Session S02 - Diverse Aspects of Elliptic PDEs and Related Problems

Wednesday, July 21, 17:30 ~ 18:00 UTC-3

Multiscale preconditioners for linear elastic topology optimization

Galvis Juan

Universidad Nacional de Colombia, Colombia   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We present a novel fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process requires the numerical solution of large high-contrast linear elastic problems with features spanning several length scales. The size of the discretized problems and the lack of clear separation between the scales, as well as the high-contrast, imposes severe challenges on the standard preconditioning techniques. We propose novel methods for the high-contrast elasticity equation with performance independent of the high-contrast and the multi-scale structure of the elasticity problem. The solvers are based on two-levels domain decomposition techniques with a carefully constructed coarse level to deal with the high-contrast and multi-scale nature of the problem. The new methods inherit the advantages of domain decomposition techniques, such as easy parallelization and scalability. The presented numerical experiments demonstrate the excellent performance of the proposed methods. This talk is based on https://doi.org/10.1016/j.cam.2020.113366.

Joint work with Boyan Lazarov (Lawrence Livermore National Laboratory, Livermore, CA, US), Sintya Serrano (Departamento de Ciencias Exactas, Universidad de las Fuerzas Armadas ESPE) and Miguel Zambrano (Departamento de Ciencias Exactas, Universidad de las Fuerzas Armadas ESPE).

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