On Generation of Node Distributions for Meshless PDE Discretizations

DOI10.1137/18M1231456WikidataQ127031806 ScholiaQ127031806MaRDI QIDQ5240807

Gregor Kosec, Jure Slak

Publication date: 29 October 2019

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.03160

zbMATH Keywords

RBF-FDmeshless methods for PDEsnode generation algorithmsvariable density discretizations

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Complexity and performance of numerical algorithms (65Y20) Numerical methods for partial differential equations, boundary value problems (65N99) Numerical approximation and computational geometry (primarily algorithms) (65D99)

Related Items (15)

An unfitted RBF-FD method in a least-squares setting for elliptic PDEs on complex geometries ⋮ A conservative network element method for diffusion-advection-reaction problems ⋮ An extended multiphase hybrid-stress finite element method for modelling interface crack propagation between two dissimilar materials ⋮ Error estimates of divergence-free generalized moving least squares (div-free GMLS) derivatives approximations in Sobolev spaces ⋮ Accelerating explicit time-stepping with spatially variable time steps through machine learning ⋮ An improved local radial basis function method for solving small-strain elasto-plasticity ⋮ Guidelines for RBF-FD discretization: numerical experiments on the interplay of a multitude of parameter choices ⋮ The kriging integration method applied to the boundary element analysis of Poisson problems ⋮ On the meshfree particle methods for fluid-structure interaction problems ⋮ A divergence-free generalized moving least squares approximation with its application ⋮ Micro-combustion modelling with RBF-FD: a high-order meshfree method for reactive flows in complex geometries ⋮ Monomial augmentation guidelines for RBF-FD from accuracy versus computational time perspective ⋮ A Least Squares Radial Basis Function Finite Difference Method with Improved Stability Properties ⋮ Fast Variable Density 3-D Node Generation ⋮ A new radial basis integration method applied to the boundary element analysis of 2D scalar wave equations

Uses Software

• Eigen
• DistMesh
• Mfree2D
• nanoflann
• GitHub

Cites Work

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• On the role of polynomials in RBF-FD approximations: II. Numerical solution of elliptic PDEs
• Refined meshless local strong form solution of Cauchy-Navier equation on an irregular domain
• A new method for evaluating options based on multiquadric RBF-FD method
• Fast generation of 2-D node distributions for mesh-free PDE discretizations
• Local radial basis function collocation method for linear thermoelasticity in two dimensions
• A steepest gradient method for optimum structural design
• A Primer on Radial Basis Functions with Applications to the Geosciences
• Robust Node Generation for Mesh-free Discretizations on Irregular Domains and Surfaces
• A Simple Mesh Generator in MATLAB
• Solving PDEs with radial basis functions
• A general advancing front technique for filling space with arbitrary objects

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