Krylov methods: general ideas and recent developments


Friday, February 23, 2024
15:30 - 16:30


For many scientific simulations the most time consuming part is the solution of one or more large and sparse linear systems of equations. For this reason the efficient solution of such systems is still a very active area of research. The first part of the talk will discuss a widely used class of iterative solution methods: the so-called Krylov Subspace Methods. We will review some well-known methods like the Conjugate Gradient method (CG) and the Generalised Minimal Residual Method (GMRES). Then we will discuss extensions and generalisations which result in the very efficient but less known class of Induced Dimension Reduction (IDR) methods. The second part introduces a new software package specifically designed for linear systems, featuring IDR-based iterative methods and polynomial preconditioners to enhance convergence. This package, written in modern Fortran, includes special routines for solving linear systems with shifts and demonstrates high efficiency on the DelftBlue supercomputer, capable of handling systems over 10^8 equations.


Computational Soft Matter, Condensed Matter Theory group


Polder House (Café Restaurant Polder, Science Park 201, 1098 XH Amsterdam) and Zoom https://uva-live.zoom.us/j/88595541121


Group Seminar


complexity, computational physics


prof. Martin van Gijzen (TUDelft)

Share this event

Back to top