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Semi-implicit krylov deferred correction methods for differential algebraic equations

Title
Semi-implicit krylov deferred correction methods for differential algebraic equations
Authors
Bu S.Huang J.Minion M.L.
Ewha Authors
부선영
Issue Date
2012
Journal Title
Mathematics of Computation
ISSN
0025-5718JCR Link
Citation
vol. 81, no. 280, pp. 2127 - 2157
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
In the recently developed Krylov deferred correction (KDC) methods for differential algebraic equation initial value problems (Huang, Jia, Minion, 2007), a Picard-type collocation formulation is preconditioned using low-order time integration schemes based on spectral deferred correction (SDC), and the resulting system is solved efficiently using Newton-Krylov methods. KDC methods have the advantage that methods with arbitrarily high order of accuracy can be easily constructed which have similar computational complexity as lower order methods. In this paper, we investigate semi-implicit KDC (SI-KDC) methods in which the stiff component of the preconditioner is treated implicitly and the non-stiff parts explicitly. For certain types of problems, such a semi-implicit treatment can significantly reduce the computational cost of the preconditioner compared to fully implicit KDC (FI-KDC) methods. Preliminary analysis and numerical experiments show that the convergence of Newton-Krylov iterations in the SI-KDC methods is similar to that in FI-KDC, and hence the SI-KDC methods offer a reduction in overall computational cost for such problems. © 2012 American Mathematical Society.
DOI
10.1090/S0025-5718-2012-02564-6
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연구기관 > 수리과학연구소 > Journal papers
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