On Element SDD Approximability
Haim Avron, Gil Shklarski, Sivan Toledo
TL;DR
This paper investigates the limitations of approximating scalar elliptic finite element matrices with SDD matrices, demonstrating cases where such approximation is poor, and analyzes a heuristic method for this purpose.
Contribution
It provides the first analysis of the approximability of finite element matrices by SDD matrices and evaluates a simple heuristic approach.
Findings
Certain scalar elliptic finite element matrices cannot be well approximated by SDD matrices
A theoretical analysis of a heuristic method for SDD approximation is presented
The results highlight limitations in using SDD matrices for finite element matrix approximation
Abstract
This short communication shows that in some cases scalar elliptic finite element matrices cannot be approximated well by an SDD matrix. We also give a theoretical analysis of a simple heuristic method for approximating an element by an SDD matrix.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Numerical Methods in Computational Mathematics · Electromagnetic Scattering and Analysis