A global jacobian method for mortar discretizations of nonlinear porous media flows

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2014
Major/Subject
Mcode
Degree programme
Language
en
Pages
Series
SIAM Journal on Scientific Computing, Volume 36, issue 2
Abstract
We describe a nonoverlapping domain decomposition algorithm for nonlinear porous media flows discretized with the multiscale mortar mixed finite element method. There are two main ideas: (1) linearize the global system in both subdomain and interface variables simultaneously to yield a single Newton iteration; and (2) algebraically eliminate subdomain velocities (and optionally, subdomain pressures) to solve linear systems for the 1st (or the 2nd) Schur complements. Solving the 1st Schur complement system gives the multiscale solution without the need to solve an interface iteration. Solving the 2nd Schur complement system gives a linear interface problem for a nonlinear model. The methods are less complex than a previously developed nonlinear mortar algorithm, which requires two nested Newton iterations and a forward difference approximation. Furthermore, efficient linear preconditioners can be applied to speed up the iteration. The methods are implemented in parallel, and a numerical study is performed to compare convergence behavior and parallel efficiency.
Description
Keywords
Global Jacobian, Interface problem, Multiscale mortar mixed finite element, Nonlinear porous media flow, Nonoverlapping domain decomposition
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Citation
Ganis, B, Juntunen, M, Pencheva, G, Wheeler, M F & Yotov, I 2014, ' A global jacobian method for mortar discretizations of nonlinear porous media flows ', SIAM Journal on Scientific Computing, vol. 36, no. 2 . https://doi.org/10.1137/130931837