To address the scalability problem of existing sparse direct approaches, WP3 focuses on several key aspects: the development of lower bounds for communication and redesign of algorithms to try and attain these lower bounds, exploitation of the advances for dense methods pioneered in WP2, the use of novel data structures to enhance parallelism, the use of mixed-precision arithmetic, the parallel factorization of highly unsymmetric matrices, and the extension of direct methods through their combination with iterative methods. WP3 will also interact closely with WP4.
We structure the work in this work package in four tasks:
- Lower Bounds on Communication for Sparse Matrices
- Direct Methods for (Near-)Symmetric Systems
- Direct Methods for Highly Unsymmetric Systems
- Hybrid Direct–Iterative Methods