Paper Info
Title
Space-time domain decomposition for advection-diffusion problems in mixed formulations.
Abstract
This paper is concerned with the numerical solution of porous-media flow and transport problems, i.e. heterogeneous, advection–diffusion problems. Its aim is to investigate numerical schemes for these problems in which different time steps can be used in different parts of the domain. Global-in-time, non-overlapping domain-decomposition methods are coupled with operator splitting making possible the different treatment of the advection and diffusion terms. Two domain-decomposition methods are considered: one uses the time-dependent Steklov–Poincaré operator and the other uses optimized Schwarz waveform relaxation (OSWR) based on Robin 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. A generalized Neumann–Neumann preconditioner is proposed for the first method. To illustrate the two methods numerical results for two-dimensional problems with strong heterogeneities are presented. These include both academic problems and more realistic prototypes for simulations for the underground storage of nuclear waste.
Year
DOI
Venue
2017
10.1016/j.matcom.2016.11.002
Mathematics and Computers in Simulation
Keywords
Field
DocType
Mixed formulations,Advection–diffusion,Optimized Schwarz waveform relaxation,Time-dependent Steklov–Poincaré operator
Space time,Operator splitting,Mathematical optimization,Preconditioner,Mathematical analysis,Flow (psychology),Waveform,Advection,Operator (computer programming),Mathematics,Domain decomposition methods
Journal
Volume
ISSN
Citations 
137
0378-4754
2
PageRank 
References 
Authors
0.38
6
4
Name
Order
Citations
PageRank
Thao-Phuong Hoang1122.10
Caroline Japhet2386.64
Michel Kern3192.67
Jean E. Roberts4577.97