Paper Info
Title
Dimensionally Consistent Preconditioning For Saddle-Point Problems
Abstract
The preconditioned iterative solution of large-scale saddle-point systems is of great importance in numerous application areas, many of them involving partial differential equations. Robustness with respect to certain problem parameters is often a concern, and it can be addressed by identifying proper scalings of preconditioner building blocks. In this paper, we consider a new perspective to finding effective and robust preconditioners. Our approach is based on the consideration of the natural physical units underlying the respective saddle-point problem. This point of view, which we refer to as dimensional consistency, suggests a natural combination of the parameters intrinsic to the problem. It turns out that the scaling obtained in this way leads to robustness with respect to problem parameters in many relevant cases. As a consequence, we advertise dimensional consistency based preconditioning as a new and systematic way to designing parameter robust preconditoners for saddle-point systems arising from models for physical phenomena.
Year
DOI
Venue
2021
10.1515/cmam-2020-0037
COMPUTATIONAL METHODS IN APPLIED MATHEMATICS
Keywords
DocType
Volume
Saddle-Point Problems, Preconditioning, Dimensional Consistency, Physical Units, Minimum Residual Method
Journal
21
Issue
ISSN
Citations 
3
1609-4840
0
PageRank 
References 
Authors
0.34
0
1
Name
Order
Citations
PageRank
Herzog Roland100.34