Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 36, Issue 2, Pages A522-A542Publisher
SIAM PUBLICATIONS
DOI: 10.1137/130931837
Keywords
global Jacobian; nonlinear porous media flow; nonoverlapping domain decomposition; multiscale mortar mixed finite element; interface problem
Categories
Funding
- Center for Frontiers of Subsurface Energy Security, an Energy Frontier Research Center - U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences [DE-SC0001114]
- NSF CDI [DMS 0835745]
- NSF [DMS 1115856]
- DOE [DE-FG02-04ER25618]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1115856] Funding Source: National Science Foundation
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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.
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