相关论文: Stability analysis of RBF-FD and WLS based local s…
Since the advent of mesh-free methods as a tool for the numerical analysis of systems of Partial Differential Equations (PDEs), many variants of differential operator approximation have been proposed. In this work, we propose a local…
Polyharmonic spline (PHS) radial basis functions (RBFs) are used together with polynomials to create local RBF-finite-difference (RBF-FD) weights on different node layouts for spatial discretization of the compressible Navier-Stokes…
Strong-form meshless methods received much attention in recent years and are being extensively researched and applied to a wide range of problems in science and engineering. However, the solution of elasto-plastic problems has proven to be…
This paper introduces a novel meshfree methodology based on Radial Basis Function-Finite Difference (RBF-FD) approximations for the numerical solution of partial differential equations (PDEs) on surfaces of codimension 1 embedded in…
Recent developments have made it possible to overcome grid-based limitations of finite difference (FD) methods by adopting the kernel-based meshless framework using radial basis functions (RBFs). Such an approach provides a meshless…
Local meshless methods obtain higher convergence rates when RBF approximations are augmented with monomials up to a given order. If the order of the approximation method is spatially variable, the numerical solution is said to be p-refined.…
Localized collocation methods based on radial basis functions (RBFs) for elliptic problems appear to be non-robust in the presence of Neumann boundary conditions. In this paper we overcome this issue by formulating the RBF-generated finite…
A semi-implicit fractional-step method that uses a staggered node layout and radial basis function-finite differences (RBF-FD) to solve the incompressible Navier-Stokes equations is developed. Polyharmonic splines (PHS) with polynomial…
Quadrature formulas (QFs) based on radial basis functions (RBFs) have become an essential tool for multivariate numerical integration of scattered data. Although numerous works have been published on RBF-QFs, their stability theory can…
Radial Basis Function-generated Finite Differences (RBF-FD) is a popular variant of local strong-form meshless methods that do not require a predefined connection between the nodes, making it easier to adapt node-distribution to the problem…
Radial basis function generated finite-difference (RBF-FD) methods have recently gained popularity due to their flexibility with irregular node distributions. However, the convergence theories in the literature, when applied to nonuniform…
In this paper, we address a way to reduce the total computational cost of meshless approximation by reducing the required stencil size through spatial variation of computational node regularity. Rather than covering the entire domain with…
A specialized mesh-free radial basis function-based finite difference (RBF-FD) discretization is used to solve the large eigenvalue problems arising in hydrodynamic stability analyses of flows in complex domains. Polyharmonic spline…
Approximation methods are widely used in many fields and many techniques have been published already. This comparative study presents a comparison of LOWESS (Locally weighted scatterplot smoothing) and RBF (Radial Basis Functions)…
In recent years, a variety of meshless methods have been developed to solve partial differential equations in complex domains. Meshless methods discretize the partial differential equations over scattered points instead of grids. Radial…
Meshless solution to differential equations using radial basis functions (RBF) is an alternative to grid based methods commonly used. Since the meshless method does not need an underlying connectivity in the form of control volumes or…
Most problems in electrodynamics do not have an analytical solution so much effort has been put in the development of numerical schemes, such as the finite-difference method, volume element methods, boundary element methods, and related…
When solving partial differential equations on scattered nodes using the Radial Basis Function-generated Finite Difference (RBF-FD) method, one of the parameters that must be chosen is the stencil size. Focusing on Polyharmonic Spline RBFs…
Hybrid methods for simulating rarefied gas flows reduce computational cost by coupling a particle-based model, typically the direct simulation Monte Carlo (DSMC) method, to a continuum-based solver, i.e. a computational fluid dynamics (CFD)…
Meshfree radial basis function (RBF) methods are popular tools used to numerically solve partial differential equations (PDEs). They take advantage of being flexible with respect to geometry, easy to implement in higher dimensions, and can…