Optimal quasi-diagonal preconditioners for pseudodifferential operators of order minus two
Numerical Analysis
2018-06-22 v1
Abstract
We present quasi-diagonal preconditioners for piecewise polynomial discretizations of pseudodifferential operators of order minus two in any space dimension. Here, quasi-diagonal means diagonal up to a sparse transformation. Considering shape regular simplicial meshes and arbitrary fixed polynomial degrees, we prove, for dimensions larger than one, that our preconditioners are asymptotically optimal. Numerical experiments in two, three and four dimensions confirm our results. For each dimension, we report on condition numbers for piecewise constant and piecewise linear polynomials.
Keywords
Cite
@article{arxiv.1806.07933,
title = {Optimal quasi-diagonal preconditioners for pseudodifferential operators of order minus two},
author = {Thomas Führer and Norbert Heuer},
journal= {arXiv preprint arXiv:1806.07933},
year = {2018}
}