Thesis defence

Generalized sweeping preconditioners for domain decomposition methods applied to Helmholtz problems



Mr Ruiyang Dai will publicly defend his thesis entitled : Generalized sweeping preconditioners for domain decomposition methods applied to Helmholtz problems

This thesis was realized under the supervision of prof. Christophe Geuzaine (ULiège) and prof. Jean-François Remacle (UCLouvain).


Summary

The numerical solution of high-frequency Helmholtz problems by discretization methods such as the finite element method is an enormous challenge. Indeed, obtaining high fidelity solutions requires assembling and solving extremely large linear systems, whose size increases more than linearly with frequency. This quickly leads to prohibitive computational costs both in assembling and solving the resulting linear systems. To overcome these difficulties, we implement an efficient quadrature approach applied to the high-order finite element method, as well as domain decomposition methods with high-order transmission conditions, in two and three dimensions, on high-performance computing architectures. To improve the convergence rate of domain decomposition methods, we generalise a family of scanning preconditioners for domain decomposition methods, where scans can be performed in several directions on Cartesian partitions. In order to apply our algorithms to practical cases that require solutions for a large number of frequencies or a large number of right-hand members, we also propose improved parallelization strategies that maintain the fast convergence rate while maximizing the use of computational resources.

R. Dai, A. Modave, J. F. Remacle, C. Geuzaine, Multidirectionnal sweeping preconditioners with non-overlapping checkerboard domain decomposition for Helmholtz problems, 2021. https://hal.archives-ouvertes.fr/hal-03240042

R. Dai, Generalized sweeping preconditioners for domain decomposition methods applied to Helmholtz problems, PhD thesis, UCLouvain and ULiège, Belgium, 2021. https://orbi.uliege.be/handle/2268/260200

Practical Information

This defence will take place on November 17, 2021 at 16:15 at the Université Catholique de Louvain (Place du Levant 1 - amphi. Barb 94).

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