Computers & Mathematics With Applications

Article	Citations
Palabos: Parallel Lattice Boltzmann Solver	217
MFEM: A modular finite element methods library	206
The deal.II finite element library: Design, features, and insights	132
Melting effect on Cattaneo–Christov and thermal radiation features for aligned MHD nanofluid flow comprising microorganisms to leading edge: FEM approach	118
OpenLB—Open source lattice Boltzmann code	100
DuMux 3 – an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling	89
FLEXI: A high order discontinuous Galerkin framework for hyperbolic–parabolic conservation laws	75
The Open Porous Media Flow reservoir simulator	68
The Dune framework: Basic concepts and recent developments	66
Numerical study of H2	64
waLBerla: A block-structured high-performance framework for multiphysics simulations	58
A global–local approach for hydraulic phase-field fracture in poroelastic media	54
Performance of the radial point interpolation method (RPIM) with implicit time integration scheme for transient wave propagation dynamics	47
Magneto-thermoelastic interactions in an unbounded orthotropic viscoelastic solid under the Hall current effect by the fourth-order Moore-Gibson-Thompson equation	47
A boundary collocation method for anomalous heat conduction analysis in functionally graded materials	47
MPI-AMRVAC: A parallel, grid-adaptive PDE toolkit	46
Direct Numerical Simulation of pulsating flow effect on the distribution of non-circular particles with increased levels of complexity: IB-LBM	45
The OSC solver for the fourth-order sub-diffusion equation with weakly singular solutions	45
Theoretical analysis of the generalized finite difference method	45
Effect of thermal radiation on conjugate natural convection flow of a micropolar fluid along a vertical surface	41
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	40
MHD natural convection in a cavity in the presence of cross partial magnetic fields and Al	40
Numerical study on flow field and pollutant dispersion in an ideal street canyon within a real tree model at different wind velocities	39
A linearized element-free Galerkin method for the complex Ginzburg–Landau equation	38
Deduction of a quadratic velocity field and its application to rolling force of extra-thick plate	38

Numerical investigation of the effect of surface roughness on flow and heat transfer characteristics of single sphere particle in supercritical water	38
A moving-domain CFD solver in FEniCS with applications to tidal turbine simulations in turbulent flows	38
The crucial features of aggregation in TiO2-water nanofluid aligned of chemically comprising microorganisms: A FEM approach	38
A robust error analysis of the OSC method for a multi-term fourth-order sub-diffusion equation	37
Numerical simulations of multi-phase electro-hydrodynamics flows using a simple incompressible smoothed particle hydrodynamics method	36
Workpiece-scale numerical simulations of SLM molten pool dynamic behavior of 316L stainless steel	36
The rapid assessment for three-dimensional potential model of large-scale particle system by a modified multilevel fast multipole algorithm	35
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	33
An alternating direction implicit Galerkin finite element method for the distributed-order time-fractional mobile–immobile equation in two dimensions	32
Bilinear immersed finite volume element method for solving matrix coefficient elliptic interface problems with non-homogeneous jump conditions	31
An efficient anisotropic diffusion model for image denoising with edge preservation	31
FEM based robust design optimization with Agros and Ārtap	31
Higher order approximations for fractional order integro-parabolic partial differential equations on an adaptive mesh with error analysis	29
Singular boundary method for 2D and 3D acoustic design sensitivity analysis	29
Vibration characteristics of plates and shells with functionally graded pores imperfections using an enhanced finite shell element	29
Transient analyses of wave propagations in nonhomogeneous media employing the novel finite element method with the appropriate enrichment function	28
Space–time least-squares finite elements for parabolic equations	28
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	28
Error-estimate-based adaptive integration for immersed isogeometric analysis	28
Stabilized reduced basis methods for parametrized steady Stokes and Navier–Stokes equations	28
Keller box simulation of magnetic pseudoplastic nano-polymer coating flow over a circular cylinder with entropy optimisation	27
A second-order ADI difference scheme based on non-uniform meshes for the three-dimensional nonlocal evolution problem	27
A space-time discretization of a nonlinear peridynamic model on a 2D lamina	26
MHD flow, radiation heat and mass transfer of fractional Burgers' fluid in porous medium with chemical reaction	26
Physics-informed neural networks combined with polynomial interpolation to solve nonlinear partial differential equations	26
Numerical analysis of an unconditionally energy-stable reduced-order finite element method for the Allen-Cahn phase field model	25
Image-based material characterization of complex microarchitectured additively manufactured structures	25
Fast image inpainting strategy based on the space-fractional modified Cahn-Hilliard equations	25
Large eddy simulation of pseudo shock structure in a convergent–long divergent duct	25
Nonlinear transient vibration of viscoelastic plates: A NURBS-based isogeometric HSDT approach	24
Non intrusive reduced order modeling of parametrized PDEs by kernel POD and neural networks	24
Numerical and sensitivity computations of three-dimensional flow and heat transfer of nanoliquid over a wedge using modified Buongiorno model	24
Thermal buckling strength of smart nanotube-reinforced doubly curved hybrid composite panels	23
Thermo-electro-mechanical buckling analysis of sandwich nanocomposite microplates reinforced with graphene platelets integrated with piezoelectric facesheets resting on elastic foundation	22
An adaptive smoothed particle hydrodynamics (SPH) scheme for efficient melt pool simulations in additive manufacturing	22
An adaptive phase-field model based on bilinear elements for tensile-compressive-shear fracture	21
GPU acceleration of CaNS for massively-parallel direct numerical simulations of canonical fluid flows	21
A variational flexible multibody formulation for partitioned fluid–structure interaction: Application to bat-inspired drones and unmanned air-vehicles	21
Reliability analysis of the uncertain heat conduction model	20
Open-source immersogeometric analysis of fluid–structure interaction using FEniCS and tIGAr	20
Investigation of nonlinear squeeze-film damping involving rarefied gas effect in micro-electro-mechanical systems	19
GPU-based algorithm for evaluating the electrical resistivity of digital rocks	19
Transient nanofluid flow and energy dissipation from wavy surface using magnetic field and two rotating cylinders	19
Equivalent finite difference and partial differential equations for the lattice Boltzmann method	19
Virtual elements for Maxwell's equations	18
A machine-learning minimal-residual (ML-MRes) framework for goal-oriented finite element discretizations	18
Fast BDF2 ADI methods for the multi-dimensional tempered fractional integrodifferential equation of parabolic type	18
Solving Poisson equation with Dirichlet conditions through multinode Shepard operators	18
2D memory-based mathematical analysis for the combined impact of calcium influx and efflux on nerve cells	18
An efficient alternating direction implicit finite difference scheme for the three-dimensional time-fractional telegraph equation	18

Numerical solutions of two-dimensional Laplace and biharmonic equations by the localized Trefftz method	18
Recurrent neural networks as optimal mesh refinement strategies	18
Analysis of hydromagnetic Williamson fluid flow over an inclined stretching sheet with Hall current using Galerkin Weighted Residual Method	18
High-order entropy stable discontinuous Galerkin methods for the shallow water equations: Curved triangular meshes and GPU acceleration	18
Nektar++: Design and implementation of an implicit, spectral/h	18
Machine learning for accelerating macroscopic parameters prediction for poroelasticity problem in stochastic media	18
Monolithic convex limiting in discontinuous Galerkin discretizations of hyperbolic conservation laws	18
Non-negative moment fitting quadrature rules for fictitious domain methods	17
OpenCAL system extension and application to the three-dimensional Richards equation for unsaturated flow	17
Pattern formation in reaction–diffusion systems on evolving surfaces	17
Numerical approximations for space–time fractional Burgers’ equations via a new semi-analytical method	17
KSPHPDDM and PCHPDDM: Extending PETSc with advanced Krylov methods and robust multilevel overlapping Schwarz preconditioners	17
Analysis of the L1 scheme for fractional wave equations with nonsmooth data	17
On the sources placement in the method of fundamental solutions for time-dependent heat conduction problems	17
Industrial scale Large Eddy Simulations with adaptive octree meshes using immersogeometric analysis	17
A weighted POD-reduction approach for parametrized PDE-constrained optimal control problems with random inputs and applications to environmental sciences	17
Space-time backward substitution method for nonlinear transient heat conduction problems in functionally graded materials	16
Banach spaces-based analysis of a fully-mixed finite element method for the steady-state model of fluidized beds	16
Numerical pricing based on fractional Black–Scholes equation with time-dependent parameters under the CEV model: Double barrier options	16
Effects of parameterization and knot placement techniques on primal and mixed isogeometric collocation formulations of spatial shear-deformable beams with varying curvature and torsion	16
Numerical analysis of a second-order IPDGFE method for the Allen–Cahn equation and the curvature-driven geometric flow	16
Physics-informed deep learning for melting heat transfer analysis with model-based transfer learning	16
An open-source framework for coupling non-matching isogeometric shells with application to aerospace structures	16
ReLU deep neural networks from the hierarchical basis perspective	16
The effect of indoor heating system location on particle deposition and convection heat transfer: DMRT-LBM	16
Efficient solvers for hybridized three-field mixed finite element coupled poromechanics	16
ntkFoam: An OpenFOAM based neutron transport kinetics solver for nuclear reactor simulation	16
Sixth order compact finite difference schemes for Poisson interface problems with singular sources	15
Acceleration of RBF-FD meshless phase-field modelling of dendritic solidification by space-time adaptive approach	15
A remeshing strategy for large deformations in the finite cell method	15
A novel localized collocation solver based on a radial Trefftz basis for thermal conduction analysis in FGMs with exponential variations	15
Fractional-order diffusion coupled with integer-order diffusion for multiplicative noise removal	15
A Lattice Boltzmann dynamic-Immersed Boundary scheme for the transport of deformable inertial capsules in low-Re flows	14
Autonomous FEs (AFE) - A stride toward personalized medicine	14
Adaptive two-layer ReLU neural network: I. Best least-squares approximation	14
Analysis and simulation of Korteweg-de Vries-Rosenau-regularised long-wave model via Galerkin finite element method	14
Global mean-square exponential stability and random periodicity of discrete-time stochastic inertial neural networks with discrete spatial diffusions and Dirichlet boundary condition	14
Nonconforming discretizations of convex minimization problems and precise relations to mixed methods	14
Polyhedral mesh quality indicator for the Virtual Element Method	14
Free vibration analysis of laminated rectangular plates with varying thickness using Legendre-radial point interpolation method	14
RBF-FD solution for a financial partial-integro differential equation utilizing the generalized multiquadric function	14
Numerical analysis of Finite-Difference Time-Domain method for 2D/3D Maxwell's equations in a Cole-Cole dispersive medium	14
Time-fractional Cahn–Hilliard equation: Well-posedness, degeneracy, and numerical solutions	13
Effects of grains shapes of porous media on combustion onset—A numerical simulation using Lattice Boltzmann method	13
A projection scheme for phase change problems with convection	13
Cell-vertex entropy-stable finite volume methods for the system of Euler equations on unstructured grids	13
Wavenumber-explicit convergence of the hp-FEM for the full-space heterogeneous Helmholtz equation with smooth coefficients	13
Rapid calculation of large-scale acoustic scattering from complex targets by a dual-level fast direct solver	13
On the condition number of high order finite element methods: Influence of p-refinement and mesh distortion	13
A novel Trefftz-based meshfree method for free vibration and buckling analysis of thin arbitrarily shaped laminated composite and isotropic plates	13
Local non-singular knot method for large-scale computation of acoustic problems in complicated geometries	13
A finite volume method for the two-dimensional time and space variable-order fractional Bloch-Torrey equation with variable coefficients on irregular domains	13
An anisotropic diffusion system with nonlinear time-delay structure tensor for image enhancement and segmentation	13
An unconditionally energy stable method for binary incompressible heat conductive fluids based on the phase–field model	13
Rothe method and numerical analysis for a new class of fractional differential hemivariational inequality with an application	12
A meshless method based on the generalized finite difference method for three-dimensional elliptic interface problems	12
Numerical study of the bi-disperse particles segregation inside a spherical tumbler with Discrete Element Method (DEM)	12
Unsteady oblique stagnation-point flow and heat transfer of fractional Maxwell fluid with convective derivative under modified pressure field	12
Finite element analysis of a Keller–Segel model with additional cross-diffusion and logistic source. Part I: Space convergence	12
An adaptive multigrid solver for DPG methods with applications in linear acoustics and electromagnetics	12
Numerical investigation of double-diffusive convection in rectangular cavities with different aspect ratio I: High-accuracy numerical method	12
A new algorithm to determine the creation or depletion term of parabolic equations from boundary measurements	12
Mathematical analysis and numerical approximation of a general linearized poro-hyperelastic model	12
The local discontinuous Galerkin method on layer-adapted meshes for time-dependent singularly perturbed convection-diffusion problems	12
Finite difference/finite element method for two-dimensional time–space fractional Bloch–Torrey equations with variable coefficients on irregular convex domains	12
Meshless Galerkin analysis of the generalized Stokes problem	12
A finite element level-set method for stress-based topology optimization of plate structures	12
Computational study of magneto-convective non-Newtonian nanofluid slip flow over a stretching/shrinking sheet embedded in a porous medium	12
On the simulation of image-based cellular materials in a meshless style	12
Isogeometric analysis with C	12
A least-squares formulation of the Moving Discontinuous Galerkin Finite Element Method with Interface Condition Enforcement	12
Three-phase hydrodynamic simulation and experimental validation of an upflow anaerobic sludge blanket reactor	12
A high-order implicit-explicit flux reconstruction lattice Boltzmann method for viscous incompressible flows	12
Efficient monolithic projection-based method for chemotaxis-driven bioconvection problems	12
A unified lattice Boltzmann model for immiscible and miscible ternary fluids	12
A new class of elliptic quasi-variational-hemivariational inequalities for fluid flow with mixed boundary conditions	11
Density-extrapolation Global Variance Reduction (DeGVR) method for large-scale radiation field calculation	11
FEM–BEM mortar coupling for the Helmholtz problem in three dimensions	11
Hamilton–Jacobi–Bellman–Isaacs equation for rational inattention in the long-run management of river environments under uncertainty	11
Pressure correction projection finite element method for the 2D/3D time-dependent thermomicropolar fluid problem	11

Two-step MPS-MFS ghost point method for solving partial differential equations	11
Inexact primal–dual active set method for solving elastodynamic frictional contact problems	11
An enriched Galerkin method for the Stokes equations	11
Kaskade 7 — A flexible finite element toolbox	11
The heterogeneous multiscale method to study particle size and partitioning effects in drug delivery	11
A parametrized level set based topology optimization method for analysing thermal problems	11
The role of stabilization in the virtual element method: A survey	11
A rotated lattice Boltzmann flux solver with improved stability for the simulation of compressible flows with intense shock waves at high Mach number	11
A Virtual Element Method coupled with a Boundary Integral Non Reflecting condition for 2D exterior Helmholtz problems	11
Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations	11
Analysis of a fully discrete approximation for the classical Keller–Segel model: Lower and a priori bounds	11
A linearly second-order, unconditionally energy stable scheme and its error estimates for the modified phase field crystal equation	11
juSFEM: A Julia-based open-source package of parallel Smoothed Finite Element Method (S-FEM) for elastic problems	11
A weak Galerkin finite element method on temporal graded meshes for the multi-term time fractional diffusion equations	11
A C1 virtual element method for the stationary quasi-geostrophic equations of the ocean	11
Radial basis function neural network (RBFNN) approximation of Cauchy inverse problems of the Laplace equation	11
HomPINNs: Homotopy physics-informed neural networks for learning multiple solutions of nonlinear elliptic differential equations	11
Virtual element methods for general linear elliptic interface problems on polygonal meshes with small edges	11
Non-intrusive reduced-order modeling for uncertainty quantification of space–time-dependent parameterized problems	11
Two-grid finite volume element method for the time-dependent Schrödinger equation	10
Shock filter as the classifier for image inpainting problem using the Cahn-Hilliard equation	10
Stabilization-free virtual element method for plane elasticity	10
Superconvergence analysis of a MFEM for BBM equation with a stable scheme	10
Bend 3d mixed virtual element method for Darcy problems	10
Model and data reduction for data assimilation: Particle filters employing projected forecasts and data with application to a shallow water model	10
An implicit lattice Boltzmann flux solver for simulation of compressible flows	10
Variational multiscale modeling with discretely divergence-free subscales	10
Flow and heat transfer of viscoelastic fluid with a novel space distributed-order constitution relationship	10
Robust preconditioning for coupled Stokes–Darcy problems with the Darcy problem in primal form	10
A novel nonlinear FE perturbation method and its application to stacking sequence optimization for snap-through response of cylindrical shell panel	10
Design and investigation of cooling system for high-power LED luminaire	10
A regularized single-phase lattice Boltzmann method for free-surface flows	10
Backward problem for time-space fractional diffusion equations in Hilbert scales	10
A compressed lattice Boltzmann method based on ConvLSTM and ResNet	10
Improved modal analyses using the novel quadrilateral overlapping elements	10
Solving steady-state lid-driven square cavity flows at high Reynolds numbers via a coupled improved element-free Galerkin–reduced integration penalty method	10
Identification of elastoplastic properties of rods from torsion test using meshless methods and a metaheuristic	10
A robust sharp interface based immersed boundary framework for moving body problems with applications to laminar incompressible flows	10
A study on the flow of couple stress fluid in a porous curved channel	10
Goal-oriented mesh adaptation method for nonlinear problems including algebraic errors	10
Numerical analysis of locally conservative weak Galerkin dual-mixed finite element method for the time-dependent Poisson–Nernst–Planck system	10
LEoPart: A particle library for FEniCS	10
Dissipative spatial discretization of a phase field model of multiphase multicomponent isothermal fluid flow	10
An efficient solver for space–time isogeometric Galerkin methods for parabolic problems	10
Spectral approximation based on a mixed scheme and its error estimates for transmission eigenvalue problems	10
Highly accurate wavelet-homotopy solutions for mixed convection hybrid nanofluid flow in an inclined square lid-driven cavity	10
SoftFEM: Revisiting the spectral finite element approximation of second-order elliptic operators	10
Time-stepping DPG formulations for the heat equation	10
An efficient peridynamic framework based on the arc-length method for fracture modeling of brittle and quasi-brittle problems with snapping instabilities	9
A hybrid collocation method for the computational study of multi-term time fractional partial differential equations	9
ENO and WENO schemes using arc-length based smoothness measurement	9
Finite difference/generalized Hermite spectral method for the distributed-order time-fractional reaction-diffusion equation on multi-dimensional unbounded domains	9
Construction of DPG Fortin operators revisited	9
Acoustic wave propagation and its application to fluid structure interaction using the Cumulant Lattice Boltzmann Method	9
Local and parallel finite element algorithms based on domain decomposition for the 2D/3D Stokes equations with damping	9
Numerical modeling of geometrically nonlinear responses of smart magneto-electro-elastic functionally graded double curved shallow shells based on improved FSDT	9
Minimal residual space-time discretizations of parabolic equations: Asymmetric spatial operators	9
Stabilization of the nonconforming virtual element method	9
On the continuous and discrete well-posedness of perturbed saddle-point formulations in Banach spaces	9
A high-order numerical scheme based on graded mesh and its analysis for the two-dimensional time-fractional convection-diffusion equation	9
On numerical simulation of flexibly supported airfoil in interaction with incompressible fluid flow using laminar–turbulence transition model	9
High-order compact difference schemes on wide computational stencils with a spectral-like accuracy	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
A modified characteristic projection finite element method for the Kelvin-Voigt viscoelastic fluid equations	9
Flexible goal-oriented adaptivity for higher-order space–time discretizations of transport problems with coupled flow	9
A partitioned scheme with multiple-time-step technique for the nonstationary dual-porosity-Stokes problem	9
Solving groundwater flow equation using physics-informed neural networks	9
Spectral discretizations analysis with time strong stability preserving properties for pseudo-parabolic models	9
The double adaptivity paradigm	9
A robust uniformly convergent finite difference scheme for the time-fractional singularly perturbed convection-diffusion problem	9
Kalman filter and classical Preisach hysteresis model applied to the state of charge battery estimation	9
Fast second-order implicit difference schemes for time distributed-order and Riesz space fractional diffusion-wave equations	9
Gradient discretization of two-phase flows coupled with mechanical deformation in fractured porous media	9
BoSSS: A package for multigrid extended discontinuous Galerkin methods	9
Convergence and positivity of Finite Element methods for a haptotaxis model of tumoral invasion	9
A finite element method for Allen–Cahn equation on deforming surface	9
Least-squares formulations for eigenvalue problems associated with linear elasticity	8
Numerical simulation of deflagration-to-detonation transition via shock–multiple flame kernels interactions	8
A novel local and parallel finite element method for the mixed Navier–Stokes–Darcy problem	8
Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression	8
Method of fundamental solutions on simulating sloshing liquids in a 2D tank	8
Unconditionally energy stable second-order numerical schemes for the Functionalized Cahn–Hilliard gradient flow equation based on the SAV approach	8
Effective properties of two-dimensional dispersed composites. Part I. Schwarz's alternating method	8
Vibration analysis of variable fractional viscoelastic plate based on shifted Chebyshev wavelets algorithm	8
The development of higher-order numerical differential formulas of Caputo derivative and their applications (I)	8
High order locally conservative finite element solutions for anisotropic diffusion problems in two dimensions	8
Deep neural networks learning forward and inverse problems of two-dimensional nonlinear wave equations with rational solitons	8
An efficient characteristic finite difference S-DDM scheme for convection–diffusion equations	8
Three-dimensional volume reconstruction from multi-slice data using a shape transformation	8
Unconditionally optimal H1-norm error estimates of a fast and linearized Galerkin method for nonlinear subdiffusion equations	8
A higher-order finite difference method for two-dimensional singularly perturbed reaction-diffusion with source-term-discontinuous problem	8
An extended mixed finite element method for elliptic interface problems	8
A leap-frog finite element method for wave propagation of Maxwell–Schrödinger equations with nonlocal effect in metamaterials	8
RANS simulations of terrain-disrupted turbulent airflow at Hong Kong International Airport	8