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Computing Exponential for Iterative Splitting Methods : Algorithms and Applications
Author
Source
Journal of Applied Mathematics
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-27, 27 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-03-29
Country of Publication
Egypt
No. of Pages
27
Main Subjects
Abstract EN
Iterative splitting methods have a huge amount to compute matrix exponential.
Here, the acceleration and recovering of higher-order schemes can be achieved.
From a theoretical point of view, iterative splitting methods are at least alternating Picards fix-point iteration schemes.
For practical applications, it is important to compute very fast matrix exponentials.
In this paper, we concentrate on developing fast algorithms to solve the iterative splitting scheme.
First, we reformulate the iterative splitting scheme into an integral notation of matrix exponential.
In this notation, we consider fast approximation schemes to the integral formulations, also known as ϕ-functions.
Second, the error analysis is explained and applied to the integral formulations.
The novelty is to compute cheaply the decoupled exp-matrices and apply only cheap matrix-vector multiplications for the higher-order terms.
In general, we discuss an elegant way of embedding recently survey on methods for computing matrix exponential with respect to iterative splitting schemes.
We present numerical benchmark examples, that compared standard splitting schemes with the higher-order iterative schemes.
A real-life application in contaminant transport as a two phase model is discussed and the fast computations of the operator splitting method is explained.
American Psychological Association (APA)
Geiser, Juergen. 2011. Computing Exponential for Iterative Splitting Methods : Algorithms and Applications. Journal of Applied Mathematics،Vol. 2011, no. 2011, pp.1-27.
https://search.emarefa.net/detail/BIM-453452
Modern Language Association (MLA)
Geiser, Juergen. Computing Exponential for Iterative Splitting Methods : Algorithms and Applications. Journal of Applied Mathematics No. 2011 (2011), pp.1-27.
https://search.emarefa.net/detail/BIM-453452
American Medical Association (AMA)
Geiser, Juergen. Computing Exponential for Iterative Splitting Methods : Algorithms and Applications. Journal of Applied Mathematics. 2011. Vol. 2011, no. 2011, pp.1-27.
https://search.emarefa.net/detail/BIM-453452
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-453452