Speaker: Alfredo Buttari Affiliation: CNRS, IRIT, Toulouse Time: Friday, 14/05/2021, 16:00
Title: Reducing the complexity of linear systems solvers through the block low-rank format
Direct linear system solvers are commonly regarded as robust methods for computing the solution of linear systems of equations. Nonetheless, their complexity makes the handling of very large size problems difficult or unfeasible due to excessive execution time or memory consumption. In this talk we discuss the use of low-rank approximation techniques that allow for reducing this complexity at the price of a loss in precision which can be reliably controlled. To take advantage of these low-rank approximations, we have designed a format called block low-rank (BLR) whose objective is to achieve a favorable compromise between complexity and efficiency of operations thanks to its regular structure. We will present the basic BLR format as well as more advanced variants and the associated algorithms; we will analyze their theoretical properties and discuss the issues related to their efficient implementation on parallel computers. We will specifically focus on the use of BLR for the solution of sparse linear systems. The ombination of this format with sparse direct methods, such as the multifrontal one, leads to efficient parallel solvers with scalable complexity. These can either be used as standalone direct solvers or in combination with other techniques such as iterative or multigrid methods. We will present experimental results on real-life problems obtained by integrating the BLR format within the MUMPS parallel sparse direct solver.
https://www.dm.unipi.it/webnew/it/seminari/reducing-complexity-linear-system...
Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4