Preconditioning for Domain Decomposition through Function Approximation

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 ...

Preconditioners for pseudodifferential equations on the sphere with radial basis functions

In a previous paper a preconditioning strategy based on overlapping domain decomposition was applied to the Galerkin approximation of elliptic partial differential equations on the sphere. In this paper the methods are extended to more general pseudodifferential equations on the sphere, using as before spherical radial basis functions for the approximation space, and again preconditioning the i...

Domain Decomposition Preconditioning for Discontinuous Galerkin Approximations of Convection-Diffusion Problems

Low-rank correction methods for algebraic domain decomposition preconditioners

This paper presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits the domain decomposition method and low-rank corrections. The domain decomposition approach decouples the matrix and once inverted, a low-rank approximation is applied by e...

Domain Decomposition and Preconditioning Method for Linear Partial Differential Equations Systems

This talk concerns a preconditioning method of AMLI type [3] for the solution of linear partial differential equations systems. An earlier idea of this study was proposed in [2] for scalar case. In this work we want to make some further extension of the study done in [1], in particular we propose to give a robust preconditioning iterative schemes using domain decomposition methods. Based on a s...