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

Benjamin Ganis*, Mika Juntunen, Gergina Pencheva, Mary F. Wheeler, Ivan Yotov

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)
137 Downloads (Pure)


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.

Original languageEnglish
JournalSIAM Journal on Scientific Computing
Issue number2
Publication statusPublished - 2014
MoE publication typeA1 Journal article-refereed


  • Global Jacobian
  • Interface problem
  • Multiscale mortar mixed finite element
  • Nonlinear porous media flow
  • Nonoverlapping domain decomposition


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