Advances in Applied Mathematics and Mechanics

Papers
(The TQCC of Advances in Applied Mathematics and Mechanics is 3. 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 2020-05-01 to 2024-05-01.)
ArticleCitations
A Localized Space-Time Method of Fundamental Solutions for Diffusion and Convection-Diffusion Problems52
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 Equation23
An Analytical Solution for Nonlinear Vibration Analysis of Functionally Graded Rectangular Plate in Contact with Fluid21
High-Order Accurate Entropy Stable Finite Difference Schemes for One- and Two-Dimensional Special Relativistic Hydrodynamics18
Multiple-Relaxation-Time Lattice Boltzmann Simulation of Magnetic Field Effect on Natural Convection of Non-Newtonian Nanofluid in Rectangular Enclosure15
Localized Method of Fundamental Solutions for Acoustic Analysis Inside a Car Cavity with Sound-Absorbing Material12
Singularity of Navier-Stokes Equations Leading to Turbulence11
Convergence Analysis and Error Estimate for Distributed Optimal Control Problems Governed by Stokes Equations with Velocity-Constraint11
A Second Order Accurate in Time, Energy Stable Finite Element Scheme for the Flory-Huggins-Cahn-Hilliard Equation10
Efficient Preconditioned Iterative Linear Solvers for 3-D Magnetostatic Problems Using Edge Elements9
Two-Grid Finite Volume Element Method Combined with Crank-Nicolson Scheme for Semilinear Parabolic Equations9
Electroelastic Analysis of Two-Dimensional Piezoelectric Structures by the Localized Method of Fundamental Solutions8
A Two-Level Factored Crank-Nicolson Method for Two-Dimensional Nonstationary Advection-Diffusion Equation With Time Dependent Dispersion Coefficients and Source Terms8
A Compact Difference Scheme for the Time-Fractional Partial Integro-Differential Equation with a Weakly Singular Kernel7
A Two-Grid Finite-Volume Method for the Schrodinger Equation7
A New Explicit Immersed Boundary Method for Simulation of Fluid-Solid Interactions7
A New Conservative Allen-Cahn Type Ohta-Kawaski Phase-Field Model for Diblock Copolymers and Its Numerical Approximations7
Ultra-Chaos: An Insurmountable Objective Obstacle of Reproducibility and Replication7
Transient Response of High Dimensional Nonlinear Dynamic System for a Rotating Cantilever Twisted Plate6
Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay6
Arbitrarily High-Order Energy-Preserving Schemes for the Camassa-Holm Equation Based on the Quadratic Auxiliary Variable Approach6
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 Images5
Non-Convex and Convex Coupling Image Segmentation via TGpV Regularization and Thresholding5
Numerical Schemes for Time-Space Fractional Vibration Equations5
An Analytical Approach for Nonlinear Buckling Analysis of Torsionally Loaded Sandwich Carbon Nanotube Reinforced Cylindrical Shells with Auxetic Core4
Unconditional Stability and Error Estimates of the Modified Characteristics FEM for the Time-Dependent Viscoelastic Oldroyd Flows4
Two-Grid Stabilized FEMs Based on Newton Type Linearization for the Steady-State Natural Convection Problem4
The Weak Galerkin Finite Element Method for Solving the Time-Dependent Integro-Differential Equations4
A Posteriori Error Estimates of the Galerkin Spectral Methods for Space-Time Fractional Diffusion Equations4
Performance Comparison on Parallel CPU and GPU Algorithms for Two Dimensional Unified Gas-Kinetic Scheme4
Lattice Boltzmann Model for Time-Fractional Nonlinear Wave Equations4
A Jacobi Collocation Method for the Fractional Ginzburg-Landau Differential Equation4
High-Order Well-Balanced Finite Volume WENO Schemes with Conservative Variables Decomposition for Shallow Water Equations4
A Stabilizer-Free Weak Galerkin Finite Element Method for the Stokes Equations4
A Variable Correction-Based Immersed Boundary Method for Compressible Flows over Stationary and Moving Bodies4
A Fifth Order Alternative Mapped WENO Scheme for Nonlinear Hyperbolic Conservation Laws4
Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation4
A Robust Riemann Solver for Multiple Hydro-Elastoplastic Solid Mediums4
Fast Prediction of Immiscible Two-Phase Displacements in Heterogeneous Porous Media with Convolutional Neural Network4
Exponential Time Differencing Schemes for the Peng-Robinson Equation of State with Preservation of Maximum Bound Principle3
Image Segmentation via Fischer-Burmeister Total Variation and Thresholding3
The Crank-Nicolson/Explicit Scheme for the Natural Convection Equations with Nonsmooth Initial Data3
An Efficient Numerical Method for the Valuation of American Better-of Options Based on the Front-Fixing Transform and the Far Field Truncation3
A Symplectic Conservative Perturbation Series Expansion Method for Linear Hamiltonian Systems with Perturbations and Its Applications3
A Fully Discrete Explicit Multistep Scheme for Solving Coupled Forward Backward Stochastic Differential Equations3
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
Waves Induced by the Appearance of Single-Point Heat Source in Constant Flow3
Broad Learning System with Preprocessing to Recover the Scattering Obstacles with Far–Field Data3
An Energy Stable SPH Method for Incompressible Fluid Flow3
Anisotropic Yield Criterion for Metals Exhibiting Tension–Compression Asymmetry3
A Discontinuous Galerkin Method by Patch Reconstruction for Convection-Diffusion Problems3
Legendre Neural Network for Solving Linear Variable Coefficients Delay Differential-Algebraic Equations with Weak Discontinuities3
A Second-Order Energy Stable BDF Numerical Scheme for the Viscous Cahn-Hilliard Equation with Logarithmic Flory-Huggins Potential3
Unconditional Optimal Error Estimates for the Transient Navier-Stokes Equations with Damping3
A Coercivity Result of Quadratic Finite Volume Element Schemes over Triangular Meshes3
Coiflet Wavelet-Homotopy Solutions to Bio-Thermal Convection in a Square Cavity3
Finite Element Methods for Nonlinear Backward Stochastic Partial Differential Equations and Their Error Estimates3
An Energy-Preserving Scheme for the Coupled Gross-Pitaevskii Equations3
Finite Element Method Coupling Penalty Method for Flexural Shell Model3
Impacts of Down-Up Hill Segment on the Threshold of Shock Formation of Ring Road Vehicular Flow3
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
A Novel B-Spline Method for Modeling Transport Problems in Anisotropic Inhomogeneous Media3
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