In this paper, we combine the Alternating Direction Implicit (ADI) algorithm with the concept of preconditioning and apply it to linear systems discretized from the 2D steady-state diffusion equations with orthotropic heterogeneous coefficients by the finite element method assuming tensor product basis functions. Specifically, we adopt the compound iteration idea and use ADI iterations as the preconditioner for the outside Krylov subspace method that is used to solve the preconditioned linear system. An efficient algorithm to perform each ADI iteration is crucial to the efficiency of the overall iterative scheme. We exploit the Kronecker product structure in the matrices, inherited from the tensor product basis functions, to achieve high efficiency in each ADI iteration. Meanwhile, in order to reduce the number of Krylov subspace iterations, we incorporate partially the coefficient information into the preconditioner by exploiting the local support property of the finite element basis functions. Numerical results demonstrated the efficiency and quality of the proposed preconditioner. © 2014 Elsevier B.V. All rights reserved.
|Original language||English (US)|
|Number of pages||22|
|Journal||Journal of Computational and Applied Mathematics|
|State||Published - Jan 2015|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work was supported in part by the King Abdullah University of Science and Technology (KAUST) Center for Numerical Porous Media and by an Academic Excellence Alliance program award from KAUST's Global Collaborative Research under the title "Seismic wave focusing for subsurface imaging and enhanced oil recovery".
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics