Computers & Mathematics With Applications

Article	Citations
Palabos: Parallel Lattice Boltzmann Solver	187
MFEM: A modular finite element methods library	163
The deal.II finite element library: Design, features, and insights	112
Melting effect on Cattaneo–Christov and thermal radiation features for aligned MHD nanofluid flow comprising microorganisms to leading edge: FEM approach	104
OpenLB—Open source lattice Boltzmann code	87
DuMux 3 – an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling	77
FLEXI: A high order discontinuous Galerkin framework for hyperbolic–parabolic conservation laws	67
A two-grid MMOC finite element method for nonlinear variable-order time-fractional mobile/immobile advection–diffusion equations	61
Numerical study of H2	60
Free vibration analysis of FG-CNTRC shell structures using the meshfree radial point interpolation method	59
The Dune framework: Basic concepts and recent developments	56
Analysis of an augmented moving least squares approximation and the associated localized method of fundamental solutions	54
The Open Porous Media Flow reservoir simulator	54
A global–local approach for hydraulic phase-field fracture in poroelastic media	47
waLBerla: A block-structured high-performance framework for multiphysics simulations	47
A boundary collocation method for anomalous heat conduction analysis in functionally graded materials	42
Performance of the radial point interpolation method (RPIM) with implicit time integration scheme for transient wave propagation dynamics	42
Direct Numerical Simulation of pulsating flow effect on the distribution of non-circular particles with increased levels of complexity: IB-LBM	40
MPI-AMRVAC: A parallel, grid-adaptive PDE toolkit	40
The OSC solver for the fourth-order sub-diffusion equation with weakly singular solutions	40
A linearized element-free Galerkin method for the complex Ginzburg–Landau equation	38
A unified view of some numerical methods for fractional diffusion	38
Insight into the dynamics of fluid conveying tiny particles over a rotating surface subject to Cattaneo–Christov heat transfer, Coriolis force, and Arrhenius activation energy	37
Heat transfer enhancement of Water-Al2	37
Theoretical analysis of the generalized finite difference method	37

Two meshless methods based on local radial basis function and barycentric rational interpolation for solving 2D viscoelastic wave equation	36
A fast method for variable-order Caputo fractional derivative with applications to time-fractional diffusion equations	36
A moving-domain CFD solver in FEniCS with applications to tidal turbine simulations in turbulent flows	35
Numerical simulations of multi-phase electro-hydrodynamics flows using a simple incompressible smoothed particle hydrodynamics method	35
The rapid assessment for three-dimensional potential model of large-scale particle system by a modified multilevel fast multipole algorithm	34
Effect of thermal radiation on conjugate natural convection flow of a micropolar fluid along a vertical surface	34
Magneto-thermoelastic interactions in an unbounded orthotropic viscoelastic solid under the Hall current effect by the fourth-order Moore-Gibson-Thompson equation	34
A robust error analysis of the OSC method for a multi-term fourth-order sub-diffusion equation	34
Numerical investigation of the effect of surface roughness on flow and heat transfer characteristics of single sphere particle in supercritical water	34
MHD natural convection in a cavity in the presence of cross partial magnetic fields and Al	33
Workpiece-scale numerical simulations of SLM molten pool dynamic behavior of 316L stainless steel	33
Temporal second order difference schemes for the multi-dimensional variable-order time fractional sub-diffusion equations	32
An implicit finite difference analysis of magnetic swimmers propelling through non-Newtonian liquid in a complex wavy channel	32
Numerical study on flow field and pollutant dispersion in an ideal street canyon within a real tree model at different wind velocities	32
Linearized ADI schemes for two-dimensional space-fractional nonlinear Ginzburg–Landau equation	32
Deduction of a quadratic velocity field and its application to rolling force of extra-thick plate	31
The crucial features of aggregation in TiO2-water nanofluid aligned of chemically comprising microorganisms: A FEM approach	31
The conforming virtual element method for polyharmonic problems	30
An alternating direction implicit Galerkin finite element method for the distributed-order time-fractional mobile–immobile equation in two dimensions	29
Generalized finite difference method for solving stationary 2D and 3D Stokes equations with a mixed boundary condition	29
FEM based robust design optimization with Agros and Ārtap	29
A mixed MoL–TMoL for the numerical solution of the 2D Richards’ equation in layered soils	28
Fractional sliding mode based on RBF neural network observer: Application to HIV infection mathematical model	28
Unconditional superconvergence analysis of a linearized Crank–Nicolson Galerkin FEM for generalized Ginzburg–Landau equation	28
Electrified fractional nanofluid flow with suspended carbon nanotubes	27
The p- and 27
Bilinear immersed finite volume element method for solving matrix coefficient elliptic interface problems with non-homogeneous jump conditions	27
A second-order ADI difference scheme based on non-uniform meshes for the three-dimensional nonlocal evolution problem	27
An efficient anisotropic diffusion model for image denoising with edge preservation	27
Large eddy simulation of pseudo shock structure in a convergent–long divergent duct	25
Singular boundary method for 2D and 3D acoustic design sensitivity analysis	25
Combined heat and mass transfer and thermodynamic irreversibilities in the stagnation-point flow of Casson rheological fluid over a cylinder with catalytic reactions and inside a porous medium under l	25
Error-estimate-based adaptive integration for immersed isogeometric analysis	25
A two-stage adaptive scheme based on RBF collocation for solving elliptic PDEs	24
Vibration characteristics of plates and shells with functionally graded pores imperfections using an enhanced finite shell element	24
Fully discrete explicit locally entropy-stable schemes for the compressible Euler and Navier–Stokes equations	24
Transient analyses of wave propagations in nonhomogeneous media employing the novel finite element method with the appropriate enrichment function	24
Keller box simulation of magnetic pseudoplastic nano-polymer coating flow over a circular cylinder with entropy optimisation	24
Space–time least-squares finite elements for parabolic equations	24
A C1	23
Stabilized reduced basis methods for parametrized steady Stokes and Navier–Stokes equations	23
Image-based material characterization of complex microarchitectured additively manufactured structures	22
A space-time discretization of a nonlinear peridynamic model on a 2D lamina	22
Thermal buckling strength of smart nanotube-reinforced doubly curved hybrid composite panels	21
Nonlinear transient vibration of viscoelastic plates: A NURBS-based isogeometric HSDT approach	20
MHD flow, radiation heat and mass transfer of fractional Burgers' fluid in porous medium with chemical reaction	20
Error analysis of interpolating element free Galerkin method to solve non-linear extended Fisher–Kolmogorov equation	20
Tent pitching and Trefftz-DG method for the acoustic wave equation	19
Thermo-electro-mechanical buckling analysis of sandwich nanocomposite microplates reinforced with graphene platelets integrated with piezoelectric facesheets resting on elastic foundation	19
Numerical and sensitivity computations of three-dimensional flow and heat transfer of nanoliquid over a wedge using modified Buongiorno model	19

TT-M finite element algorithm for a two-dimensional space fractional Gray–Scott model	19
Wavelet approximation scheme for distributed order fractional differential equations	19
A complex variable boundary point interpolation method for the nonlinear Signorini problem	19
An extended ghost interlayer model in peridynamic theory for high-velocity impact fracture of laminated glass structures	19
Reliability analysis of the uncertain heat conduction model	18
Fast image inpainting strategy based on the space-fractional modified Cahn-Hilliard equations	18
An adaptive phase-field model based on bilinear elements for tensile-compressive-shear fracture	17
A class of generalized mixed variational–hemivariational inequalities I: Existence and uniqueness results	17
Fast BDF2 ADI methods for the multi-dimensional tempered fractional integrodifferential equation of parabolic type	17
Numerical analysis of an unconditionally energy-stable reduced-order finite element method for the Allen-Cahn phase field model	17
Analysis of the L1 scheme for fractional wave equations with nonsmooth data	17
Monolithic convex limiting in discontinuous Galerkin discretizations of hyperbolic conservation laws	16
A fourth order numerical method based on B-spline functions for pricing Asian options	16
Non intrusive reduced order modeling of parametrized PDEs by kernel POD and neural networks	16
Galilean invariance study on different lattice Boltzmann fluid–solid interface approaches for vortex-induced vibrations	16
A Hybrid High-Order method for the incompressible Navier–Stokes problem robust for large irrotational body forces	16
Virtual elements for Maxwell's equations	16
A strongly conservative finite element method for the coupled Stokes–Biot Model	16
A novel finite element method for the distributed-order time fractional Cable equation in two dimensions	16
Monolithic and splitting solution schemes for fully coupled quasi-static thermo-poroelasticity with nonlinear convective transport	16
OpenCAL system extension and application to the three-dimensional Richards equation for unsaturated flow	16
Recurrent neural networks as optimal mesh refinement strategies	16
KSPHPDDM and PCHPDDM: Extending PETSc with advanced Krylov methods and robust multilevel overlapping Schwarz preconditioners	16
Numerical solutions of two-dimensional Laplace and biharmonic equations by the localized Trefftz method	16
Numerical approximations for space–time fractional Burgers’ equations via a new semi-analytical method	15
Nektar++: Design and implementation of an implicit, spectral/h	15
Investigation of bending behavior for laminated composite magneto-electro-elastic cylindrical shells subjected to mechanical or electric/magnetic loads	15
Study of a chemo-repulsion model with quadratic production. Part II: Analysis of an unconditionally energy-stable fully discrete scheme	15
Industrial scale Large Eddy Simulations with adaptive octree meshes using immersogeometric analysis	15
Numerical solution of fractional diffusion–reaction problems based on BURA	15
Solving Poisson equation with Dirichlet conditions through multinode Shepard operators	15
High-order entropy stable discontinuous Galerkin methods for the shallow water equations: Curved triangular meshes and GPU acceleration	15
GPU-based algorithm for evaluating the electrical resistivity of digital rocks	15
A simple direct heating thermal immersed boundary-lattice Boltzmann method for its application in incompressible flow	14
A higher order hybrid-numerical approximation for a class of singularly perturbed two-dimensional convection-diffusion elliptic problem with non-smooth convection and source terms	14
GPU acceleration of CaNS for massively-parallel direct numerical simulations of canonical fluid flows	14
Numerical simulation and passive control of condensing flow through turbine blade by NVD Method Using Eulerian–Lagrangian Model	14
Transient nanofluid flow and energy dissipation from wavy surface using magnetic field and two rotating cylinders	14
A new fifth-order finite difference well-balanced multi-resolution WENO scheme for solving shallow water equations	14
Physics-informed neural networks combined with polynomial interpolation to solve nonlinear partial differential equations	14
The effect of indoor heating system location on particle deposition and convection heat transfer: DMRT-LBM	14
Machine learning for accelerating macroscopic parameters prediction for poroelasticity problem in stochastic media	14
A novel localized collocation solver based on a radial Trefftz basis for thermal conduction analysis in FGMs with exponential variations	14
Solving a chemotaxis–haptotaxis system in 2D using Generalized Finite Difference Method	14
Numerical analysis of a second-order IPDGFE method for the Allen–Cahn equation and the curvature-driven geometric flow	14
On the sources placement in the method of fundamental solutions for time-dependent heat conduction problems	14
A machine-learning minimal-residual (ML-MRes) framework for goal-oriented finite element discretizations	14
Matrix-oriented discretization methods for reaction–diffusion PDEs: Comparisons and applications	14
Efficient solvers for hybridized three-field mixed finite element coupled poromechanics	14
Open-source immersogeometric analysis of fluid–structure interaction using FEniCS and tIGAr	14
A variational flexible multibody formulation for partitioned fluid–structure interaction: Application to bat-inspired drones and unmanned air-vehicles	14
Modeling and analysis of cross-ply and angle-ply laminated plates under patch loads using RBF based meshfree method and new HSDT	14
Local non-singular knot method for large-scale computation of acoustic problems in complicated geometries	13
An efficient alternating direction implicit finite difference scheme for the three-dimensional time-fractional telegraph equation	13
A discrete comparison principle for the time-fractional diffusion equation	13
A Lattice Boltzmann dynamic-Immersed Boundary scheme for the transport of deformable inertial capsules in low-Re flows	13
Autonomous FEs (AFE) - A stride toward personalized medicine	13
A non-uniform time-stepping convex splitting scheme for the time-fractional Cahn–Hilliard equation	13
Equivalent finite difference and partial differential equations for the lattice Boltzmann method	13
Investigation of nonlinear squeeze-film damping involving rarefied gas effect in micro-electro-mechanical systems	13
Banach spaces-based analysis of a fully-mixed finite element method for the steady-state model of fluidized beds	13
An anisotropic PDE model for image inpainting	13
Sixth order compact finite difference schemes for Poisson interface problems with singular sources	13
Effects of grains shapes of porous media on combustion onset—A numerical simulation using Lattice Boltzmann method	12
Eliminating Gibbs phenomena: A non-linear Petrov–Galerkin method for the convection–diffusion–reaction equation	12
Cell-vertex entropy-stable finite volume methods for the system of Euler equations on unstructured grids	12
ntkFoam: An OpenFOAM based neutron transport kinetics solver for nuclear reactor simulation	12
Dynamical behavior of reaction–diffusion neural networks and their synchronization arising in modeling epileptic seizure: A numerical simulation study	12
A block triple-relaxation-time lattice Boltzmann model for nonlinear anisotropic convection–diffusion equations	12
The DPG-star method	12
Legendre wavelets based numerical algorithm for simulation of multidimensional Benjamin–Bona–Mahony–Burgers and Sobolev equations	12
Numerical analysis of Finite-Difference Time-Domain method for 2D/3D Maxwell's equations in a Cole-Cole dispersive medium	12
Numerical pricing based on fractional Black–Scholes equation with time-dependent parameters under the CEV model: Double barrier options	12
Non-negative moment fitting quadrature rules for fictitious domain methods	12
Isogeometric analysis for geometric modelling and acoustic attenuation performances of reactive mufflers	12
Pattern formation in reaction–diffusion systems on evolving surfaces	12
The numerical solutions for the energy-dissipative and mass-conservative Allen–Cahn equation	12
Three-dimensional asymptotic nonlocal elasticity theory for the free vibration analysis of embedded single-walled carbon nanotubes	12
A weighted POD-reduction approach for parametrized PDE-constrained optimal control problems with random inputs and applications to environmental sciences	12
Finite difference/finite element method for two-dimensional time–space fractional Bloch–Torrey equations with variable coefficients on irregular convex domains	12

Rapid calculation of large-scale acoustic scattering from complex targets by a dual-level fast direct solver	11
Higher order approximations for fractional order integro-parabolic partial differential equations on an adaptive mesh with error analysis	11
Finite difference/spectral methods for the two-dimensional distributed-order time-fractional cable equation	11
Compressive total variation for image reconstruction and restoration	11
High-order upwind compact finite-difference lattice Boltzmann method for viscous incompressible flows	11
Nonconforming discretizations of convex minimization problems and precise relations to mixed methods	11
Three-phase hydrodynamic simulation and experimental validation of an upflow anaerobic sludge blanket reactor	11
Certified Reduced Basis VMS-Smagorinsky model for natural convection flow in a cavity with variable height	11
Space-time backward substitution method for nonlinear transient heat conduction problems in functionally graded materials	11
On the simulation of image-based cellular materials in a meshless style	11
Mathematical analysis and numerical approximation of a general linearized poro-hyperelastic model	11
Fractional-order diffusion coupled with integer-order diffusion for multiplicative noise removal	11
Numerical verification of a non-residual orthogonal term-by-term stabilized finite element formulation for incompressible convective flow problems	11
Method of analytical regularization in the analysis of axially symmetric excitation of imperfect circular disk antennas	11
Effects of parameterization and knot placement techniques on primal and mixed isogeometric collocation formulations of spatial shear-deformable beams with varying curvature and torsion	11
Hamilton–Jacobi–Bellman–Isaacs equation for rational inattention in the long-run management of river environments under uncertainty	11
Inexact primal–dual active set method for solving elastodynamic frictional contact problems	11
A C1 virtual element method for the stationary quasi-geostrophic equations of the ocean	11
Numerical study of the bi-disperse particles segregation inside a spherical tumbler with Discrete Element Method (DEM)	11
An anisotropic diffusion system with nonlinear time-delay structure tensor for image enhancement and segmentation	11
An open-source framework for coupling non-matching isogeometric shells with application to aerospace structures	11
Kaskade 7 — A flexible finite element toolbox	11
A unified lattice Boltzmann model for immiscible and miscible ternary fluids	11
A locking-free weak Galerkin finite element method for Reissner–Mindlin plate on polygonal meshes	11
Dissipation-preserving Galerkin–Legendre spectral methods for two-dimensional fractional nonlinear wave equations	11
A remeshing strategy for large deformations in the finite cell method	11
On the spatial dynamics of vaccination: A spatial SIRS–V model	11
Wavenumber-explicit convergence of the hp-FEM for the full-space heterogeneous Helmholtz equation with smooth coefficients	11
A new algorithm to determine the creation or depletion term of parabolic equations from boundary measurements	11
The local discontinuous Galerkin method on layer-adapted meshes for time-dependent singularly perturbed convection-diffusion problems	11
On the condition number of high order finite element methods: Influence of p-refinement and mesh distortion	11
A Virtual Element Method coupled with a Boundary Integral Non Reflecting condition for 2D exterior Helmholtz problems	11
Efficient monolithic projection-based method for chemotaxis-driven bioconvection problems	10
Robust preconditioning for coupled Stokes–Darcy problems with the Darcy problem in primal form	10
A new eighth-order implicit finite difference method to solve the three-dimensional Helmholtz equation	10
A simplified finite volume lattice Boltzmann method for simulations of fluid flows from laminar to turbulent regime, Part II: Extension towards turbulent flow simulation	10
Analysis and simulation of Korteweg-de Vries-Rosenau-regularised long-wave model via Galerkin finite element method	10
Analysis of a fully discrete approximation for the classical Keller–Segel model: Lower and a priori bounds	10
Discontinuous Galerkin methods for the Stokes equations with nonlinear damping term on general meshes	10
A rotational velocity-correction projection method for unsteady incompressible magnetohydrodynamics equations	10
A weighted finite difference method for subdiffusive Black–Scholes model	10
Two-grid discretizations and a local finite element scheme for a non-selfadjoint Stekloff eigenvalue problem	10
A finite volume method for the two-dimensional time and space variable-order fractional Bloch-Torrey equation with variable coefficients on irregular domains	10
Adaptive two-layer ReLU neural network: I. Best least-squares approximation	10
An unconditionally energy stable method for binary incompressible heat conductive fluids based on the phase–field model	10
Isogeometric analysis with C	10
Homoclinic breather and rogue wave solutions to Maccari equation	10
Uniform preconditioners for problems of positive order	10
An improved algorithm for checking the injectivity of 2D toric surface patches	10
A finite element level-set method for stress-based topology optimization of plate structures	10
Study of a chemo-repulsion model with quadratic production. Part I: Analysis of the continuous problem and time-discrete numerical schemes	10
Time-stepping DPG formulations for the heat equation	10
A regularized single-phase lattice Boltzmann method for free-surface flows	10
Boundary layer flows of viscoelastic fluids over a non-uniform permeable surface	10
Two-step MPS-MFS ghost point method for solving partial differential equations	10
ReLU deep neural networks from the hierarchical basis perspective	10
Time-fractional Cahn–Hilliard equation: Well-posedness, degeneracy, and numerical solutions	10
Free vibration analysis of laminated rectangular plates with varying thickness using Legendre-radial point interpolation method	10
On Tikhonov’s method and optimal error bound for inverse source problem for a time-fractional diffusion equation	10
Physics-based model of wildfire propagation towards faster-than-real-time simulations	9
A parametrized level set based topology optimization method for analysing thermal problems	9
A robust sharp interface based immersed boundary framework for moving body problems with applications to laminar incompressible flows	9
RBF-FD solution for a financial partial-integro differential equation utilizing the generalized multiquadric function	9
Rothe method and numerical analysis for a new class of fractional differential hemivariational inequality with an application	9
Characteristic orthogonal polynomials-Ritz method for vibration behavior of functionally graded piezoelectric plates using FSDT	9
Algebraic cubature on polygonal elements with a circular edge	9
Unsteady oblique stagnation-point flow and heat transfer of fractional Maxwell fluid with convective derivative under modified pressure field	9
A domain decomposition method for Isogeometric multi-patch problems with inexact local solvers	9
Highly accurate wavelet-homotopy solutions for mixed convection hybrid nanofluid flow in an inclined square lid-driven cavity	9
Minimal residual space-time discretizations of parabolic equations: Asymmetric spatial operators	9
Isogeometric boundary element for analyzing steady-state heat conduction problems under spatially varying conductivity and internal heat source	9
Identification of elastoplastic properties of rods from torsion test using meshless methods and a metaheuristic	9
FEM–BEM mortar coupling for the Helmholtz problem in three dimensions	9
Level-set based topology optimization of transient flow using lattice Boltzmann method considering an oscillating flow condition	9
A family of quadratic finite volume element schemes over triangular meshes for elliptic equations	9
Polyhedral mesh quality indicator for the Virtual Element Method	9
On numerical simulation of flexibly supported airfoil in interaction with incompressible fluid flow using laminar–turbulence transition model	9
A least-squares formulation of the Moving Discontinuous Galerkin Finite Element Method with Interface Condition Enforcement	9
Time discretization of fractional subdiffusion equations via fractional resolvent operators	9
Global mean-square exponential stability and random periodicity of discrete-time stochastic inertial neural networks with discrete spatial diffusions and Dirichlet boundary condition	9
Meshless Galerkin analysis of the generalized Stokes problem	9
Finite element analysis of a Keller–Segel model with additional cross-diffusion and logistic source. Part I: Space convergence	9
A weak Galerkin finite element method on temporal graded meshes for the multi-term time fractional diffusion equations	9
Computational study of magneto-convective non-Newtonian nanofluid slip flow over a stretching/shrinking sheet embedded in a porous medium	9
SoftFEM: Revisiting the spectral finite element approximation of second-order elliptic operators	9
A projection scheme for phase change problems with convection	9
A non-overlapping optimized Schwarz method for the heat equation with non linear boundary conditions and with applications to de-icing	9
An optimal error estimate for the two-dimensional nonlinear time fractional advection–diffusion equation with smooth and non-smooth solutions	9
Construction of DPG Fortin operators revisited	9
A new class of elliptic quasi-variational-hemivariational inequalities for fluid flow with mixed boundary conditions	9
High-order time-stepping methods for two-dimensional Riesz fractional nonlinear reaction–diffusion equations	9
juSFEM: A Julia-based open-source package of parallel Smoothed Finite Element Method (S-FEM) for elastic problems	9
Numerical investigation of double-diffusive convection in rectangular cavities with different aspect ratio I: High-accuracy numerical method	9
Convergence and positivity of Finite Element methods for a haptotaxis model of tumoral invasion	9
An adaptive multigrid solver for DPG methods with applications in linear acoustics and electromagnetics	9