Spectral analysis and preconditioning techniques for radial basis function collocation matrices
نویسندگان
چکیده
منابع مشابه
Spectral analysis and preconditioning techniques for radial basis function collocation matrices
Meshless collocation methods based on radial basis functions lead to structured linear systems which, for equispaced grid points, have almost a multilevel Toeplitz structure. In particular, if we consider partial differential equations (PDEs) in two dimensions then we find almost (up to a “low-rank” correction given by the boundary conditions) two-level Toeplitz matrices, i.e., block Toeplitz w...
متن کاملCollocation Method using Compactly Supported Radial Basis Function for Solving Volterra's Population Model
In this paper, indirect collocation approach based on compactly supported radial basis function (CSRBF) is applied for solving Volterra's population model. The method reduces the solution of this problem to the solution of a system of algebraic equations. Volterra's model is a non-linear integro-differential equation where the integral term represents the effect of toxin. To solve the pr...
متن کاملSpace-time radial basis function collocation method for one-dimensional advection-diffusion problem
The parabolic partial differential equation arises in many application of technologies. In this paper, we propose an approximate method for solution of the heat and advection-diffusion equations using Laguerre-Gaussians radial basis functions (LG-RBFs). The results of numerical experiments are compared with the other radial basis functions and the results of other schemes to confirm the validit...
متن کاملPreconditioning for Radial Basis Function Partition of Unity Methods
Meshfree radial basis function (RBF) methods are of interest for solving partial differential equations due to attractive convergence properties, flexibility with respect to geometry, and ease of implementation. For global RBF methods, the computational cost grows rapidly with dimension and problem size, so localised approaches, such as partition of unity or stencil based RBF methods, are curre...
متن کاملA Radial Basis Function Collocation Approach in Computational Fluid Dynamics
This paper explores the application of the mesh-free radial basis function collocation method for solution of heat transfer and fluid flow problems. The solution procedure is represented for a Poisson reformulated general transport equation in terms of a-symmetric, symmetric and modified (double consideration of the boundary nodes) collocation approaches. In continuation, specifics of a primiti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Numerical Linear Algebra with Applications
سال: 2011
ISSN: 1070-5325
DOI: 10.1002/nla.774