Fast and Robust Linear Solvers based on Hierarchical Matrices (LDRD Final Report)

Technical Report · 01 November 2019

DOI:https://doi.org/10.2172/1574609· OSTI ID:1574609

Boman, Erik Gunnar ^[1]; Darve, Eric ^[1]; Lehoucq, Richard B. ^[1]; Rajamanickam, Sivasankaran ^[1]; Tuminaro, Raymond S. ^[1]; Yamazaki, Ichitaro ^[1]

---

1. Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)

This report is the final report for the LDRD project "Fast and Robust Linear Solvers using Hierarchical Matrices". The project was a success. We developed two novel algorithms for solving sparse linear systems. We demonstrated their effectiveness on ill-conditioned linear systems from ice sheet simulations. We showed that in many cases, we can obtain near-linear scaling. We believe this approach has strong potential for difficult linear systems and should be considered for other Sandia and DOE applications. We also report on some related research activities in dense solvers and randomized linear algebra.

• Research Organization: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sandia National Lab. (SNL-CA), Livermore, CA (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• DOE Contract Number: AC04-94AL85000; NA0003525
• OSTI ID: 1574609
• Report Number(s): SAND-2019-13939R; 681453
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING