Finite element method; Domain decomposition methods; Preconditionners
Abstract :
[en] The main part of this thesis explores a family of generalized sweeping preconditionners for Helmholtz problems with non-overlapping checkerboard partition of the computational domain. The domain decomposition procedure relies on high-order transmission conditions and cross-point treatments, which cannot scale without an efficient preconditioning technique when the number of subdomains increases. With the proposed approach, existing sweeping preconditioners, such as the symmetric Gauss-Seidel and parallel double sweep preconditioners, can be applied to checkerboard partitions with different sweeping directions (e.g. horizontal and diagonal). Several directions can be combined thanks to the flexible version of GMRES, allowing for the rapid transfer of information in the different zones of the computational domain, then accelerating the convergence of the final iterative solution procedure. Several two-dimensional finite element results are proposed to study and to compare the sweeping preconditioners, and to illustrate the performance on cases of increasing complexity.
Disciplines :
Electrical & electronics engineering
Author, co-author :
Dai, Ruiyang ; Université de Liège - ULiège > Montefiore Institute
Language :
English
Title :
Generalized sweeping preconditioners for domain decomposition methods applied to Helmholtz problems
Alternative titles :
[en] Generalized sweeping preconditioners for domain decomposition methods applied to Helmholtz problems
Defense date :
08 June 2021
Number of pages :
131
Institution :
ULiège - Université de Liège UCL - Université Catholique de Louvain