Fast multiscale contrast independent preconditioners for linear elastic topology optimization problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:389

Article

Zambrano, Miguel^1,4  Serrano, Sintya^1,4  Lazarov, Boyan S.^2,3  Galvis, Juan¹ 

[1] Univ Nacl Colombia, Dept Matemat, Carrera 45 26-85,Edificio Uriel Gutierrez, Bogota, Colombia

[2] Lawrence Livermore Natl Lab, Livermore, CA 94550 USA

[3] Univ Manchester, Sch Mech Aerosp & Civil Engn, Manchester, Lancs, England

[4] Univ Fuerzas Armadas ESPE, Dept Ciencias Exactas, Sangolqui, Ecuador

关键词: Preconditioning;    Multiscale;    High contrast;    Topology optimization;    Linear solvers;    Iterative methods;   

DOI  :  10.1016/j.cam.2020.113366

来源: Elsevier

【 摘 要 】

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an adjoint analysis, which requires the numerical solution of large high-contrast linear elastic problems with features spanning several length scales. The size of the discretized problems forces the utilization of iterative linear solvers with solution time dependent on the quality of the preconditioner. The lack of clear separation between the scales, as well as the high-contrast, imposes severe challenges on the standard preconditioning techniques. Thus, here we propose new 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 construction utilizes spectral equivalence between scalar diffusion and each displacement block of the elasticity problems and, in contrast to previous solutions proposed in the literature, is able to select the appropriate dimension of the coarse space automatically. 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. Published by Elsevier B.V.

【 授权许可】

Free