OOIR: Observatory of International Research

Papers

(The median citation count of Numerical Mathematics-Theory Methods and Applications is 0. 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 2021-04-01 to 2025-04-01.)

Article	Citations
The Discontinuous Galerkin Method by Divergence-Free Patch Reconstruction for Stokes Eigenvalue Problems	32
Symmetric-Adjoint and Symplectic-Adjoint Runge-Kutta Methods and Their Applications	25
A Robust Hybrid Spectral Method for Nonlocal Problems with Weakly Singular Kernels	18
Two-Phase Image Segmentation by the Allen-Cahn Equation and a Nonlocal Edge Detection Operator	15
A Second-Order Semi-Implicit Method for the Inertial Landau-Lifshitz-Gilbert Equation	15
Finding Symmetry Groups of Some Quadratic Programming Problems	9
A Third Order Accurate in Time, BDF-Type Energy Stable Scheme for the Cahn-Hilliard Equation	7
Novel High-Order Mass- and Energy-Conservative Runge-Kutta Integrators for the Regularized Logarithmic Schrödinger Equation	7
An Efficient Cartesian Grid-Based Method for Scattering Problems with Inhomogeneous Media	7
A Convergence Analysis of a Structure-Preserving Gradient Flow Method for the All-Electron Kohn-Sham Model	7
Long Time Energy and Kinetic Energy Conservations of Exponential Integrators for Highly Oscillatory Conservative Systems	5
An Alternating Direction Method of Multipliers for Inverse Lithography Problem	5
Character Modelling with Sketches and ODE-Based Shape Creation	5
A Fast Compact Block-Centered Finite Difference Method on Graded Meshes for Time-Fractional Reaction-Diffusion Equations and Its Robust Analysis	4
Analysis and Optimal Control of a System of Hemivariational Inequalities Arising in Non-Stationary Navier-Stokes Equation with Thermal Effects	4
Energy-Preserving Parareal-RKN Algorithms for Hamiltonian Systems	4
Analysis and Efficient Implementation of Quadratic Spline Collocation ADI Methods for Variable-Order Time-Fractional Mobile-Immobile Diffusion Equations	3
Frontal Slice Approaches for Tensor Linear Systems	3
A Modularized Algorithmic Framework for Interface Related Optimization Problems Using Characteristic Functions	3
L1/Local Discontinuous Galerkin Method for the Time-Fractional Stokes Equation	3
A Third-Order Implicit-Explicit Runge-Kutta Method for Landau-Lifshitz Equation with Arbitrary Damping Parameters	3
A Stabilized Physics Informed Neural Networks Method for Wave Equations	2
A Priori Error Estimate of Nonconforming Virtual Element Method for Convection Dominated Diffusion Equation	2
Error Analysis for Empirical Risk Minimization over Clipped ReLU Networks in Solving Linear Kolmogorov Partial Differential Equations	2
Linearized Double-Shock Approximate Riemann Solver for Augmented Linear Elastic Solid	2

An Algebraic Multigrid-Based Physical Factorization Preconditioner for the Multi-Group Radiation Diffusion Equations in Three Dimensions	2
A Second Order Accurate in Time, Energy Stable Finite Element Scheme for a Liquid Thin Film Coarsening Model	2
$R$-Adaptive DeepONet: Learning Solution Operators for PDEs with Discontinuous Solutions Using an R-Adaptive Strategy	2
Spectral Analysis for Preconditioning of Multi-Dimensional Riesz Fractional Diffusion Equations	2
An Accurate Numerical Scheme for Mean-Field Forward and Backward SDEs with Jumps	2
Mixed Finite Element Methods for the Ferrofluid Model with Magnetization Paralleled to the Magnetic Field	2
A Generalized Selectively Relaxed Matrix Splitting Preconditioning Strategy for Three-Dimensional Flux-Limited Multi-Group Radiation Diffusion Equations	2
Divergence-Free Virtual Element Method for the Stokes Equations with Damping on Polygonal Meshes	2
Robust Globally Divergence-Free Weak Galerkin Methods for Stationary Incompressible Convective Brinkman-Forchheimer Equations	2
Fusing Infrared and Visible Images via a First-Order Model	2
New Log Basis Functions with a Scaling Factor and Their Applications	2
On Discontinuous and Continuous Approximations to Second-Kind Volterra Integral Equations	1
The Recovery Guarantee for Orthogonal Matching Pursuit Method to Reconstruct Sparse Polynomials	1
Efficient and Accurate Numerical Methods Using the Accelerated Spectral Deferred Correction for Solving Fractional Differential Equations	1
Fast Second-Order Evaluation for Variable-Order Caputo Fractional Derivative with Applications to Fractional Sub-Diffusion Equations	1
A Variant Modified Skew-Normal Splitting Iterative Method for Non-Hermitian Positive Definite Linear Systems	1
The Variable-Step L1 Scheme Preserving a Compatible Energy Law for Time-Fractional Allen-Cahn Equation	1
The Direct Discontinuous Galerkin Method with Explicit-Implicit-Null Time Discretizations for Nonlinear Diffusion Equations	1
Convergent and Orthogonality Preserving Schemes for Approximating the Kohn-Sham Orbitals	1
An Extended Two-Step Method for Inverse Eigenvalue Problems with Multiple Eigenvalues	1
Sparse Deep Neural Network for Nonlinear Partial Differential Equations	1
Finite Element Error Estimation for Parabolic Optimal Control Problems with Pointwise Observations	1
Numerical Solution of Partial Differential Equations in Arbitrary Shaped Domains Using Cartesian Cut-Stencil Finite Difference Method. Part II: Higher-Order Schemes	1
Numerical Solution of a One-Dimensional Nonlocal Helmholtz Equation by Perfectly Matched Layers	1
Analysis of Anisotropic Nonlocal Diffusion Models: Well-Posedness of Fractional Problems for Anomalous Transport	1
Splitting ADI Scheme for Fractional Laplacian Wave Equations	1
A Nonlocal Stokes System with Volume Constraints	1
Absorbing Interface Conditions for the Simulation of Wave Propagation on Non-Uniform Meshes	1
Finite Difference Method for Inhomogeneous Fractional Dirichlet Problem	1
Convergence Analysis of a Quasi-Monte Carlo-Based Deep Learning Algorithm for Solving Partial Differential Equations	1
An Efficient Mapped WENO Scheme Using Approximate Constant Mapping	1
Space-Time Decomposition of Kalman Filter	1
The Direct Method of Lines for Forward and Inverse Linear Elasticity Problems of Composite Materials in Star-Shaped Domains	1
New Rational Interpolation Basis Functions on the Unbounded Intervals and Their Applications	1
The Immersed Interface Hybridized Difference Method for Parabolic Interface Problems	1
Convergence Analysis of OT-Flow for Sample Generation	1
Constructing Order Two Superconvergent WG Finite Elements on Rectangular Meshes	1
A New Fixed-Time Dynamical System for Absolute Value Equations	1
A Local Deep Learning Method for Solving High Order Partial Differential Equations	0
Conservative Three-Level Linearized Finite Difference Schemes for the Fisher Equation and Its Maximum Error Estimates	0
Semi-Discrete and Fully Discrete Weak Galerkin Finite Element Methods for a Quasistatic Maxwell Viscoelastic Model	0
Efficiently Training Physics-Informed Neural Networks via Anomaly-Aware Optimization	0
Stability of Spike Solutions to the Fractional Gierer-Meinhardt System in a One-Dimensional Domain	0
A Posteriori Error Analysis of a $P_2$-CDG Space-Time Finite Element Method for the Wave Equation	0
The Stabilized Finite Element Method for the Cahn-Hilliard Phase-Field Model of Diblock Copolymers on Evolving Surfaces	0
A Survey of the L1 Scheme in the Discretisation of Time-Fractional Problems	0
A Dual-Horizon Nonlocal Diffusion Model and Its Finite Element Discretization	0
Error Analysis of the Mixed Residual Method for Elliptic Equations	0
Penalized Schemes for Hamilton-Jacobi-Bellman Quasi-Variational Inequalities Arising in Regime Switching Utility Maximization with Optimal Stopping	0
PI-VEGAN: Physics Informed Variational Embedding Generative Adversarial Networks for Stochastic Differential Equations	0

Multidomain Hybrid Direct DG and Central Difference Methods for Viscous Terms in Hyperbolic-Parabolic Equations	0
Convergence of a Generalized Primal-Dual Algorithm with an Improved Condition for Saddle Point Problems	0
Finding Cheeger Cuts via 1-Laplacian of Graphs	0
Two-Step Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems	0
Richardson Extrapolation of the Euler Scheme for Backward Stochastic Differential Equations	0
Stability and Convergence of the Integral-Averaged Interpolation Operator Based on $Q_1$-Element in $\mathbb{R}^n$	0
Non-Local and Fully Connected Tensor Network Decomposition for Remote Sensing Image Denoising	0
Low Rank and Total Variation Based Two-Phase Method for Image Deblurring with Salt-and-Pepper Impulse Noise	0
Error Estimate of a New Conservative Finite Difference Scheme for the Klein-Gordon-Dirac System	0
High Order Mixed Finite Elements with Mass Lumping for Elasticity on Triangular Grids	0
A Class of Efficient Multistep Methods for Forward Backward Stochastic Differential Equations	0
An Efficient Variational Model for Multiplicative Noise Removal	0
A Riemannian Inertial Mann Algorithm for Nonexpansive Mappings on Hadamard Manifolds	0
Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations	0
Geometric Design of Letters in Times Roman Font via RBF Meshless Collocation Method	0
Analysis of Deep Ritz Methods for Semilinear Elliptic Equations	0
A Hybrid Scheme of Level Set and Diffuse Interface Methods for Simulating Multi-Phase Compressible Flows	0
Efficient Hermite Spectral-Galerkin Methods for Nonlocal Diffusion Equations in Unbounded Domains	0
An Adaptive Physics-Informed Neural Network with Two-Stage Learning Strategy to Solve Partial Differential Equations	0
On Lagrange-Projection Schemes for Shallow Water Flows over Movable Bottom with Suspended and Bedload Transport	0
HRW: Hybrid Residual and Weak Form Loss for Solving Elliptic Interface Problems with Neural Network	0
An Extended Courant Element on a Polytope with Application in Approximating an Obstacle Problem	0
Galerkin Finite Element Approximation for Semilinear Stochastic Time-Tempered Fractional Wave Equations with Multiplicative Gaussian Noise and Additive Fractional Gaussian Noise	0
Manifold Triangular Mesh Editing Based on Finite Differences and Fourier Series	0
Application of Adapted-Bubbles to the Helmholtz Equation with Large Wavenumbers in 2D	0
On Polar Decomposition of Tensors with Einstein Product and a Novel Iterative Parametric Method	0
Enhancing RBF-FD Efficiency for Highly Non-Uniform Node Distributions via Adaptivity	0
A Structure-Preserving JKO Scheme for the Size-Modified Poisson-Nernst-Planck-Cahn-Hilliard Equations	0
A Novel Iterative Method to Find the Moore-Penrose Inverse of a Tensor with Einstein Product	0
A Finite Volume Simple WENO Scheme for Convection-Diffusion Equations	0
A BDF2-SSAV Numerical Scheme with Fourier-Spectral Method for a Droplet Thin Film Coarsening Model	0
Maximum-Principle-Preserving High-Order Conservative Difference Schemes for Convection-Dominated Diffusion Equations	0
Unconditional Convergence of Linearized TL1 Difference Methods for a Time-Fractional Coupled Nonlinear Schrödinger System	0
On Quadratic Wasserstein Metric with Squaring Scaling for Seismic Velocity Inversion	0
A Study on CFL Conditions for the DG Solution of Conservation Laws on Adaptive Moving Meshes	0
Multi-Phase Segmentation Using Modified Complex Cahn-Hilliard Equations	0
On the Recovery of Source Term for Fractional Evolution PDEs by MC-fPINNs	0
New Sixth-Order Compact Schemes for Poisson/Helmholtz Equations	0
Stability and Error Analysis of SAV Semi-Discrete Scheme for Cahn-Hilliard-Navier-Stokes Model	0
Fourier Convergence Analysis for a Fokker-Planck Equation of Tempered Fractional Langevin-Brownian Motion	0
A Convergence Study of SGD-Type Methods for Stochastic Optimization	0
ODE-Based Multistep Schemes for Backward Stochastic Differential Equations	0
The MFE-CFE-GFE Method for the Fully Coupled Quasi-Static Thermo-Poroelastic Problem	0
The Relation Between a Tensor and Its Associated Semi-Symmetric Form	0
Novel Partitioned Time-Stepping Algorithms for Fast Computation of Random Interface-Coupled Problems with Uncertain Parameters	0
Approximation of the Spectral Fractional Powers of the Laplace-Beltrami Operator	0
A Unified Fast Memory-Saving Time-Stepping Method for Fractional Operators and Its Applications	0
Numerical Integration Formulas for Hypersingular Integrals	0
Artificial Boundary Conditions for Time-Fractional Telegraph Equation	0
Multi-Dimensional Image Recovery via SelfSupervised Nonlinear Transform Based a Three-Directional Tensor Nuclear Norm	0
Two Dynamical Models Based on Projection Operator for Solving the System of Absolute Value Equations Associated with Second-Order Cone	0
Dual Control Methods for a Mixed Control Problem with Optimal Stopping Arising in Optimal Consumption and Investment	0
Greedy Kaczmarz Algorithm Using Optimal Intermediate Projection Technique for Coherent Linear Systems	0
A Physics-Informed Structure-Preserving Numerical Scheme for the Phase-Field Hydrodynamic Model of Ternary Fluid Flows	0
Green Function Method for Quantum Transport Based on the Generalized Fourier Transform	0
A Stabilizer Free Weak Galerkin Finite Element Method for Elliptic Equation with Lower Regularity	0
Numerical Continuation and Bifurcation for Differential Geometric PDEs	0
A Divergence-Free Pk CDG Finite Element for the Stokes Equations on Triangular and Tetrahedral Meshes	0
Convergence of Weak Galerkin Finite Element Method for Second Order Linear Wave Equation in Heterogeneous Media	0
A Lagrangian Discontinuous Galerkin Scheme for the Compressible Euler Equations on Unstructured Triangular Meshes	0
MC-Nonlocal-PINNs: Handling Nonlocal Operators in PINNs via Monte Carlo Sampling	0
A Robust Modified Weak Galerkin Finite Element Method for Reaction-Diffusion Equations	0
An Energy Stable Filtered Backward Euler Scheme for the MBE Equation with Slope Selection	0
Numerical Algorithm with Fourth-Order Spatial Accuracy for Solving the Time-Fractional Dual-Phase-Lagging Nanoscale Heat Conduction Equation	0
New Splitting Algorithms for Multiplicative Noise Removal Based on Aubert-Aujol Model	0
Convergence Analysis of Split-Douglas-Rachford Algorithm and a Novel Preconditioned ADMM with an Improved Condition	0
Linearized Transformed $L1$ Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schrödinger Equations	0
Local MFS Matrix Decomposition Algorithms for Elliptic BVPs in Annuli	0
Hierarchical Absorbing Interface Conditions for Wave Propagation on Non-Uniform Meshes	0
Projection Improved SPAI Preconditioner for FGMRES	0
A Novel Class of Energy-Preserving Runge-Kutta Methods for the Korteweg-de Vries Equation	0