The overlapped radial basis function-finite difference (RBF-FD) method: a generalization of RBF-FD

DOI10.1016/j.jcp.2017.04.037zbMath1380.65180arXiv1606.03135OpenAlexW2568756429MaRDI QIDQ1686618

Varun Shankar

Publication date: 15 December 2017

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.03135

zbMATH Keywords

domain decompositionradial basis functionhigh-order methodmeshfree methodone-sided stencil

Mathematics Subject Classification ID

Heat equation (35K05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55)

Related Items (31)

An unfitted RBF-FD method in a least-squares setting for elliptic PDEs on complex geometries ⋮ A high-order accurate meshless method for solution of incompressible fluid flow problems ⋮ An efficient high-order meshless method for advection-diffusion equations on time-varying irregular domains ⋮ Local RBF method for transformed three dimensional sub-diffusion equations ⋮ RBF-FD meshless optimization using direct search (GLODS) in the analysis of composite plates ⋮ Domain-Decomposition Localized Method of Fundamental Solutions for Large-Scale Heat Conduction in Anisotropic Layered Materials ⋮ Reduced order modeling of time-dependent incompressible Navier-Stokes equation with variable density based on a local radial basis functions-finite difference (LRBF-FD) technique and the POD/DEIM method ⋮ Robust Node Generation for Mesh-free Discretizations on Irregular Domains and Surfaces ⋮ \(h\)-adaptive radial basis function finite difference method for linear elasticity problems ⋮ Radial basis solutions of second‐order quasi‐linear hyperbolic boundary value problem ⋮ A fault detection method based on partition of unity and kernel approximation ⋮ Towards stability results for global radial basis function based quadrature formulas ⋮ Guidelines for RBF-FD discretization: numerical experiments on the interplay of a multitude of parameter choices ⋮ The D-RBF-PU method for solving surface PDEs ⋮ Error bounds for a least squares meshless finite difference method on closed manifolds ⋮ Asymptotic and Numerical Analysis of a Stochastic PDE Model of Volume Transmission ⋮ A stabilized radial basis-finite difference (RBF-FD) method with hybrid kernels ⋮ Simulation flows with multiple phases and components via the radial basis functions-finite difference (RBF-FD) procedure: Shan-Chen model ⋮ A Robust Hyperviscosity Formulation for Stable RBF-FD Discretizations of Advection-Diffusion-Reaction Equations on Manifolds ⋮ Mesh-free semi-Lagrangian methods for transport on a sphere using radial basis functions ⋮ Numerical simulation of a prostate tumor growth model by the RBF-FD scheme and a semi-implicit time discretization ⋮ A strong-form local meshless approach based on radial basis function-finite difference (RBF-FD) method for solving multi-dimensional coupled damped Schrödinger system appearing in Bose-Einstein condensates ⋮ Hyperviscosity-based stabilization for radial basis function-finite difference (RBF-FD) discretizations of advection-diffusion equations ⋮ A local radial basis function-finite difference (RBF-FD) method for solving 1D and 2D coupled Schrödinger-Boussinesq (SBq) equations ⋮ RBF-LOI: augmenting radial basis functions (RBFs) with least orthogonal interpolation (LOI) for solving PDEs on surfaces ⋮ A meshless finite difference method based on polynomial interpolation ⋮ A Least Squares Radial Basis Function Finite Difference Method with Improved Stability Properties ⋮ A POD-RBF-FD scheme for simulating chemotaxis models on surfaces ⋮ The Direct Radial Basis Function Partition of Unity (D-RBF-PU) Method for Solving PDEs ⋮ A compact radial basis function partition of unity method ⋮ RBF-FD discretization of the Navier-Stokes equations on scattered but staggered nodes

Uses Software

• Gmsh
• Matlab
• DistMesh
• rbf_qr

Cites Work

• Unnamed Item
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