Paper Info
Title
Sparsifying Preconditioner for Pseudospectral Approximations of Indefinite Systems on Periodic Structures
Abstract
This paper introduces the sparsifying preconditioner for the pseudospectral approximation of highly indefinite systems on periodic structures, which include the frequency-domain response problems of the Helmholtz equation and the Schrodinger equation as examples. This approach transforms the dense system of the pseudospectral discretization approximately into a sparse system via an equivalent integral reformulation and a specially designed sparsifying operator. The resulting sparse system is then solved efficiently with sparse linear algebra algorithms and serves as a reasonably accurate preconditioner. When combined with standard iterative methods, this new preconditioner results in small iteration counts. Numerical results are provided for the Helmholtz equation and the Schrodinger in both two and three dimensions to demonstrate the effectiveness of this new preconditioner.
Year
DOI
Venue
2015
10.1137/140985159
MULTISCALE MODELING & SIMULATION
Keywords
Field
DocType
Helmholtz equation,Schrodinger equation,preconditioner,pseudospectral approximation,indefinite matrix,periodic structure,sparse linear algebra
Linear algebra,Discretization,Mathematical optimization,Preconditioner,Mathematical analysis,Iterative method,Schrödinger equation,Pseudospectral optimal control,Helmholtz equation,Operator (computer programming),Mathematics
Journal
Volume
Issue
ISSN
13
2
1540-3459
Citations 
PageRank 
References 
2
0.45
1
Authors
1
Name
Order
Citations
PageRank
Lexing Ying11273103.92