K101 K101 FSv ČVUT

Seminář katedry matematiky

Aktuálně Přednášky Fotogalerie Program

Seminář katedry matematiky

Seminář katedry matematiky

Příští přednáška semináře Katedry matematiky FSv ČVUT v Praze se bude konat

v pátek 20. 1. 2023

od 11:00

v zasedací místnosti B-365 budovy fakulty stavební v Thákurově ulici č. 7.

Název přednášky: On the convergence of FFT-based homogenization methods

Přednášející: Ing. Martin Ladecký, Ph.D.

Katedra matematiky, Fakulta stavební, ČVUT v Praze 

Abstrakt: The discretisation of elliptic problems on fine grids leads to systems of linear equations with millions to billions of unknowns, which favour iterative solvers over direct solvers. However, the number of iterations of iterative solvers can grow with increasing system size. This issue may be overcome by the discrete Green's operator (DGO) preconditioning, which makes iteration count independent of the system/grid size. This approach uses the inverse of a linear system matrix of a reference elliptic problem discretised on the same grid as the preconditioner.

We studied the DGO preconditioning from a linear algebra viewpoint and showed that all individual eigenvalues of such preconditioned systems can be bounded purely from the knowledge of the material data of the problems, both original and reference. We developed a simple algorithm to compute these bounds.

In this lecture, we will discuss the theoretical aspects of these results and practical applications of the DGO preconditioning to periodic homogenization problems discretised on regular grids.

Design stránek: Stanislav Olivík, 2013