Semi-implicit Krylov deferred correction methods for differential algebraic equations
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- by Sunyoung Bu, Jingfang Huang and Michael L. Minion PDF
- Math. Comp. 81 (2012), 2127-2157 Request permission
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.References
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Additional Information
- Sunyoung Bu
- Affiliation: Department of Mathematics, University of North Carolina, CB #3250, Phillips Hall, Chapel Hill North Carolina 27599-3250
- Address at time of publication: Institute of Mathematical Sciences, Ewha Womans University, Seoul 120-750, Korea
- Email: syboo@ewha.ac.kr
- Jingfang Huang
- Affiliation: Department of Mathematics, University of North Carolina, CB #3250, Phillips Hall, Chapel Hill North Carolina 27599-3250
- Email: huang@email.unc.edu
- Michael L. Minion
- Affiliation: Department of Mathematics, University of North Carolina, CB #3250, Phillips Hall, Chapel Hill North Carolina 27599-3250
- Email: minion@email.unc.edu
- Received by editor(s): July 21, 2010
- Received by editor(s) in revised form: March 18, 2011
- Published electronically: April 26, 2012
- Additional Notes: The work of Bu was partially supported by the Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0028298). Part of the work was done while Bu was a visiting member of the Institute for Mathematics and Its Applications at the University of Minnesota.
The work of Huang and Bu was supported by NSF grants 0811130 and 0941235
The work of Minion was supported by NSF grant 0854961 - © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 81 (2012), 2127-2157
- MSC (2010): Primary 65B10, 65F10, 65L20, 65L80, 65N35
- DOI: https://doi.org/10.1090/S0025-5718-2012-02564-6
- MathSciNet review: 2945149