Paper Info
Title
Two Classes of Vector Domain Decomposition Schemes for Time-Dependent Problems with Overlapping Subdomains.
Abstract
The domain decomposition methods for time-dependent problems are based on special schemes of splitting into subdomains. To construct homogeneous numerical algorithms, overlapping subdomain methods are preferable. The domain decomposition is associated with corresponding additive representation of the problem operator. Such regionally-additive schemes are based on the general theory of additive operator-difference schemes. There are variants of decomposition operators differing by distinct types of data exchanges on interfaces. New classes of domain decomposition schemes for transient problems based on subdomains overlapping are constructed. The boundary value problem for the parabolic equation of second order is considered as a model problem. We propose a general approach to construct vector domain decomposition schemes for time-dependent systems of equations. Using a partition of unity for a computational domain we perform a transition to finding the individual components of the solution in the subdomains. General stability conditions are obtained for vector regionally-additive schemes with first and second order accuracy.
Year
DOI
Venue
2017
10.1007/978-3-319-73441-5_8
Lecture Notes in Computer Science
Field
DocType
Volume
Homogeneous,Computer science,Algorithm,Data type,Operator (computer programming),Domain decomposition methods,Decomposition
Conference
10665
ISSN
Citations 
PageRank 
0302-9743
0
0.34
References 
Authors
1
1
Name
Order
Citations
PageRank
Petr N. Vabishchevich13727.46