Computers & Mathematics With Applications

Article	Citations
Palabos: Parallel Lattice Boltzmann Solver	195
MFEM: A modular finite element methods library	173
The deal.II finite element library: Design, features, and insights	116
Melting effect on Cattaneo–Christov and thermal radiation features for aligned MHD nanofluid flow comprising microorganisms to leading edge: FEM approach	107
OpenLB—Open source lattice Boltzmann code	90
DuMux 3 – an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling	79
FLEXI: A high order discontinuous Galerkin framework for hyperbolic–parabolic conservation laws	68
A two-grid MMOC finite element method for nonlinear variable-order time-fractional mobile/immobile advection–diffusion equations	62
Numerical study of H2	61
The Dune framework: Basic concepts and recent developments	59
Free vibration analysis of FG-CNTRC shell structures using the meshfree radial point interpolation method	59
The Open Porous Media Flow reservoir simulator	58
Analysis of an augmented moving least squares approximation and the associated localized method of fundamental solutions	54
A global–local approach for hydraulic phase-field fracture in poroelastic media	49
waLBerla: A block-structured high-performance framework for multiphysics simulations	47
A boundary collocation method for anomalous heat conduction analysis in functionally graded materials	44
Performance of the radial point interpolation method (RPIM) with implicit time integration scheme for transient wave propagation dynamics	43
MPI-AMRVAC: A parallel, grid-adaptive PDE toolkit	42
Direct Numerical Simulation of pulsating flow effect on the distribution of non-circular particles with increased levels of complexity: IB-LBM	42
The OSC solver for the fourth-order sub-diffusion equation with weakly singular solutions	41
A unified view of some numerical methods for fractional diffusion	40
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	39
Theoretical analysis of the generalized finite difference method	38
Magneto-thermoelastic interactions in an unbounded orthotropic viscoelastic solid under the Hall current effect by the fourth-order Moore-Gibson-Thompson equation	38
A linearized element-free Galerkin method for the complex Ginzburg–Landau equation	38

Numerical simulations of multi-phase electro-hydrodynamics flows using a simple incompressible smoothed particle hydrodynamics method	37
Two meshless methods based on local radial basis function and barycentric rational interpolation for solving 2D viscoelastic wave equation	37
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
Effect of thermal radiation on conjugate natural convection flow of a micropolar fluid along a vertical surface	35
Deduction of a quadratic velocity field and its application to rolling force of extra-thick plate	35
The rapid assessment for three-dimensional potential model of large-scale particle system by a modified multilevel fast multipole algorithm	35
Numerical investigation of the effect of surface roughness on flow and heat transfer characteristics of single sphere particle in supercritical water	34
A robust error analysis of the OSC method for a multi-term fourth-order sub-diffusion equation	34
MHD natural convection in a cavity in the presence of cross partial magnetic fields and Al	34
The crucial features of aggregation in TiO2-water nanofluid aligned of chemically comprising microorganisms: A FEM approach	33
Linearized ADI schemes for two-dimensional space-fractional nonlinear Ginzburg–Landau equation	33
Workpiece-scale numerical simulations of SLM molten pool dynamic behavior of 316L stainless steel	33
Numerical study on flow field and pollutant dispersion in an ideal street canyon within a real tree model at different wind velocities	32
Temporal second order difference schemes for the multi-dimensional variable-order time fractional sub-diffusion equations	32
Generalized finite difference method for solving stationary 2D and 3D Stokes equations with a mixed boundary condition	30
An alternating direction implicit Galerkin finite element method for the distributed-order time-fractional mobile–immobile equation in two dimensions	30
FEM based robust design optimization with Agros and Ārtap	29
Electrified fractional nanofluid flow with suspended carbon nanotubes	28
An efficient anisotropic diffusion model for image denoising with edge preservation	28
Fractional sliding mode based on RBF neural network observer: Application to HIV infection mathematical model	28
Bilinear immersed finite volume element method for solving matrix coefficient elliptic interface problems with non-homogeneous jump conditions	27
A two-stage adaptive scheme based on RBF collocation for solving elliptic PDEs	27
A second-order ADI difference scheme based on non-uniform meshes for the three-dimensional nonlocal evolution problem	27
Singular boundary method for 2D and 3D acoustic design sensitivity analysis	26
Transient analyses of wave propagations in nonhomogeneous media employing the novel finite element method with the appropriate enrichment function	26
Space–time least-squares finite elements for parabolic equations	26
Keller box simulation of magnetic pseudoplastic nano-polymer coating flow over a circular cylinder with entropy optimisation	25
Error-estimate-based adaptive integration for immersed isogeometric 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
Large eddy simulation of pseudo shock structure in a convergent–long divergent duct	25
A space-time discretization of a nonlinear peridynamic model on a 2D lamina	24
Fully discrete explicit locally entropy-stable schemes for the compressible Euler and Navier–Stokes equations	24
Vibration characteristics of plates and shells with functionally graded pores imperfections using an enhanced finite shell element	24
Stabilized reduced basis methods for parametrized steady Stokes and Navier–Stokes equations	23
Fast image inpainting strategy based on the space-fractional modified Cahn-Hilliard equations	22
Image-based material characterization of complex microarchitectured additively manufactured structures	22
Thermal buckling strength of smart nanotube-reinforced doubly curved hybrid composite panels	22
MHD flow, radiation heat and mass transfer of fractional Burgers' fluid in porous medium with chemical reaction	21
Error analysis of interpolating element free Galerkin method to solve non-linear extended Fisher–Kolmogorov equation	21
Tent pitching and Trefftz-DG method for the acoustic wave equation	21
Numerical and sensitivity computations of three-dimensional flow and heat transfer of nanoliquid over a wedge using modified Buongiorno model	20
Reliability analysis of the uncertain heat conduction model	20
Nonlinear transient vibration of viscoelastic plates: A NURBS-based isogeometric HSDT approach	20
TT-M finite element algorithm for a two-dimensional space fractional Gray–Scott model	20
A complex variable boundary point interpolation method for the nonlinear Signorini problem	19
Thermo-electro-mechanical buckling analysis of sandwich nanocomposite microplates reinforced with graphene platelets integrated with piezoelectric facesheets resting on elastic foundation	19
A class of generalized mixed variational–hemivariational inequalities I: Existence and uniqueness results	19
Wavelet approximation scheme for distributed order fractional differential equations	19
Numerical analysis of an unconditionally energy-stable reduced-order finite element method for the Allen-Cahn phase field model	19

An extended ghost interlayer model in peridynamic theory for high-velocity impact fracture of laminated glass structures	19
Non intrusive reduced order modeling of parametrized PDEs by kernel POD and neural networks	18
OpenCAL system extension and application to the three-dimensional Richards equation for unsaturated flow	17
An adaptive phase-field model based on bilinear elements for tensile-compressive-shear fracture	17
Fast BDF2 ADI methods for the multi-dimensional tempered fractional integrodifferential equation of parabolic type	17
A simple direct heating thermal immersed boundary-lattice Boltzmann method for its application in incompressible flow	17
A novel finite element method for the distributed-order time fractional Cable equation in two dimensions	17
Analysis of the L1 scheme for fractional wave equations with nonsmooth data	17
Nektar++: Design and implementation of an implicit, spectral/h	17
Numerical solutions of two-dimensional Laplace and biharmonic equations by the localized Trefftz method	17
Solving Poisson equation with Dirichlet conditions through multinode Shepard operators	16
KSPHPDDM and PCHPDDM: Extending PETSc with advanced Krylov methods and robust multilevel overlapping Schwarz preconditioners	16
Physics-informed neural networks combined with polynomial interpolation to solve nonlinear partial differential equations	16
Machine learning for accelerating macroscopic parameters prediction for poroelasticity problem in stochastic media	16
A Hybrid High-Order method for the incompressible Navier–Stokes problem robust for large irrotational body forces	16
Monolithic convex limiting in discontinuous Galerkin discretizations of hyperbolic conservation laws	16
A strongly conservative finite element method for the coupled Stokes–Biot Model	16
A fourth order numerical method based on B-spline functions for pricing Asian options	16
Industrial scale Large Eddy Simulations with adaptive octree meshes using immersogeometric analysis	16
Numerical solution of fractional diffusion–reaction problems based on BURA	16
Monolithic and splitting solution schemes for fully coupled quasi-static thermo-poroelasticity with nonlinear convective transport	16
A variational flexible multibody formulation for partitioned fluid–structure interaction: Application to bat-inspired drones and unmanned air-vehicles	16
Virtual elements for Maxwell's equations	16
Galilean invariance study on different lattice Boltzmann fluid–solid interface approaches for vortex-induced vibrations	16
Recurrent neural networks as optimal mesh refinement strategies	16
Sixth order compact finite difference schemes for Poisson interface problems with singular sources	15
Study of a chemo-repulsion model with quadratic production. Part II: Analysis of an unconditionally energy-stable fully discrete scheme	15
On the sources placement in the method of fundamental solutions for time-dependent heat conduction problems	15
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	15
Efficient solvers for hybridized three-field mixed finite element coupled poromechanics	15
Numerical analysis of a second-order IPDGFE method for the Allen–Cahn equation and the curvature-driven geometric flow	15
The effect of indoor heating system location on particle deposition and convection heat transfer: DMRT-LBM	15
GPU-based algorithm for evaluating the electrical resistivity of digital rocks	15
Numerical simulation and passive control of condensing flow through turbine blade by NVD Method Using Eulerian–Lagrangian Model	15
Numerical approximations for space–time fractional Burgers’ equations via a new semi-analytical method	15
High-order entropy stable discontinuous Galerkin methods for the shallow water equations: Curved triangular meshes and GPU acceleration	15
A machine-learning minimal-residual (ML-MRes) framework for goal-oriented finite element discretizations	15
Investigation of bending behavior for laminated composite magneto-electro-elastic cylindrical shells subjected to mechanical or electric/magnetic loads	15
Transient nanofluid flow and energy dissipation from wavy surface using magnetic field and two rotating cylinders	14
GPU acceleration of CaNS for massively-parallel direct numerical simulations of canonical fluid flows	14
Equivalent finite difference and partial differential equations for the lattice Boltzmann method	14
A new fifth-order finite difference well-balanced multi-resolution WENO scheme for solving shallow water equations	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
Investigation of nonlinear squeeze-film damping involving rarefied gas effect in micro-electro-mechanical systems	14
An anisotropic PDE model for image inpainting	14
Open-source immersogeometric analysis of fluid–structure interaction using FEniCS and tIGAr	14
Autonomous FEs (AFE) - A stride toward personalized medicine	13
Rapid calculation of large-scale acoustic scattering from complex targets by a dual-level fast direct solver	13
Effects of grains shapes of porous media on combustion onset—A numerical simulation using Lattice Boltzmann method	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
Local non-singular knot method for large-scale computation of acoustic problems in complicated geometries	13
A non-uniform time-stepping convex splitting scheme for the time-fractional Cahn–Hilliard equation	13
Banach spaces-based analysis of a fully-mixed finite element method for the steady-state model of fluidized beds	13
Numerical analysis of Finite-Difference Time-Domain method for 2D/3D Maxwell's equations in a Cole-Cole dispersive medium	13
Global mean-square exponential stability and random periodicity of discrete-time stochastic inertial neural networks with discrete spatial diffusions and Dirichlet boundary condition	13
Fractional-order diffusion coupled with integer-order diffusion for multiplicative noise removal	13
An efficient alternating direction implicit finite difference scheme for the three-dimensional time-fractional telegraph equation	13
Pattern formation in reaction–diffusion systems on evolving surfaces	13
An adaptive smoothed particle hydrodynamics (SPH) scheme for efficient melt pool simulations in additive manufacturing	13
Finite difference/finite element method for two-dimensional time–space fractional Bloch–Torrey equations with variable coefficients on irregular convex domains	12
Isogeometric analysis for geometric modelling and acoustic attenuation performances of reactive mufflers	12
Higher order approximations for fractional order integro-parabolic partial differential equations on an adaptive mesh with error analysis	12
Eliminating Gibbs phenomena: A non-linear Petrov–Galerkin method for the convection–diffusion–reaction equation	12
On the simulation of image-based cellular materials in a meshless style	12
Three-dimensional asymptotic nonlocal elasticity theory for the free vibration analysis of embedded single-walled carbon nanotubes	12
Dynamical behavior of reaction–diffusion neural networks and their synchronization arising in modeling epileptic seizure: A numerical simulation study	12
2D memory-based mathematical analysis for the combined impact of calcium influx and efflux on nerve cells	12
A block triple-relaxation-time lattice Boltzmann model for nonlinear anisotropic convection–diffusion equations	12
The DPG-star method	12
A weighted finite difference method for subdiffusive Black–Scholes model	12
A new algorithm to determine the creation or depletion term of parabolic equations from boundary measurements	12
An anisotropic diffusion system with nonlinear time-delay structure tensor for image enhancement and segmentation	12
A weighted POD-reduction approach for parametrized PDE-constrained optimal control problems with random inputs and applications to environmental sciences	12
ntkFoam: An OpenFOAM based neutron transport kinetics solver for nuclear reactor simulation	12
Non-negative moment fitting quadrature rules for fictitious domain methods	12
Numerical study of the bi-disperse particles segregation inside a spherical tumbler with Discrete Element Method (DEM)	12
Efficient monolithic projection-based method for chemotaxis-driven bioconvection problems	12
Legendre wavelets based numerical algorithm for simulation of multidimensional Benjamin–Bona–Mahony–Burgers and Sobolev equations	12

On the condition number of high order finite element methods: Influence of p-refinement and mesh distortion	12
Cell-vertex entropy-stable finite volume methods for the system of Euler equations on unstructured grids	12
Numerical pricing based on fractional Black–Scholes equation with time-dependent parameters under the CEV model: Double barrier options	12
An optimal error estimate for the two-dimensional nonlinear time fractional advection–diffusion equation with smooth and non-smooth solutions	11
Mathematical analysis and numerical approximation of a general linearized poro-hyperelastic model	11
A Virtual Element Method coupled with a Boundary Integral Non Reflecting condition for 2D exterior Helmholtz problems	11
Time-fractional Cahn–Hilliard equation: Well-posedness, degeneracy, and numerical solutions	11
High-order upwind compact finite-difference lattice Boltzmann method for viscous incompressible flows	11
Finite difference/spectral methods for the two-dimensional distributed-order time-fractional cable equation	11
A locking-free weak Galerkin finite element method for Reissner–Mindlin plate on polygonal meshes	11
Three-phase hydrodynamic simulation and experimental validation of an upflow anaerobic sludge blanket reactor	11
Method of analytical regularization in the analysis of axially symmetric excitation of imperfect circular disk antennas	11
Dissipation-preserving Galerkin–Legendre spectral methods for two-dimensional fractional nonlinear wave equations	11
The numerical solutions for the energy-dissipative and mass-conservative Allen–Cahn equation	11
A unified lattice Boltzmann model for immiscible and miscible ternary fluids	11
Compressive total variation for image reconstruction and restoration	11
Polyhedral mesh quality indicator for the Virtual Element Method	11
Certified Reduced Basis VMS-Smagorinsky model for natural convection flow in a cavity with variable height	11
An open-source framework for coupling non-matching isogeometric shells with application to aerospace structures	11
Wavenumber-explicit convergence of the hp-FEM for the full-space heterogeneous Helmholtz equation with smooth coefficients	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
Inexact primal–dual active set method for solving elastodynamic frictional contact problems	11
Kaskade 7 — A flexible finite element toolbox	11
Space-time backward substitution method for nonlinear transient heat conduction problems in functionally graded materials	11
Numerical investigation of double-diffusive convection in rectangular cavities with different aspect ratio I: High-accuracy numerical method	11
Meshless Galerkin analysis of the generalized Stokes problem	11
A C1 virtual element method for the stationary quasi-geostrophic equations of the ocean	11
Nonconforming discretizations of convex minimization problems and precise relations to mixed methods	11
A new eighth-order implicit finite difference method to solve the three-dimensional Helmholtz equation	11
Analysis and simulation of Korteweg-de Vries-Rosenau-regularised long-wave model via Galerkin finite element method	11
An unconditionally energy stable method for binary incompressible heat conductive fluids based on the phase–field model	11
A least-squares formulation of the Moving Discontinuous Galerkin Finite Element Method with Interface Condition Enforcement	11
A remeshing strategy for large deformations in the finite cell method	11
ReLU deep neural networks from the hierarchical basis perspective	11
An improved algorithm for checking the injectivity of 2D toric surface patches	11
The local discontinuous Galerkin method on layer-adapted meshes for time-dependent singularly perturbed convection-diffusion problems	11
A finite volume method for the two-dimensional time and space variable-order fractional Bloch-Torrey equation with variable coefficients on irregular domains	11
Numerical verification of a non-residual orthogonal term-by-term stabilized finite element formulation for incompressible convective flow problems	11
Hamilton–Jacobi–Bellman–Isaacs equation for rational inattention in the long-run management of river environments under uncertainty	11
On the spatial dynamics of vaccination: A spatial SIRS–V model	11
A regularized single-phase lattice Boltzmann method for free-surface flows	10
High-order time-stepping methods for two-dimensional Riesz fractional nonlinear reaction–diffusion equations	10
Analysis of a fully discrete approximation for the classical Keller–Segel model: Lower and a priori bounds	10
juSFEM: A Julia-based open-source package of parallel Smoothed Finite Element Method (S-FEM) for elastic problems	10
An adaptive multigrid solver for DPG methods with applications in linear acoustics and electromagnetics	10
On Tikhonov’s method and optimal error bound for inverse source problem for a time-fractional diffusion equation	10
Robust preconditioning for coupled Stokes–Darcy problems with the Darcy problem in primal form	10
Rothe method and numerical analysis for a new class of fractional differential hemivariational inequality with an application	10
Adaptive two-layer ReLU neural network: I. Best least-squares approximation	10
Two-step MPS-MFS ghost point method for solving partial differential equations	10
Virtual element methods for general linear elliptic interface problems on polygonal meshes with small edges	10
Free vibration analysis of laminated rectangular plates with varying thickness using Legendre-radial point interpolation method	10
A note on preconditioning for the 3 × 3 block saddle point problem	10
A finite element level-set method for stress-based topology optimization of plate structures	10
A projection scheme for phase change problems with convection	10
A parametrized level set based topology optimization method for analysing thermal problems	10
RBF-FD solution for a financial partial-integro differential equation utilizing the generalized multiquadric function	10
Time discretization of fractional subdiffusion equations via fractional resolvent operators	10
Isogeometric analysis with C	10
Uniform preconditioners for problems of positive order	10
A rotational velocity-correction projection method for unsteady incompressible magnetohydrodynamics equations	10
The heterogeneous multiscale method to study particle size and partitioning effects in drug delivery	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 family of quadratic finite volume element schemes over triangular meshes for elliptic equations	10
Variational multiscale modeling with discretely divergence-free subscales	9
FEM–BEM mortar coupling for the Helmholtz problem in three dimensions	9
Physics-based model of wildfire propagation towards faster-than-real-time simulations	9
A non-overlapping optimized Schwarz method for the heat equation with non linear boundary conditions and with applications to de-icing	9
A domain decomposition method for Isogeometric multi-patch problems with inexact local solvers	9
Characteristic orthogonal polynomials-Ritz method for vibration behavior of functionally graded piezoelectric plates using FSDT	9
Backward problem for time-space fractional diffusion equations in Hilbert scales	9
An efficient solver for space–time isogeometric Galerkin methods for parabolic problems	9
Unsteady oblique stagnation-point flow and heat transfer of fractional Maxwell fluid with convective derivative under modified pressure field	9
Isogeometric boundary element for analyzing steady-state heat conduction problems under spatially varying conductivity and internal heat source	9
Minimal residual space-time discretizations of parabolic equations: Asymmetric spatial operators	9
SoftFEM: Revisiting the spectral finite element approximation of second-order elliptic operators	9
Identification of elastoplastic properties of rods from torsion test using meshless methods and a metaheuristic	9
A robust sharp interface based immersed boundary framework for moving body problems with applications to laminar incompressible flows	9
On numerical simulation of flexibly supported airfoil in interaction with incompressible fluid flow using laminar–turbulence transition model	9
A family of symmetric, optimized quadrature rules for pentatopes	9
Dissipative spatial discretization of a phase field model of multiphase multicomponent isothermal fluid flow	9
A linearly second-order, unconditionally energy stable scheme and its error estimates for the modified phase field crystal equation	9
A partitioned scheme with multiple-time-step technique for the nonstationary dual-porosity-Stokes problem	9
A weak Galerkin finite element method on temporal graded meshes for the multi-term time fractional diffusion equations	9
Finite element analysis of a Keller–Segel model with additional cross-diffusion and logistic source. Part I: Space convergence	9
Spectral discretizations analysis with time strong stability preserving properties for pseudo-parabolic models	9
Computational study of magneto-convective non-Newtonian nanofluid slip flow over a stretching/shrinking sheet embedded in a porous medium	9
Level-set based topology optimization of transient flow using lattice Boltzmann method considering an oscillating flow condition	9
Construction of DPG Fortin operators revisited	9
Local and parallel finite element algorithms based on domain decomposition for the 2D/3D Stokes equations with damping	9
A compressed lattice Boltzmann method based on ConvLSTM and ResNet	9
A new class of elliptic quasi-variational-hemivariational inequalities for fluid flow with mixed boundary conditions	9
Convergence and positivity of Finite Element methods for a haptotaxis model of tumoral invasion	9
Highly accurate wavelet-homotopy solutions for mixed convection hybrid nanofluid flow in an inclined square lid-driven cavity	9