2020/10/29 by Manu Jayadharan, Jayadharan, Manu, Eldar Khattatov +3
Engineering · #Advanced Numerical Methods in Computational Mathematics #Numerical methods in engineering #Electromagnetic Simulation and Numerical Methods
paper · pdf · doi:10.48550/arxiv.2010.15353
We develop non-overlapping domain decomposition methods for the Biot system\nof poroelasticity in a mixed form. The solid deformation is modeled with a\nmixed three-field formulation with weak stress symmetry. The fluid flow is\nmodeled with a mixed Darcy formulation. We introduce displacement and pressure\nLagrange multipliers on the subdomain interfaces to impose weakly continuity of\nnormal stress and normal velocity, respectively. The global problem is reduced\nto an interface problem for the Lagrange multipliers, which is solved by a\nKrylov space iterative method. We study both monolithic and split methods. In\nthe monolithic method, a coupled displacement-pressure interface problem is\nsolved, with each iteration requiring the solution of local Biot problems. We\nshow that the resulting interface operator is positive definite and analyze the\nconvergence of the iteration. We further study drained split and fixed stress\nBiot splittings, in which case we solve separate interface problems requiring\nelasticity and Darcy solves. We analyze the stability of the split\nformulations. Numerical experiments are presented to illustrate the convergence\nof the domain decomposition methods and compare their accuracy and efficiency.\n