Towards a scalable hybrid sparse solver

Consider the solution of very large, sparse linear systems. The most popular techniques can be broadly classified as either ‘direct’ or ‘iterative’. When the sparse matrix is symmetric and positive definite, direct methods use Cholesky factorization while iterative methods rely on Conjugate Gradients. Our goal is to develop a scalable and memory-efficient hybrid of the two methods that can be implemented with high efficiency on both serial and parallel computers and be suitable for a wide range of problems. We discuss our overall design with emphasis on performance and scalability issues, and report on progress to date.