A partially parallel-in-time fixed-stress splitting method for Biot's consolidation model. (15th March 2019)

• Record Type: Journal Article
• Authors: Borregales, Manuel; Kumar, Kundan; Radu, Florin Adrian; Rodrigo, Carmen; Gaspar, Francisco José
• Is Part Of: Computers & mathematics with applications. Volume 77:issue 6(2019)
• Page Start: 1466
• Page End: 1478
• Publication Date: 2019-03-15
• Subjects: Iterative fixed-stress splitting scheme -- Parallel-in-time -- Biot's model -- Poromechanics -- Finite elements -- Convergence analysis; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.09.005
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this work, we study the parallel-in-time iterative solution of coupled flow and geomechanics in porous media, modelled by a two-field formulation of Biot's equations. In particular, we propose a new version of the fixed-stress splitting method, which has been widely used as solution method of these problems. This new approach forgets about the sequential nature of the temporal variable and considers the time direction as a further direction for parallelization. The method is partially parallel-in-time. We present a rigorous convergence analysis of the method and numerical experiments to demonstrate the robust behaviour of the algorithm.