A Robust RBF-FD Formulation based on Polyharmonic Splines and Polynomials
نویسندگان
چکیده
{To be written...}
منابع مشابه
On the role of polynomials in RBF-FD approximations: I. Interpolation and accuracy
Radial basis function-generated finite difference (RBF-FD) approximations generalize classical grid-based finite differences (FD) from lattice-based to scattered node layouts. This greatly increases the geometric flexibility of the discretizations and makes it easier to carry out local refinement in critical areas. Many different types of radial functions have been considered in this RBF-FD con...
متن کاملThe 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 کاملThe overlapped radial basis function-finite difference (RBF-FD) method: A generalization of RBF-FD
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 کاملPOLYHARMONIC SPLINES ON GRIDS Z× aZ AND THEIR LIMITS
Radial Basis Functions (RBF) have found a wide area of applications. We consider the case of polyharmonic RBF (called sometimes polyharmonic splines) where the data are on special grids of the form Z× aZn having practical importance. The main purpose of the paper is to consider the behavior of the polyharmonic interpolation splines Ia on such grids for the limiting process a → 0, a > 0. For a l...
متن کاملPolyharmonic splines on grids ℤ x aℤn and their limits
Radial Basis Functions (RBF) have found a wide area of applications. We consider the case of polyharmonic RBF (called sometimes polyharmonic splines) where the data are on special grids of the form Z× aZn having practical importance. The main purpose of the paper is to consider the behavior of the polyharmonic interpolation splines Ia on such grids for the limiting process a → 0, a > 0. For a l...
متن کامل