Stability and preconditioning for a hybrid approximation on the sphere
Numerical Analysis
2010-09-23 v1
Abstract
This paper proposes a new preconditioning scheme for a linear system with a saddle-point structure arising from a hybrid approximation scheme on the sphere, an approximation scheme that combines (local) spherical radial basis functions and (global) spherical polynomials. Making use of a recently derived inf-sup condition [13] and the Brezzi stability and convergence theorem for this approximation scheme, we show that the linear system can be optimally preconditioned with a suitable block-diagonal preconditioner. Numerical experiments with a non-uniform distribution of data points support the theoretical conclusions.
Cite
@article{arxiv.1009.4275,
title = {Stability and preconditioning for a hybrid approximation on the sphere},
author = {Q. T. Le Gia and Ian H. Sloan and Andrew J. Wathen},
journal= {arXiv preprint arXiv:1009.4275},
year = {2010}
}
Comments
14 pages, 1 figure, submitted