Abstract
The Virtual Element Method (VEM) is a recent numerical technology for the solution of partial differential equations on computational grids constituted by polygonal or polyhedral elements of very general shape. The aim of this work is to develop effective linear solvers for a general order VEM approximation designed to approximate three-dimensional scalar elliptic equations in mixed form. The proposed Balancing Domain Decomposition by Constraints (BDDC) preconditioner allows to use conjugate gradient iterations, albeit the algebraic linear systems arising from the discretization of the problem are indefinite, ill-conditioned, and of saddle point nature. The condition number of the resulting positive definite preconditioned system is adaptively controlled by means of deluxe scaling operators and suitable local generalized eigenvalue problems for the selection of optimal primal constraints. Numerical results confirm the theoretical estimates and the reliability of the adaptive procedure, with the experimental condition numbers always very close to the prescribed adaptive tolerance parameter. The scalability and quasi-optimality of the preconditioner are demonstrated, and the performances of the proposed solver are compared with state-of-the-art parallel direct solvers and block preconditioning techniques in a distributed memory setting.
Original language | English (US) |
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Pages (from-to) | 114620 |
Journal | Computer Methods in Applied Mechanics and Engineering |
Volume | 391 |
DOIs | |
State | Published - Feb 7 2022 |
Bibliographical note
KAUST Repository Item: Exported on 2022-04-26Acknowledgements: The authors would like to acknowledge INDAM-GNCS, Italy for the support. Moreover they would like to thank Lourenco Beirão da Veiga and Alessandro Russo for many helpful discussions and suggestions.
ASJC Scopus subject areas
- General Physics and Astronomy
- Mechanics of Materials
- Mechanical Engineering
- Computational Mechanics
- Computer Science Applications