OOIR: Observatory of International Research

Papers

(The TQCC of Numerical Mathematics-Theory Methods and Applications is 1. 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
A Second-Order Semi-Implicit Method for the Inertial Landau-Lifshitz-Gilbert Equation	15
Two-Phase Image Segmentation by the Allen-Cahn Equation and a Nonlocal Edge Detection Operator	15
Finding Symmetry Groups of Some Quadratic Programming Problems	9
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
A Third Order Accurate in Time, BDF-Type Energy Stable Scheme for the Cahn-Hilliard Equation	7
An Alternating Direction Method of Multipliers for Inverse Lithography Problem	5
Character Modelling with Sketches and ODE-Based Shape Creation	5
Long Time Energy and Kinetic Energy Conservations of Exponential Integrators for Highly Oscillatory Conservative Systems	5
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
A Fast Compact Block-Centered Finite Difference Method on Graded Meshes for Time-Fractional Reaction-Diffusion Equations and Its Robust Analysis	4
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
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 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
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
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
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