Meshfree explicit local radial basis function collocation method for diffusion problems

DOI10.1016/j.camwa.2006.04.013zbMath1168.41003OpenAlexW1968293773MaRDI QIDQ936705

Publication date: 19 August 2008

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2006.04.013

zbMATH Keywords

Kansa method heat diffusion problem meshfree collocation method multiquadrics radial basis functions

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multidimensional problems (41A63)

Related Items

3D elastic dental analysis by a local RBF collocation method ⋮ Numerical solution of time-fractional fourth-order reaction-diffusion model arising in composite environments ⋮ A meshless collocation method for band structure simulation of nanoscale phononic crystals based on nonlocal elasticity theory ⋮ Meshless approach to the large-eddy simulation of the continuous casting process ⋮ Multicloud: Multigrid convergence with a meshless operator ⋮ Meshless symplectic and multi-symplectic local RBF collocation methods for nonlinear Schrödinger equation ⋮ On the solution of the non-local parabolic partial differential equations via radial basis functions ⋮ Localized method of approximate particular solutions with polynomial basis functions ⋮ Meshless procedure for highly oscillatory kernel based one-dimensional Volterra integral equations ⋮ A meshless scheme for incompressible fluid flow using a velocity-pressure correction method ⋮ Local RBF method for transformed three dimensional sub-diffusion equations ⋮ A meshless multi-symplectic local radial basis function collocation scheme for the ``good Boussinesq equation ⋮ Simulation of laminar backward facing step flow under magnetic field with explicit local radial basis function collocation method ⋮ Generalized polyharmonic multiquadrics ⋮ Extrapolated local radial basis function collocation method for shallow water problems ⋮ Numerical solution of stochastic elliptic partial differential equations using the meshless method of radial basis functions ⋮ Estimating the temperature evolution of foodstuffs during freezing with a 3D meshless numerical method ⋮ Meshless methods for multivariate highly oscillatory Fredholm integral equations ⋮ Local radial basis function collocation method for solving thermo-driven fluid-flow problems with free surface ⋮ The localized method of approximated particular solutions for solving two-dimensional incompressible viscous flow field ⋮ Simulation of elastic wave propagation in layered materials by the method of fundamental solutions ⋮ Band structure computation of in-plane elastic waves in 2D phononic crystals by a meshfree local RBF collocation method ⋮ Improved localized radial basis function collocation method for multi-dimensional convection-dominated problems ⋮ An alternative local collocation strategy for high-convergence meshless PDE solutions, using radial basis functions ⋮ The local meshless method based on Pascal polynomial basis functions for solving fourth-order PDEs ⋮ Three kinds of novel multi-symplectic methods for stochastic Hamiltonian partial differential equations ⋮ Application of the generalized finite difference method to three-dimensional transient electromagnetic problems ⋮ Phase field simulation of Rayleigh-Taylor instability with a meshless method ⋮ Domain-decomposition generalized finite difference method for stress analysis in multi-layered elastic materials ⋮ Modeling nonlinear waves in a numerical wave tank with localized meshless RBF method ⋮ ADI method based on \(C^2\)-continuous two-node integrated-RBF elements for viscous flows ⋮ RBF-FD formulas and convergence properties ⋮ Optimal variable shape parameter for multiquadric based RBF-FD method ⋮ A comparison of three explicit local meshless methods using radial basis functions ⋮ An element-free smoothed radial point interpolation method (EFS-RPIM) for 2D and 3D solid mechanics problems ⋮ Radial basis function collocation method for the numerical solution of the two-dimensional transient nonlinear coupled Burgers equations ⋮ A localized approach for the method of approximate particular solutions ⋮ An adaptive domain partitioning technique for meshfree-type methods ⋮ A least-square radial point collocation method for adaptive analysis in linear elasticity ⋮ An integrated-RBF technique based on Galerkin formulation for elliptic differential equations ⋮ An order-\(N\) complexity meshless algorithm for transport-type PDEs, based on local Hermitian interpolation ⋮ A localized collocation meshless method (LCMM) for incompressible flows CFD modeling with applications to transient hemodynamics ⋮ Comparison of local weak and strong form meshless methods for 2-D diffusion equation ⋮ An overview of the method of fundamental solutions -- solvability, uniqueness, convergence, and stability ⋮ An improved local radial basis function collocation method based on the domain decomposition for composite wall ⋮ The radial point interpolation mixed collocation method for the solution of transient diffusion problems ⋮ Solution of transient direct-chill aluminium billet casting problem with simultaneous material and interphase moving boundaries by a meshless method ⋮ The generalized finite difference method for long-time dynamic modeling of three-dimensional coupled thermoelasticity problems ⋮ The modified localized method of approximated particular solutions for solving elliptic equations with mixed boundary conditions on scattered data ⋮ A model-integrated localized collocation meshless method for large scale three-dimensional heat transfer problems ⋮ Simulation of macrosegregation with mesosegregates in binary metallic casts by a meshless method ⋮ Solution of a continuous casting of steel benchmark test by a meshless method ⋮ A comparison study of meshfree techniques for solving the two-dimensional linear hyperbolic telegraph equation ⋮ Optimization, conditioning and accuracy of radial basis function method for partial differential equations with nonlocal boundary conditions -- a case of two-dimensional Poisson equation ⋮ Optimal constant shape parameter for multiquadric based RBF-FD method ⋮ Novel multilevel techniques for convergence acceleration in the solution of systems of equations arising from RBF-FD meshless discretizations ⋮ Meshless modeling of coupled transdermal pharmacokinetics with analytical validation ⋮ Localized method of fundamental solutions for two- and three-dimensional transient convection-diffusion-reaction equations ⋮ Localized radial basis functions-based pseudo-spectral method (LRBF-PSM) for nonlocal diffusion problems ⋮ Localized method of fundamental solutions for solving two-dimensional Laplace and biharmonic equations ⋮ A new method for evaluating options based on multiquadric RBF-FD method ⋮ Meshless simulation of a lid-driven cavity problem with a non-Newtonian fluid ⋮ Meshless methods for two-dimensional oscillatory Fredholm integral equations ⋮ Localized Chebyshev collocation method for solving elliptic partial differential equations in arbitrary 2D domains ⋮ Local radial basis function based gridfree scheme for unsteady incompressible viscous flows ⋮ A local radial basis function collocation method for band structure computation of 3D phononic crystals ⋮ Pricing European and American options with two stochastic factors: a highly efficient radial basis function approach ⋮ The Kansa RBF method with auxiliary boundary centres for fourth order boundary value problems ⋮ Two algorithms for fast 2D node generation: application to RBF meshless discretization of diffusion problems and image halftoning ⋮ Fully meshless solution of the one-dimensional multigroup neutron transport equation with the radial basis function collocation method ⋮ An improved localized method of approximate particular solutions for solving elliptic PDEs ⋮ An adaptive RBF finite collocation approach to track transport processes across moving fronts ⋮ Modeling of transport of first-order reaction networks in porous media using meshfree radial point collocation method ⋮ Local method of approximate particular solutions for two-dimensional unsteady Burgers' equations ⋮ Meshfree numerical approach based on the finite pointset method for static linear elasticity problems ⋮ A local reproducing kernel method accompanied by some different edge improvement techniques: application to the Burgers' equation ⋮ Localized method of approximate particular solutions for solving unsteady Navier-Stokes problem ⋮ The method of fundamental solutions for the Stokes flow with the subdomain technique ⋮ Nonlinear elastic-plastic analysis of reinforced concrete column-steel beam connection by RBF-FD method ⋮ Localized MQ-RBF meshless techniques for modeling unsaturated flow ⋮ Method of particular solutions using polynomial basis functions for the simulation of plate bending vibration problems ⋮ Local radial basis function collocation method for bending analyses of quasicrystal plates ⋮ Multi-level meshless methods based on direct multi-elliptic interpolation ⋮ A local radial basis function collocation method for band structure computation of phononic crystals with scatterers of arbitrary geometry ⋮ Meshless symplectic and multi-symplectic local RBF collocation methods for Hamiltonian PDEs ⋮ The localized radial basis functions for parameterized level set based structural optimization ⋮ Equivalent-PDE based stabilization of strong-form meshless methods applied to advection-dominated problems ⋮ Finite and infinite block Petrov-Galerkin method for cracks in functionally graded materials ⋮ The use of PDE centres in the local RBF Hermitian method for 3D convective-diffusion problems ⋮ Solving biharmonic equation as an optimal control problem using localized radial basis functions collocation method ⋮ Application of the local RBF collocation method to natural convection in a 3D cavity influenced by a magnetic field ⋮ Numerical study of high order nonlinear dispersive PDEs using different RBF approaches ⋮ Meshless symplectic and multi-symplectic algorithm for Klein-Gordon-Schrödinger system with local RBF collocation ⋮ A meshless solution of the compressible viscous flow in axisymmetric tubes with varying cross-sections ⋮ A shock-capturing meshless scheme using RBF blended interpolation and moving least squares ⋮ Numerical simulations of nonlocal phase-field and hyperbolic nonlocal phase-field models via localized radial basis functions-based pseudo-spectral method (LRBF-PSM) ⋮ In-silico study about the influence of electroporation parameters on the chemotherapeutic drug transport in cancer tissues using the meshless method of approximate particular solutions ⋮ Acceleration of RBF-FD meshless phase-field modelling of dendritic solidification by space-time adaptive approach ⋮ A novel meshfree approach based on the finite pointset method for linear elasticity problems ⋮ Simulation of electromagnetic wave propagations in negative index materials by the localized RBF-collocation method ⋮ On the numerical solution of Fredholm integral equations utilizing the local radial basis function method ⋮ A localized meshless approach for modeling spatial-temporal calcium dynamics in ventricular myocytes ⋮ From Global to Local Radial Basis Function Collocation Method for Transport Phenomena ⋮ A meshfree local RBF collocation method for anti-plane transverse elastic wave propagation analysis in 2D phononic crystals ⋮ Meshless and Multi-Resolution Collocation Techniques for Steady State Interface Models ⋮ A Comparative Study on Polynomial Expansion Method and Polynomial Method of Particular Solutions ⋮ Circulant matrix and conformal mapping for solving partial differential equations ⋮ A numerical method based on boundary integral equations and radial basis functions for plane anisotropic thermoelastostatic equations with general variable coefficients ⋮ A novel localized collocation solver based on Trefftz basis for potential-based inverse electromyography ⋮ Solving biharmonic equation using the localized method of approximate particular solutions ⋮ A gradient reproducing kernel based stabilized collocation method for the static and dynamic problems of thin elastic beams and plates ⋮ Numerical study of generalized 2-D nonlinear Schrödinger equation using Kansa method ⋮ Numerical solution of COVID-19 pandemic model via finite difference and meshless techniques ⋮ A meshless multiscale method for simulating hemodynamics ⋮ A new hybrid boundary node method based on Taylor expansion and the Shepard interpolation method ⋮ Simulation of reactive transport in porous media using radial point collocation method ⋮ A direct Chebyshev collocation method for the numerical solutions of three-dimensional Helmholtz-type equations ⋮ Solution of three-dimensional temperature and turbulent velocity field in continuously cast steel billets with electromagnetic stirring by a meshless method ⋮ Meshless structure-preserving GRBF collocation methods for stochastic Maxwell equations with multiplicative noise ⋮ A local hybrid kernel meshless method for numerical solutions of two‐dimensional fractional cable equation in neuronal dynamics ⋮ A localized Fourier collocation method for solving high-order partial differential equations ⋮ Meshless methods for one-dimensional oscillatory Fredholm integral equations ⋮ An improved local radial basis function method for solving small-strain elasto-plasticity ⋮ An efficient hybrid collocation scheme for vibro-acoustic analysis of the underwater functionally graded structures in the shallow ocean ⋮ Local radial basis function scheme for solving a class of fractional integro‐differential equations based on the use of mixed integral equations ⋮ An adaptive support domain for the in-compressible fluid flow based on the localized radial basis function collocation method ⋮ Solution of a low Prandtl number natural convection benchmark by a local meshless method ⋮ Local radial basis function collocation method for linear thermoelasticity in two dimensions ⋮ Implementation of a generalized exponential basis functions method for linear and non‐linear problems ⋮ Meshless symplectic and multi-symplectic scheme for the coupled nonlinear Schrödinger system based on local RBF approximation ⋮ A multidomain integrated-radial-basis-function collocation method for elliptic problems ⋮ Solving an eigenvalue problem on a periodic domain using a radial basis function finite difference scheme ⋮ A comparison study of the LMAPS method and the LDQ method for time-dependent problems ⋮ The localized RBFs collocation methods for solving high dimensional PDEs ⋮ Local RBFs Based Collocation Methods for Unsteady Navier-Stokes Equations ⋮ A Regularized Singular Boundary Method for Inverse Cauchy Problem in Three-Dimensional Elastostatics ⋮ Upwind Strategy for Localized Method of Approximate Particular Solutions with Applications to Convection Dominated Diffusion Problems ⋮ A Radial Basis Function Meshless Numerical Method for Solving Interface Problems in Irregular Domains ⋮ A scalable and implicit meshless RBF method for the 3D unsteady nonlinear Richards equation with single and multi-zone domains ⋮ A control volume technique based on integrated RBFNs for the convection-diffusion equation ⋮ A numerical study of 2D integrated RBFNs incorporating Cartesian grids for solving 2D elliptic differential problems ⋮ Assessment of global and local meshless methods based on collocation with radial basis functions for parabolic partial differential equations in three dimensions ⋮ A local hermitian RBF meshless numerical method for the solution of multi-zone problems ⋮ Meshless local radial basis function collocation method for convective‐diffusive solid‐liquid phase change problems ⋮ Solution of Burgers’ Equation Using a Local-RBF Meshless Method ⋮ The method of fundamental solution for the inverse source problem for the space-fractional diffusion equation ⋮ <scp>S</scp>chwarz alternating domain decomposition approach for the solution of two‐dimensional <scp>N</scp>avier–<scp>S</scp>tokes flow problems by the method of approximate particular solutions ⋮ A MESHLESS LOCAL GALERKIN INTEGRAL EQUATION METHOD FOR SOLVING A TYPE OF DARBOUX PROBLEMS BASED ON RADIAL BASIS FUNCTIONS ⋮ Educating local radial basis functions using the highest gradient of interest in three dimensional geometries

Cites Work