Sparse hierarchical solvers with guaranteed convergence
Abstract
Solving sparse linear systems from discretized partial differential equations is challenging. Direct solvers have, in many cases, quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and efficient. Approximate factorization preconditioners such as incomplete LU factorization provide cheap approximations to the system matrix. However, even a highly accurate preconditioner may have deteriorating performance when the condition number of the system matrix increases. By increasing the accuracy on low‐frequency errors, we propose a novel hierarchical solver with improved robustness with respect to the condition number of the linear system. This solver retains the linear computational cost and memory footprint of the original algorithm.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jul 25, 2019
- Source ID
- 10.1002/nme.6166
Entities
People
- Eric F Darve
- Hadi Pouransari
- Kai Yang
Organizations
- Stanford University
- United States Army Research Laboratory