A comparison of efficiency and error convergence of multiquadric collocation method and finite element method.

DOI10.1016/S0955-7997(02)00081-4zbMath1044.76050OpenAlexW2014070176MaRDI QIDQ1412687

Jichun Li, Ching-Shyang Chen, Alexander H.-D. Cheng

Publication date: 25 November 2003

Published in: Engineering Analysis with Boundary Elements (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0955-7997(02)00081-4

zbMATH Keywords

radial basis functionexponential convergence

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Finite element methods applied to problems in fluid mechanics (76M10)

Related Items

Applying multiquadric quasi-interpolation to solve Burgers' equation, Multicloud: Multigrid convergence with a meshless operator, A new approach based on the genetic algorithm for finding a good shape parameter in solving partial differential equations by Kansa's method, Performance analyses of mesh-based local finite element method and meshless global RBF collocation method for solving Poisson and Stokes equations, Radial basis function method for a multidimensional linear elliptic equation with nonlocal boundary conditions, An investigation of radial basis function-finite difference (RBF-FD) method for numerical solution of elliptic partial differential equations, A meshless radial basis function method for 2D steady-state heat conduction problems in anisotropic and inhomogeneous media, A meshless radial basis function method for steady-state advection-diffusion-reaction equation in arbitrary 2D domains, A meshless radial basis function based method for modeling dual-phase-lag heat transfer in irregular domains, A gradient reproducing kernel based stabilized collocation method for the static and dynamic problems of thin elastic beams and plates, Solving PDEs with a Hybrid Radial Basis Function: Power-Generalized Multiquadric Kernel, Pharmacokinetic parameter identification using a meshless method approach for transdermal drug delivery, Frictional contact analysis of functionally graded materials with Lagrange finite block method, Stabilized Lagrange interpolation collocation method: a meshfree method incorporating the advantages of finite element method, Multiquadric radial basis function approximation method and asymptotic numerical method for nonlinear and linear static analysis of single-walled carbon nanotubes, A new variable shape parameter strategy for RBF approximation using neural networks, Computing the survival probability density function in jump-diffusion models: a new approach based on radial basis functions, An efficient solution for stochastic fractional partial differential equations with additive noise by a meshless method, A meshless method for solving mKdV equation, On the enriched RBF method for singular potential problems, Dimension reduction analysis with mapping and direct integration algorithm, Simulating backward wave propagation in metamaterial with radial basis functions, Results on meshless collocation techniques, The methods of external and internal excitation for problems of free vibrations of non-homogeneous membranes, A comparison of the meshless RBF collocation method with finite element and boundary element methods in neutron diffusion calculations, The method of approximate particular solutions for solving anisotropic elliptic problems, Numerical solution of the two-phase incompressible Navier-Stokes equations using a GPU-accelerated meshless method, Optimization, conditioning and accuracy of radial basis function method for partial differential equations with nonlocal boundary conditions -- a case of two-dimensional Poisson equation, Method of particular solutions for solving PDEs of the second and fourth orders with variable coefficients, Meshless modeling of coupled transdermal pharmacokinetics with analytical validation, Meshless Solution of Singular Potential Flows in Strong Formulation, Hybrid radial basis function methods of lines for the numerical solution of viscous Burgers' equation, Two numerical meshless techniques based on radial basis functions (RBFs) and the method of generalized moving least squares (GMLS) for simulation of coupled Klein-Gordon-Schrödinger (KGS) equations, A novel meshless method for fully nonlinear advection-diffusion-reaction problems to model transfer in anisotropic media, A numerical study of compact approximations based on flat integrated radial basis functions for second-order differential equations, Improved numerical solver for Kansa's method based on affine space decomposition, Solutions of partial differential equations with random Dirichlet boundary conditions by multiquadric collocation method, A multiquadric quasi-interpolation with linear reproducing and preserving monotonicity, A meshfree stabilized collocation method (SCM) based on reproducing kernel approximation, Finite integration method for solving multi-dimensional partial differential equations, Finite integration method for partial differential equations, A Fast Block-Greedy Algorithm for Quasi-optimal Meshless Trial Subspace Selection, A radial basis function approach to compute the first-passage probability density function in two-dimensional jump-diffusion models for financial and other applications, The method of approximate fundamental solutions (MAFS) for elliptic equations of general type with variable coefficients, A hybrid finite difference and moving least square method for elasticity problems, Solving Poisson equation with Dirichlet conditions through multinode Shepard operators, An improved meshless artificial viscosity technology combined with local radial point interpolation method for 2D shallow water equations, A reproducing kernel Hilbert space approach in meshless collocation method, A meshless method for numerical solution of the one-dimensional wave equation with an integral condition using radial basis functions, A leap-frog meshless method with radial basis functions for simulating electromagnetic wave splitter and rotator, Unnamed Item, Exponential convergence for numerical solution of integral equations using radial basis functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Interpolation of scattered data: distance matrices and conditionally positive definite functions
• Theory and applications of the multiquadric-biharmonic method. 20 years of discovery 1968-1988
• A numerical study of some radial basis function based solution methods for elliptic PDEs
• Toward a universal h-p adaptive finite element strategy. I: Constrained approximation and data structure
• Toward a universal h-p adaptive finite element strategy. III: Design of h-p meshes
• Multiquadric method for the numerical solution of a biphasic mixture model
• Miscellaneous error bounds for multiquadric and related interpolators
• The method of fundamental solutions for elliptic boundary value problems
• A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics
• An efficient numerical scheme for Burger equation
• Solving partial differential equations by collocation using radial basis functions
• The partition of unity finite element method: basic theory and applications
• Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations
• Adaptive interpolation by scaled multiquadrics
• Numerical comparisons of two meshless methods using radial basis functions
• Stable computation of multiquadric interpolants for all values of the shape parameter
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• Compactly supported radial basis functions for shallow water equations.
• Error estimates and condition numbers for radial basis function interpolation
• The parameter \(R^ 2\) in multiquadric interpolation
• Scattered Data Interpolation: Tests of Some Method
• A numerical method for heat transfer problems using collocation and radial basis functions
• Improved error bounds for scattered data interpolation by radial basis functions
• Element‐free Galerkin methods
• Thepandh-pVersions of the Finite Element Method, Basic Principles and Properties
• Exponential convergence andH-c multiquadric collocation method for partial differential equations
• Multivariate Interpolation and Conditionally Positive Definite Functions. II