Communications in Computational Physics

Article	Citations
A Third Order Bound-Preserving Nodal Discontinuous Galerkin Method for Miscible Displacements in Porous Media	32
An Efficient Numerical Algorithm for Solving Coupled Time-Dependent Ginzburg-Landau Equation for Superconductivity and Elasticity	23
Convergence Analysis of PINNs with Over-Parameterization	20
Capturing Vertical Information in Radially Symmetric Flow Using Hyperbolic Shallow Water Moment Equations	19
An Improved Diffuse-Interface Lattice Boltzmann Method for Particulate Flows	17
On the Solution Accuracy Downstream of Shocks When Using Godunov-Type Schemes. I. Sources of Errors in One-Dimensional Problems	17
High-Order Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for Euler Equations with Gravitation on Unstructured Meshes	16
Asymptotic-Preserving Discretization of Three-Dimensional Plasma Fluid Models	16
Mandelic Acid Single-Crystal Growth: Experiments VS Numerical Simulations	16
Monotonicity Correction for the Finite Element Method of Anisotropic Diffusion Problems	15
A Multiscale Algorithm to Drastically Reduce Computational Times When Simulating Liquid/Solid Interaction at Atomic Resolution with Realistic Hydrodynamics Effects	15
Geometric Decomposition and Efficient Implementation of High Order Face and Edge Elements	15
A Well-Balanced Positivity-Preserving Quasi-Lagrange Moving Mesh DG Method for the Shallow Water Equations	15
A Priori Subcell Limiting Approach for the FR/CPR Method on Unstructured Meshes	14
Adaptive Ensemble Kalman Inversion with Statistical Linearization	14
A Simulation Approach Including Underresolved Scales for Two-Component Fluid Flows in Multiscale Porous Structures	14
Thermal Regulation in Thin Vascular Systems: A Sensitivity Analysis	14
Dynamical Demixing of a Binary Mixture Under Sedimentation	12
Tree-Based Implementation of the Small Matrix Path Integral for System-Bath Dynamics	12
A Conservative and Monotone Characteristic Finite Element Solver for Three-Dimensional Transport and Incompressible Navier-Stokes Equations on Unstructured Grids	12
A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions	11
Numerical Integrators for Dispersion-Managed KdV Equation	11
Modeling of Bound Electron Effects in Particle-in-Cell Simulation	11
A Unifying Moving Mesh Method for Curves, Surfaces, and Domains Based on Mesh Equidistribution and Alignment	11
Dimension-Free Ergodicity of Path Integral Molecular Dynamics	11

Splitting Physics-Informed Neural Networks for Inferring the Dynamics of Integer- and Fractional-Order Neuron Models	11
A 2D Fourth-Order CESE Scheme for Solving the Ideal MHD Equations	10
High Order Deep Neural Network for Solving High Frequency Partial Differential Equations	10
A Second-Order Length-Preserving and Unconditionally Energy Stable Rotational Discrete Gradient Method for Oseen-Frank Gradient Flows	10
Application of MUSIC Algorithm for Object Localization Without Diagonal Elements of Multi-Static Response Matrix	10
Kinetic Slip Boundary Condition for Isothermal Rarefied Gas Flows Through Static Non-Planar Geometries Based on the Regularized Lattice-Boltzmann Method	9
Stabilized Continuous Linear Element Method for the Biharmonic Problems	9
A New Upwind Finite Volume Element Method for Convection-Diffusion-Reaction Problems on Quadrilateral Meshes	8
The Lowest-Order Stabilized Virtual Element Method for the Stokes Problem	8
A Mixed Finite Element Scheme for Biharmonic Equation with Variable Coefficient and von Kármán Equations	8
A Parallel Domain Decomposition Method for the Fully-Mixed Stokes-Dual-Permeability Fluid Flow Model with Beavers-Joseph Interface Conditions	8
A Simple GPU Implementation of Spectral-Element Methods for Solving 3D Poisson Type Equations on Rectangular Domains and Its Applications	7
A Quadratic Serendipity Finite Volume Element Method on Arbitrary Convex Polygonal Meshes	7
A Parallel Fully Implicit Unstructured Finite Volume Lattice Boltzmann Method for Incompressible Flows	7
A Penalty-Free or Penalty-Factor-Free DG Method with a Locally Reconstructed Curl Operator for the Maxwell Eigenproblem	7
A Noise and Vibration Tolerant ResNet for Field Reconstruction with Sparse Sensors	7
Modeling Thermal Regulation in Thin Vascular Systems: A Mathematical Analysis	7
An Augmented Lagrangian Deep Learning Method for Variational Problems with Essential Boundary Conditions	7
Unconstrained ETD Methods on the Diffuse-Interface Model with the Peng-Robinson Equation of State	7
Active Nematodynamics on Curved Surfaces – The Influence of Geometric Forces on Motion Patterns of Topological Defects	7
Anomalous Sorption Kinetics of Self-Interacting Particles by a Spherical Trap	7
Mesh Adaptation for Curing the Pathological Behaviors of an Upwind Scheme	7
First-Principle-Like Reinforcement Learning of Nonlinear Numerical Schemes for Conservation Laws	7
Nonconforming Finite Elements for the −curl∆curl and Brinkman Problems on Cubical Meshes	6
A Simple Strategy for Multi-Material Diffusion and Its Application to Three-Temperature Multi-Material Flows	6
An Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Scheme for Compressible Multi-Material Flows on Adaptive Quadrilateral Meshes	6
Two-Scale Neural Networks for Partial Differential Equations with Small Parameters	6
Unified Gas-Kinetic Wave-Particle Methods VI: Disperse Dilute Gas-Particle Multiphase Flow	6
A Novel Structure-Preserving Algorithm with Green’s Function Approach for Computing Band Structures of Photonic Quasicrystals	6
Extension of Near-Wall Domain Decomposition to Modeling Flows with Laminar-Turbulent Transition	6
A DDG Method with a Residual-Based Artificial Viscosity for the Transonic/Supersonic Compressible Flow	6
Fast Implementation of FEM for Integral Fractional Laplacian on Rectangular Meshes	6
Frame Invariance and Scalability of Neural Operators for Partial Differential Equations	6
An Efficient Iterative Method for the Formulation of Flow Networks	6
MHDnet: Physics-Preserving Learning for Solving Magnetohydrodynamics Problems	5
A Quantitative Comparison of Physical Accuracy and Numerical Stability of Lattice Boltzmann Color Gradient and Pseudopotential Multicomponent Models for Microfluidic Applications	5
A Well-Balanced Lattice Boltzmann Model for Binary Fluids Based on the Incompressible Phase-Field Theory	5
A Weak Galerkin Mixed Finite Element Method for Second Order Elliptic Equations on 2D Curved Domains	5
Weak Collocation Regression for Inferring Stochastic Dynamics with Lévy Noise	5
Optimal Error Estimates of a Discontinuous Galerkin Method for Stochastic Allen-Cahn Equation Driven by Multiplicative Noise	5
An Adaptive Modal Discontinuous Galerkin Finite Element Parallel Method Using Unsplit Multi-Axial Perfectly Matched Layer for Seismic Wave Modeling	5
Finite Difference Approximation with ADI Scheme for Two-Dimensional Keller-Segel Equations	5
Second-Order Linear Stabilized Semi-Implicit Crank-Nicolson Scheme for the Cahn-Hilliard Model with Dynamic Boundary Conditions	5
Well-Balanced Central Scheme for the System of MHD Equations with Gravitational Source Term	5
Reliability Investigation of BiCGStab and IDR Solvers for the Advection-Diffusion-Reaction Equation	5
High-Order Accurate Entropy Stable Finite Difference Schemes for the Compressible Euler Equations with the van der Waals Equation of State on Adaptive Moving Meshes	5
On the Monotonicity of $Q^2$ Spectral Element Method for Laplacian on Quasi-Uniform Rectangular Meshes	5
High Order Compact Hermite Reconstructions and Their Application in the Improved Two-Stage Fourth Order Time-Stepping Framework for Hyperbolic Problems: Two-Dimensional Case	5
Efficient Splitting Methods Based on Modified Potentials: Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrödinger Equation	5
Numerical Study on Viscous Fingering Using Electric Fields in a Hele-Shaw Cell	4

Application of Computational Modelling to Particle Physics	4
A GPU-Accelerated Cartesian Grid Method for PDEs on Irregular Domain	4
High Order Finite Difference Hermite WENO Fixed-Point Fast Sweeping Method for Static Hamilton-Jacobi Equations	4
A Correction and Comments on “Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains CiCP, 28 (5): 1970–2001, 2020”	4
A Posteriori Error Estimate of Weak Galerkin FEM for Stokes Problem Using Auxiliary Subspace Techniques	4
Learning PDEs from Data on Closed Surfaces with Sparse Optimization	4
An Improved Peridynamic Model with Energy-Based Micromodulus Correction Method for Fracture in Particle Reinforced Composites	4
Exact Solution of the Riemann Problem for the One-Dimensional Blood Flow Equations with General Constant Momentum Correction Coefficient	4
Investigating and Mitigating Failure Modes in Physics-Informed Neural Networks (PINNs)	4
Structure-Preserving Finite-Element Schemes for the Euler-Poisson Equations	4
Hamiltonian Reduction Using a Convolutional Auto-Encoder Coupled to a Hamiltonian Neural Network	4
Discontinuous Galerkin Method for the Coupled Dual-Porosity-Navier-Stokes Model	4
A Fourth-Order Kernel-Free Boundary Integral Method for Interface Problems	4
A Network Based Approach for Unbalanced Optimal Transport on Surfaces	4
Immersed Boundary Approach to Biofilm Spread on Surfaces	4
High Moment and Pathwise Error Estimates for Fully Discrete Mixed Finite Element Approximations of Stochastic Navier-Stokes Equations with Additive Noise	4
A Nonnested Augmented Subspace Method for Kohn-Sham Equation	4
Towards the Efficient Calculation of Quantity of Interest from Steady Euler Equations I: A Dual-Consistent DWR-Based $h$-Adaptive Newton-GMG Solver	4
High-Order Cell-Centered Lagrangian Spectral Volume Method on Curvilinear Meshes	4
A Hybrid WENO Scheme for Steady Euler Equations in Curved Geometries on Cartesian Grids	4
An Adaptive Method Based on Local Dynamic Mode Decomposition for Parametric Dynamical Systems	4
An Iterative Thresholding Method for the Minimum Compliance Problem	3
Within-Cluster Variability Exponent for Identifying Coherent Structures in Dynamical Systems	3
Implicit Quadrature-Free Direct Reconstruction Method for Efficient Scale-Resolving Simulations	3
Effective Force Stabilising Technique for the Immersed Boundary Method	3
Fourier Collocation and Reduced Basis Methods for Fast Modeling of Compressible Flows	3
A Symplectic Based Neural Network Algorithm for Quantum Controls under Uncertainty	3
The Corrected Finite Volume Element Methods for Diffusion Equations Satisfying Discrete Extremum Principle	3
Multilevel Constrained Pressure-Temperature Residual Preconditioners for Large-Scale Non-Isothermal Reservoir Simulation via Restricted Additive Schwarz Algorithms	3
High-Order Low-Dissipation Shock-Resolving TENO-THINC Schemes for Hyperbolic Conservation Laws	3
Direct Simulation of Charge Transport in Graphene Nanoribbons	3
Asymptotic-Preserving Neural Networks for Multiscale Kinetic Equations	3
RBMD: A Molecular Dynamics Package Enabling to Simulate 10 Million All-Atom Particles in a Single Graphics Processing Unit	3
Monotonic Diamond and DDFV Type Finite-Volume Schemes for 2D Elliptic Problems	3
A Second-Order Implicit-Explicit Scheme for the Baroclinic-Barotropic Split System of Primitive Equations	3
Development of a Less Dissipative Interface Variable Reconstruction to Solve the Euler Equations by Q Learning Method	3
An Efficient High-Order Gas-Kinetic Scheme with Hybrid WENO-AO Method for the Euler and Navier-Stokes Solutions	3
AutoAMG($θ$): An Auto-Tuned AMG Method Based on Deep Learning for Strong Threshold	3
Entropic Multi-Relaxation-Time Lattice Boltzmann Model for Large Density Ratio Two-Phase Flows	3
The Effects of Spatial Reconstruction and Flux Solver on the Performance of High-Order Finite-Volume Compressible Flow Solvers	3
High-Order Spectral Simulation of Dispersive Two-Dimensional Materials	3
Convergence of Physics-Informed Neural Networks Applied to Linear Second-Order Elliptic Interface Problems	3
The Bulk-Surface Virtual Element Method for Reaction-Diffusion PDEs: Analysis and Applications	3
Convergence Rate Analysis for Deep Ritz Method	3
Deep Learning-Based Computational Method for Soft Matter Dynamics: Deep Onsager-Machlup Method	3
A Stochastic Gradient Descent Method for Computational Design of Random Rough Surfaces in Solar Cells	3
Chromodynamic Lattice Boltzmann Method for the Simulation of Drops, Erythrocytes, and Other Vesicles	3
A New Function Space from Barron Class and Application to Neural Network Approximation	3
Inverse Design of Strained Graphene Surfaces for Electron Control	3
A Review on Contact and Collision Methods for Multi-Body Hydrodynamic Problems in Complex Flows	3
AFEPack: A General-Purpose C++ Library for Numerical Solutions of Partial Differential Equations	2
A High Order Positivity-Preserving Discontinuous Galerkin Remapping Method Based on a Moving Mesh Solver for ALE Simulation of the Compressible Fluid Flow	2
A Two-Dimensional Third-Order CESE Scheme for Ideal MHD Equations	2
Eulerian Algorithms for Computing the Forward Finite Time Lyapunov Exponent Without Finite Difference upon the Flow Map	2
Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Scheme for the Thermal Rotating Shallow Water Equations	2
An Adaptive Moving Mesh Method for the Five-Equation Model	2
A One-Dimensional Second-Order Cell-Centered Lagrangian Scheme Satisfying the Entropy Condition	2
Nonlinear Reduced DNN Models for State Estimation	2
An Explicit Multi-Time Stepping Algorithm for Multi-Time Scale Coupling Problems in SPH	2
High Order Bound- and Positivity-Preserving Finite Difference Affine-Invariant AWENO Scheme for the Five-Equation Model of Two-Medium Flows	2
Improved Randomized Neural Network Methods with Boundary Processing for Solving Elliptic Equations	2
A New Mapped WENO Scheme Using Order-Preserving Mapping	2
Analysis of a Mixed Finite Element Method for Stochastic Cahn-Hilliard Equation with Multiplicative Noise	2
A Provably Positive-Preserving HLLD Riemann Solver for Ideal Magnetohydrodynamics. Part I: The One-Dimensional Case	2
New Insights on Convergence Properties of Peridynamic Models for Transient Diffusion and Elastodynamics	2
A Characteristic Mapping Method for Vlasov-Poisson with Extreme Resolution Properties	2
Variational Low-Light Image Enhancement Based on Fractional-Order Differential	2
An Adaptive Polygonal Finite Volume Element Method Based on the Mean Value Coordinates for Anisotropic Diffusion Problems	2
Inexact Block LU Preconditioners for Incompressible Fluids with Flow Rate Conditions	2
Integral Equation Method for a Non-Selfadjoint Steklov Eigenvalue Problem	2
Lattice Boltzmann Modeling of Cholesteric Liquid Crystal Droplets Under an Oscillatory Electric Field	2
A Multigrid Discretization of Discontinuous Galerkin Method for the Stokes Eigenvalue Problem	2
A High Order Bound Preserving Finite Difference Linear Scheme for Incompressible Flows	2
A Fast Offline/Online Forward Solver for Stationary Transport Equation with Multiple Inflow Boundary Conditions and Varying Coefficients	2
A Rate of Convergence of Weak Adversarial Neural Networks for the Second Order Parabolic PDEs	2
A Novel High-Order Shock-Capturing Limiter for RKDG Method on Unstructured Meshes via TENO Selection Strategies	2
Ghost-Fluid-Based Sharp Interface Methods for Multi-Material Dynamics: A Review	2
Comparison of Lattice Boltzmann, Finite Element and Volume of Fluid Multicomponent Methods for Microfluidic Flow Problems and the Jetting of Microdroplets	2
Hybrid Finite Difference Fifth-Order Multi-Resolution WENO Scheme for Hamilton-Jacobi Equations	2
A Deep Spatio-Temporal Forecasting Model for Multi-Site Weather Prediction Post-Processing	2

Analysis of Discontinuity Detectors and Hybrid WCNS Schemes Based on Waveform Recognition	2
Application of Continuous Data Assimilation in High-Resolution Ocean Modeling	2
Computational Method of Grain Boundary Energy Consistent for Different Orientations and Applications to Double Gyroid Beyond Twinning	2
New Algebraic Fast Algorithms for $N$-Body Problems in Two and Three Dimensions	2
General Synthetic Iterative Scheme for Unsteady Rarefied Gas Flows	2
Generalization Error Analysis of Neural Networks with Gradient Based Regularization	2
High Order Multiscale Methods for Advection-Diffusion Equation in Highly Oscillatory Regimes: Application to Surfactant Diffusion and Generalization to Arbitrary Domains	2
Learning Specialized Activation Functions for Physics-Informed Neural Networks	2
Solution Remapping Method with Lower Bound Preservation for Navier-Stokes Equations in Aerodynamic Shape Optimization	2
A Genuinely Two-Dimensional Approximate Riemann Solver with Stress Continuity for Hypo-Elastic Solids	2
Symmetry Preservation by a Compatible Staggered Lagrangian Scheme Using the Control-Volume Discretization Method in $r–z$ Coordinate	2
Benchmark Computation of Morphological Complexity in the Functionalized Cahn-Hilliard Gradient Flow	2
Lattice Boltzmann Modeling of Non-Newtonian Fluid Flows Under Non-Linear Slip Velocity Boundary Conditions in Microchannels	2
A New Approximate Method to Mean Field Stochastic Differential Equation with One-Sided Lipschitz Drift Coefficient	1
Modelling and Numerical Shape and Topology Optimization for a Hemivariational Inequality in Stokes Flows with Slip Boundary Conditions	1
Convergence Analysis for Over-Parameterized Deep Learning	1
Three Dimensional Dynamics of Polar Fluids: A Lattice Boltzmann Approach	1
Finite-Volume TENO Scheme with a New Cell-Interface Flux Evaluation Strategy for Unstructured Meshes	1
Aerodynamic Performance and Data-Driven Optimization of Flow Past an Inclined Rounded Square Cylinder	1
VAE-KRnet and Its Applications to Variational Bayes	1
Lattice Boltzmann Simulations of Two Linear Microswimmers Using the Immersed Boundary Method	1
Random Batch Particle Methods for the Homogeneous Landau Equation	1
Adaptive Interface-PINNs (AdaI-PINNs): An Efficient Physics-Informed Neural Networks Framework for Interface Problems	1
A $H^T_N$-Based UGKS Scheme for the Three-Temperature Radiative Transfer Equations	1
VPVnet: A Velocity-Pressure-Vorticity Neural Network Method for the Stokes’ Equations under Reduced Regularity	1
A Rate of Convergence of Physics Informed Neural Networks for the Linear Second Order Elliptic PDEs	1
Bjorken Flow Revisited: Analytic and Numerical Solutions in Flat Space-Time Coordinates	1
A Conservative and Positivity-Preserving Method for Solving Anisotropic Diffusion Equations with Deep Learning	1
Closed-Loop Geothermal Systems: Modeling and Predictions	1
Adaptive Neural Network Basis Methods for Partial Differential Equations with Low-Regular Solutions	1
Sixth-Order Compact Finite Difference Method for 2D Helmholtz Equations with Singular Sources and Reduced Pollution Effect	1
Numerical Reconstruction of Locally Rough Surfaces with a Newton Iterative Algorithm	1
A Lightweight Data-Driven Model Enhanced Discontinuous Galerkin Method for Rapidly Simulating Transonic Airfoil Flowfields	1
A Second-Order Langevin Sampler Preserving Positive Volume for Isothermal–Isobaric Ensemble	1
Fast-Converging and Asymptotic-Preserving Simulation of Frequency Domain Thermoreflectance	1
A Determinant Aided Fixed Point Method for Nonlinear Coupled Constitutive Relation of Rarefied Nonequilibrium Flows	1
Numerical Solutions of the Electromagnetic Scattering by Overfilled Cavities with Inhomogeneous Anisotropic Media	1
A Class of Second-Order Energy-Stable Schemes for the Cahn-Hilliard Equation and Their Linear Iteration Algorithm	1
Asymptotic-Preserving Schemes for Kinetic-Fluid Modeling of Mixture Flows	1
A New Directional Algebraic Fast Multipole Method Based Iterative Solver for the Lippmann-Schwinger Equation Accelerated with HODLR Preconditioner	1
Efficient Energy-Stable Parametric Finite Element Methods for Surface Diffusion Flow and Applications in Solid-State Dewetting	1
Operator Splitting and Local Time-Stepping Methods for Transport Problems in Fractured Porous Media	1
Solving Time Dependent Fokker-Planck Equations via Temporal Normalizing Flow	1
Random Walk Approximation for Irreversible Drift-Diffusion Process on Manifold: Ergodicity, Unconditional Stability and Convergence	1
A Positivity-Preserving and Well-Balanced High Order Compact Finite Difference Scheme for Shallow Water Equations	1
Generalized Lagrangian Neural Networks	1
A Second Order Numerical Scheme of the Cahn-Hilliard-Navier-Stokes System with Flory-Huggins Potential	1
Data Generation-Based Operator Learning for Solving Partial Differential Equations on Unbounded Domains	1
Weak Galerkin Method for Second-Order Elliptic Equations with Newton Boundary Condition	1
Unfitted Spectral Element Method for Interfacial Models	1
A Consensus-Based Global Optimization Method with Adaptive Momentum Estimation	1
Hyperbolic Divergence Cleaning in Lattice Boltzmann Magnetohydrodynamics	1
A Moving Mesh Finite Element Method for Bernoulli Free Boundary Problems	1
Electromagnetic Gyrokinetic Simulation of Tokamak Plasma with Semi-Lagrangian Scheme	1
Mortar Finite Element Method for the Coupling of Time Dependent Navier-Stokes and Darcy Equations	1
A Stable Arbitrarily High Order Time-Stepping Method for Thermal Phase Change Problems	1
The Positivity-Preserving Finite Volume Coupled with Finite Element Method for the Keller-Segel-Navier-Stokes Model	1
Moment-Based Multi-Resolution HWENO Scheme for Hyperbolic Conservation Laws	1
A Normalizing Field Flow Induced Two-Stage Stochastic Homogenization Method for Random Composite Materials	1
A Genuinely Two-Dimensional HLL-Type Approximate Riemann Solver for Hypo-Elastic Plastic Flow	1
An Arbitrary Order Mixed Finite Element Method with Boundary Value Correction for the Darcy Flow on Curved Domains	1
Numerical Solution of the Incompressible Navier-Stokes Equation by a Deep Branching Algorithm	1
Approximating the Gaussian as a Sum of Exponentials and Its Applications to the Fast Gauss Transform	1
Uncertainty Quantification for Charge Transport in GNRs Through Particle Galerkin Methods for the Semiclassical Boltzmann Equation	1
Transition Pathways in Cylinder-Gyroid Interface	1
A Four-State HLL Riemann Solver for Numerical Simulation of Magneto-Hydrodynamics Based on the Least Squares Solution for the Middle Wave	1
Vortex Spline Method for Two-Dimensional Rayleigh-Taylor Interfaces Between Inviscid and Perfect Dielectric Fluids with External Electric Fields	1
Solution of Inverse Geometric Problems Using a Non-Iterative MFS	1
On a Hybrid Approach for Recovering Multiple Obstacles	1
A Modified Characteristic-Wise WENO Reconstruction for Capturing the Contact Discontinuity in Multi-Component Flows	1
MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs	1
A $p$-Adaptive Treecode Solution of the Poisson Equation in the General Domain	1
A Five-Point TENO Scheme with Adaptive Dissipation Based on a New Scale Sensor	1
A Continuous Finite Element Method with Homotopy Vanishing Viscosity for Solving the Static Eikonal Equation	1
A Comparative Study of Hydrodynamic Lattice Boltzmann Equation in Phase-Field-Based Multiphase Flow Models	1
The Effect of Global Smoothness on the Accuracy of Treecodes	1
A Fast Cartesian Grid-Based Integral Equation Method for Unbounded Interface Problems with Non-Homogeneous Source Terms	1