The Direct Radial Basis Function Partition of Unity (D-RBF-PU) Method for Solving PDEs

نویسندگان

چکیده

In this paper, a new localized radial basis function (RBF) method based on partition of unity (PU) is proposed for solving boundary and initial-boundary value problems. The benefits from direct discretization approach called the “direct RBF (D-RBF-PU)” method. Thanks to avoiding all derivatives PU weight functions as well lower local approximants, faster simpler than standard RBF-PU Besides, discontinuous can now be utilized develop in more efficient less expensive way. Alternatively, an RBF-generated finite difference (RBF-FD) setting which much some situations accurate original RBF-FD. polyharmonic splines are used approximations, error stability issues considered. Some numerical experiments irregular two- three-dimensional domains, cost comparison tests, performed support theoretical analysis show efficiency

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Stable Gaussian radial basis function method for solving Helmholtz equations

‎Radial basis functions (RBFs) are a powerful tool for approximating the solution of high-dimensional problems‎. ‎They are often referred to as a meshfree method and can be spectrally accurate‎. ‎In this paper, we analyze a new stable method for evaluating Gaussian radial basis function interpolants based on the eigenfunction expansion‎. ‎We develop our approach in two-dimensional spaces for so...

متن کامل

Preconditioning 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 کامل

The Overlapped Radial Basis Function-Finite Difference (RBF-FD) Method for the Numerical Solution of PDEs

We present a generalization of the RBF-FD method that allows full control of the overlap between RBF-FD stencils. We accomplish this by introducing a continuous overlap parameter δ ∈ [0, 1] such that δ = 1 recovers the standard RBF-FD method and δ = 0 results in a full decoupling of the RBF-FD stencils. We show with a simple example that global interpolation with both RBFs and RBFs augmented wi...

متن کامل

A radial basis function partition of unity collocation method for convection-diffusion equations ⋆

Numerical solution of multi-dimensional PDEs is a challenging problem with respect to computational cost and memory requirements, as well as regarding representation of realistic geometries and adaption to solution features. Meshfree methods such as global radial basis function approximation have been successfully applied to several types of problems. However, due to the dense linear systems th...

متن کامل

Radial basis function partition of unity operator splitting method for pricing multi-asset American options

The operator splitting method in combination with finite differences has been shown to be an efficient approach for pricing American options numerically. Here, the operator splitting formulation is extended to the radial basis function partition of unity method. An approach that has previously often been used together with radial basis function methods to deal with the free boundary arising in ...

متن کامل

ذخیره 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: SIAM Journal on Scientific Computing

سال: 2021

ISSN: ['1095-7197', '1064-8275']

DOI: https://doi.org/10.1137/19m128911x