Krylov subspace approximations for the exponential Euler method: Error estimates and the harmonic Ritz approximant
Carr, Elliot Joseph, Turner, Ian, & Ilic, Milos (2011) Krylov subspace approximations for the exponential Euler method: Error estimates and the harmonic Ritz approximant. ANZIAM Journal, 52, C612-C627.
We study Krylov subspace methods for approximating the matrix-function vector product φ(tA)b where φ(z) = [exp(z) - 1]/z. This product arises in the numerical integration of large stiff systems of differential equations by the Exponential Euler Method, where A is the Jacobian matrix of the system. Recently, this method has found application in the simulation of transport phenomena in porous media within mathematical models of wood drying and groundwater flow. We develop an a posteriori upper bound on the Krylov subspace approximation error and provide a new interpretation of a previously published error estimate. This leads to an alternative Krylov approximation to φ(tA)b, the so-called Harmonic Ritz approximant, which we find does not exhibit oscillatory behaviour of the residual error.
Impact and interest:
Citation counts are sourced monthly from and citation databases.
These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.
Citations counts from theindexing service can be viewed at the linked Google Scholar™ search.
Full-text downloads displays the total number of times this work’s files (e.g., a PDF) have been downloaded from QUT ePrints as well as the number of downloads in the previous 365 days. The count includes downloads for all files if a work has more than one.
|Item Type:||Journal Article|
|Keywords:||Krylov subspace methods, Matrix function approximation, Exponential integrators, Phi function, Arnoldi Method, Error estimates|
|Subjects:||Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300)
|Divisions:||Past > Schools > Mathematical Sciences|
|Copyright Owner:||Copyright 2011 Austral, Mathematical Society|
|Deposited On:||18 Aug 2011 23:46|
|Last Modified:||05 May 2016 03:06|
Repository Staff Only: item control page