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Approximating the matrix exponential of an advection-diffusion operator using the incomplete orthogonalization method
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
2015 (English)In: Lecture Notes in Computational Science and Engineering, ISSN 1439-7358, 345-353 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we give first results for the approximation of eAb, i.e. the matrix exponential times a vector, using the incomplete orthogonalization method. The benefits compared to the Arnoldi iteration are clear: shorter orthogonalization lengths make the algorithm faster and a large memory saving is also possible. For the case of three term orthogonalization recursions, simple error bounds are derived using the norm and the field of values of the projected operator. In addition, an a posteriori error estimate is given which in numerical examples is shown to work well for the approximation. In the numerical examples we particularly consider the case where the operator A arises from spatial discretization of an advection-diffusion operator.

Place, publisher, year, edition, pages
2015. 345-353 p.
Keyword [en]
Advection, Error analysis, A-posteriori error estimates, Advection-diffusion operators, Arnoldi iterations, Field of values, Matrix exponentials, Memory savings, Orthogonalization, Spatial discretizations, Iterative methods
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-167774Scopus ID: 2-s2.0-84919797963OAI: oai:DiVA.org:kth-167774DiVA: diva2:814277
Note

QC 20150526

Available from: 2015-05-26 Created: 2015-05-22 Last updated: 2017-06-02Bibliographically approved

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