A partially parallel-in-time fixed-stress splitting method for Biot's consolidation model

作者: Manuel Borregales , Kundan Kumar , Florin Adrian Radu , Carmen Rodrigo , Francisco José Gaspar

DOI: 10.1016/J.CAMWA.2018.09.005

关键词:

摘要: 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 Biot's equations. particular, propose new version fixed-stress splitting method, which has been widely used as method these problems. This approach forgets about sequential nature temporal variable considers time direction further for parallelization. The is partially parallel-in-time. We present rigorous convergence analysis numerical experiments to demonstrate robust behaviour algorithm.

参考文章(38)
N. Castelletto, J. A. White, H. A. Tchelepi, Accuracy and convergence properties of the fixed‐stress iterative solution of two‐way coupled poromechanics International Journal for Numerical and Analytical Methods in Geomechanics. ,vol. 39, pp. 1593- 1618 ,(2015) , 10.1002/NAG.2400
Márcio A. Murad, Abimael F. D. Loula, On stability and convergence of finite element approximations of Biot's consolidation problem International Journal for Numerical Methods in Engineering. ,vol. 37, pp. 645- 667 ,(1994) , 10.1002/NME.1620370407
J. Kim, H.A. Tchelepi, R. Juanes, Stability and convergence of sequential methods for coupled flow and geomechanics: Fixed-stress and fixed-strain splits Computer Methods in Applied Mechanics and Engineering. ,vol. 200, pp. 1591- 1606 ,(2011) , 10.1016/J.CMA.2010.12.022
Karl Terzaghi, Theoretical Soil Mechanics ,(1943)
J. Mandel, Consolidation Des Sols (Étude Mathématique) Geotechnique. ,vol. 3, pp. 287- 299 ,(1953) , 10.1680/GEOT.1953.3.7.287
Phillip Joseph Phillips, Mary F. Wheeler, A coupling of mixed and continuous Galerkin finite element methods for poroelasticity I: the continuous in time case Computational Geosciences. ,vol. 11, pp. 131- 144 ,(2007) , 10.1007/S10596-007-9044-Z
Ch. Lubich, A. Ostermann, Multi-grid dynamic iteration for parabolic equations Bit Numerical Mathematics. ,vol. 27, pp. 216- 234 ,(1987) , 10.1007/BF01934186
Matthew Emmett, Michael Minion, TOWARD AN EFFICIENT PARALLEL IN TIME METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS Communications in Applied Mathematics and Computational Science. ,vol. 7, pp. 105- 132 ,(2012) , 10.2140/CAMCOS.2012.7.105
Luca Bergamaschi, Massimiliano Ferronato, Giuseppe Gambolati, Novel preconditioners for the iterative solution to FE-discretized coupled consolidation equations Computer Methods in Applied Mechanics and Engineering. ,vol. 196, pp. 2647- 2656 ,(2007) , 10.1016/J.CMA.2007.01.013
Márcio A. Murad, Vidar Thomée, Abimael F. D. Loula, Asymptotic behavior of semidiscrete finite-element approximations of Biot's consolidation problem SIAM Journal on Numerical Analysis. ,vol. 33, pp. 1065- 1083 ,(1996) , 10.1137/0733052