Optimal Quasi-diagonal Preconditioners for Pseudodifferential Operators of Order Minus Two
Loading...
Date
2019
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
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.
Description
Keywords
Pseudodifferential operator of negative order, Diagonal scaling, Additive Schwarz method, Preconditioner, Negative order Sobolev spaces