Paper Info
Title
Space-Time Domain Decomposition for Reduced Fracture Models in Mixed Formulation.
Abstract
In this paper we are interested in the "fast path" fracture and we aim to use global-in-time, nonoverlapping domain decomposition methods to model flow and transport problems in a porous medium containing such a fracture. We consider a reduced model in which the fracture is treated as an interface between the two subdomains. Two domain decomposition methods are considered: one uses the time-dependent Steklov-Poincare operator and the other uses optimized Schwarz waveform relaxation (OSWR) based on Ventcell transmission conditions. For each method, a mixed formulation of an interface problem on the space-time interface is derived, and different time grids are employed to adapt to different time scales in the subdomains and in the fracture. Demonstrations of the well-posedness of the Ventcell subdomain problems is given for the mixed formulation. An analysis for the convergence factor of the OSWR algorithm is given in the case with fractures to compute the optimized parameters. Numerical results for two-dimensional problems with strong heterogeneities are presented to illustrate the performance of the two methods.
Year
DOI
Venue
2016
10.1137/15M1009651
SIAM JOURNAL ON NUMERICAL ANALYSIS
Keywords
DocType
Volume
mixed formulations,domain decomposition,reduced fracture model,optimized Schwarz waveform relaxation,Ventcell transmission conditions,time-dependent Steklov-Poincare operator,convergence factor,nonconforming time grids
Journal
54
Issue
ISSN
Citations 
1
0036-1429
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Thao-Phuong Hoang1122.10
Caroline Japhet2386.64
Michel Kern3192.67
Jean E. Roberts4577.97