plate in Contact with Fluid	24
Multiple-Relaxation-Time Lattice Boltzmann Simulation of Magnetic Field Effect on Natural Convection of Non-Newtonian Nanofluid in Rectangular Enclosure	15
A Second Order Accurate in Time, Energy Stable Finite Element Scheme for the Flory-Huggins-Cahn-Hilliard Equation	14
Convergence Analysis and Error Estimate for Distributed Optimal Control Problems Governed by Stokes Equations with Velocity-Constraint	13
Localized Method of Fundamental Solutions for Acoustic Analysis Inside a Car Cavity with Sound-Absorbing Material	13
Singularity of Navier-Stokes Equations Leading to Turbulence	12
Electroelastic Analysis of Two-Dimensional Piezoelectric Structures by the Localized Method of Fundamental Solutions	12
A Two-Level Factored Crank-Nicolson Method for Two-Dimensional Nonstationary Advection-Diffusion Equation with Time Dependent Dispersion Coefficients and Source Terms	10
Two-Grid Finite Volume Element Method Combined with Crank-Nicolson Scheme for Semilinear Parabolic Equations	10
An Energy-Stable Finite Element Method for Incompressible Magnetohydrodynamic-Cahn-Hilliard Coupled Model	9
Ultra-Chaos: An Insurmountable Objective Obstacle of Reproducibility and Replication	9
A New Conservative Allen-Cahn Type Ohta-Kawaski Phase-Field Model for Diblock Copolymers and Its Numerical Approximations	7
Arbitrarily High-Order Energy-Preserving Schemes for the Camassa-Holm Equation Based on the Quadratic Auxiliary Variable Approach	7
A Two-Grid Finite-Volume Method for the Schrödinger Equation	7
A Stabilizer-Free Weak Galerkin Finite Element Method for the Stokes Equations	7
Lattice Boltzmann Model for Time-Fractional Nonlinear Wave Equations	6
A New Explicit Immersed Boundary Method for Simulation of Fluid-Solid Interactions	6
Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation	6
Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay	6
A Patch-Based Low-Rank Minimization Approach for Speckle Noise Reduction in Ultrasound Images	6
A Fifth Order Alternative Mapped WENO Scheme for Nonlinear Hyperbolic Conservation Laws	5

Finite Element Method Coupling Penalty Method for Flexural Shell Model	5
Numerical Schemes for Time-Space Fractional Vibration Equations	5
Buckling Analysis of FG Porous Truncated Conical Shells Resting on Elastic Foundations in the Framework of the Shear Deformation Theory	4
Exponential Time Differencing Schemes for the Peng-Robinson Equation of State with Preservation of Maximum Bound Principle	4
High Order Efficient Algorithm for Computation of MHD Flow Ensembles	4
Reconstructing the Absorption Function in a Quasi-Linear Sorption Dynamic Model via an Iterative Regularizing Algorithm	4
Unconditional Stability and Error Estimates of the Modified Characteristics FEM for the Time-Dependent Viscoelastic Oldroyd Flows	4
An Energy-Preserving Scheme for the Coupled Gross-Pitaevskii Equations	4
Fast Prediction of Immiscible Two-Phase Displacements in Heterogeneous Porous Media with Convolutional Neural Network	4
A Second-Order Energy Stable BDF Numerical Scheme for the Viscous Cahn-Hilliard Equation with Logarithmic Flory-Huggins Potential	4
A Coercivity Result of Quadratic Finite Volume Element Schemes over Triangular Meshes	4
High-Order Well-Balanced Finite Volume WENO Schemes with Conservative Variables Decomposition for Shallow Water Equations	4
An Analytical Approach for Nonlinear Buckling Analysis of Torsionally Loaded Sandwich Carbon Nanotube Reinforced Cylindrical Shells with Auxetic Core	4
Unconditional Optimal Error Estimates for the Transient Navier-Stokes Equations with Damping	4
Temperature Effect on the Fundamental Breakdown Mechanism of Mack Mode Disturbances in Hypersonic Boundary Layers	3
Waves Induced by the Appearance of Single-Point Heat Source in Constant Flow	3
Avoiding Small Denominator Problems by Means of the Homotopy Analysis Method	3
Image Segmentation via Fischer-Burmeister Total Variation and Thresholding	3
A Symplectic Conservative Perturbation Series Expansion Method for Linear Hamiltonian Systems with Perturbations and Its Applications	3
Legendre Neural Network for Solving Linear Variable Coefficients Delay Differential-Algebraic Equations with Weak Discontinuities	3
A Well-Balanced Runge-Kutta Discontinuous Galerkin Method for Multilayer Shallow Water Equations with Non-Flat Bottom Topography	3
A Kernel-Independent Sum-of-Gaussians Method by de la Vallée-Poussin Sums	3
Broad Learning System with Preprocessing to Recover the Scattering Obstacles with Far–Field Data	3
Anisotropic Yield Criterion for Metals Exhibiting Tension–Compression Asymmetry	3
An SAV Method for Imaginary Time Gradient Flow Model in Density Functional Theory	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
Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations	3
A Novel B-Spline Method for Modeling Transport Problems in Anisotropic Inhomogeneous Media	3
Coiflet Wavelet-Homotopy Solutions to Bio-Thermal Convection in a Square Cavity	3
An Energy Stable SPH Method for Incompressible Fluid Flow	3
Impacts of Down-Up Hill Segment on the Threshold of Shock Formation of Ring Road Vehicular Flow	3
Bifurcation and Chaos of Functionally Graded Carbon Nanotube Reinforced Composite Beam with Piezoelectric Layer	3
Domain-Decomposition Localized Method of Fundamental Solutions for Large-Scale Heat Conduction in Anisotropic Layered Materials	3
Investigating Droplet and Bubble Deformation under Shear Flow Using the Multi-Pseudo-Potential Scheme of Lattice Boltzmann Method	2
Optimization of Identifying Point Pollution Sources for the Convection-Diffusion-Reaction Equations	2
A Radial Basis Function Meshless Numerical Method for Solving Interface Problems in Irregular Domains	2
A Direct-Forcing Immersed Boundary Projection Method for Thermal Fluid-Solid Interaction Problems	2
Piecewise Spectral Collocation Method for Second Order Volterra Integro-Differential Equations with Nonvanishing Delay	2
A Self-Adaptive Algorithm of the Clean Numerical Simulation (CNS) for Chaos	2
Semi-Discrete and Fully Discrete Mixed Finite Element Methods for Maxwell Viscoelastic Model of Wave Propagation	2
Characterising Mechanical Properties of Flowing Microcapsules Using a Deep Convolutional Neural Network	2
New Energy Analysis of Yee Scheme for Metamaterial Maxwell's Equations on Non-Uniform Rectangular Meshes	2
Extremum-Preserving Correction of the Nine-Point Scheme for Diffusion Equation on Distorted Meshes	2
Optimal Convergence Rate of $\theta$--Maruyama Method for Stochastic Volterra Integro-Differential Equations with Riemann--Liouville Fractional Brownian Motion	2
A Novel Immersed Boundary Method Implemented by Imposing Reconstructed Velocity on Virtual Boundary	2
Direct Numerical Simulations of Self-Sustained Oscillations in Two-Dimensional Open Cavity for Subsonic and Supersonic Flow	2
A Discontinuous Galerkin Finite Element Method Without Interior Penalty Terms	2
Calculation of Four-Dimensional Unsteady Gas Flow via Different Quadrature Schemes and Runge-Kutta 4th Order Method	2
Dynamic Loadings Induced Vibration of Third Order Shear Deformable FG-CNTRC Beams: Gram-Schmidt-Ritz Method	2

A Class of Robust Low Dissipation Nested Multi-Resolution WENO Schemes for Solving Hyperbolic Conservation Laws	2
Finite-Time Stability and Instability of Nonlinear Impulsive Systems	2
A Linear Doubly Stabilized Crank-Nicolson Scheme for the Allen–Cahn Equation with a General Mobility	2
Interacting Stress Intensity Factors of Multiple Elliptical-Holes and Cracks Under Far-Field and Arbitrary Surface Stresses	2
A Simplified Lattice Boltzmann Method for Turbulent Flow Simulation	2
WENO Interpolation-Based and Upwind-Biased Free-Stream Preserving Nonlinear Schemes	2
Free Vibration of Stiffened Plate with Cracked Stiffeners	2
Construction of Non-Equilibrium Gas Distribution Functions Through Expansions in Peculiar Velocity Space	2
A Combination of High-Order Compact Finite Difference Schemes and a Splitting Method that Preserves Accuracy for the Multi-Dimensional Burgers' Equation	2
An Extension of the Order-Preserving Mapping to the WENO-Z-Type Schemes	2
$(1+s)$-Order Convergence Analysis of Weak Galerkin Finite Element Methods for Second Order Elliptic Equations	2
Numerical Solution for Neutral Delay Differential Equation of Constant or Proportional Type Using Hybrid Block Method	2
An Efficient Second-Order Finite Volume ADI Method for Nonlinear Three-Dimensional Space-Fractional Reaction-Diffusion Equations	2
Discontinuous Galerkin Methods for Semilinear Elliptic Boundary Value Problem	2
A Non-Singular Boundary Element Method for Interactions Between Acoustical Field Sources and Structures	2
A Well-Balanced FVC Scheme for 2D Shallow Water Flows on Unstructured Triangular Meshes	2
Vibration Behavior of a Sandwich Porous Elliptical Micro-Shell with a Magneto-Rheological Core Based on the Modified Couple Stress Theory	2