Preconditioning for radial basis functions with domain decomposition methods

Preconditioning for radial basis functions with domain decomposition methods

In our previous work, an effective preconditioning scheme that is based upon constructing least-squares approximation cardinal basis functions (ACBFs) from linear combinations of the RBF-PDE matrix elements has shown very attractive numerical results. The preconditioner costs O(N2) flops to set up and O(N) storage. The preconditioning technique is sufficiently general that it can be applied to ...

On Approximate Cardinal Preconditioning Methods for Solving PDEs with Radial Basis Functions

The approximate cardinal basis function (ACBF) preconditioning technique has been used to solve partial differential equations (PDEs) with radial basis functions (RBFs). In [31], a preconditioning scheme that is based upon constructing the least-squares approximate cardinal basis function from linear combinations of the RBF-PDE matrix elements has shown very attractive numerical results. This p...

THE COMPARISON OF EFFICIENT RADIAL BASIS FUNCTIONS COLLOCATION METHODS FOR NUMERICAL SOLUTION OF THE PARABOLIC PDE’S

In this paper, we apply the compare the collocation methods of meshfree RBF over differential equation containing partial derivation of one dimension time dependent with a compound boundary nonlocal condition.

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...

Additive Schwarz Domain Decomposition with Radial Basis Approximation