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Algorithms and Data Structures for Multi-Adaptive Time-Stepping
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.ORCID iD: 0000-0002-1695-8809
2008 (English)In: ACM Transactions on Mathematical Software, ISSN 0098-3500, E-ISSN 1557-7295, Vol. 35, no 3Article in journal (Refereed) Published
Abstract [en]

Multi-adaptive Galerkin methods are extensions of the standard continuous and discontinuous Galerkin methods for the numerical solution of initial value problems for ordinary or partial differential equations. In particular, the multi-adaptive methods allow individual and adaptive time steps to be used for different components or in different regions of space. We present algorithms for efficient multi-adaptive time-stepping, including the recursive construction of time slabs and adaptive time step selection. We also present data structures for efficient storage and interpolation of the multi-adaptive solution. The efficiency of the proposed algorithms and data structures is demonstrated for a series of benchmark problems.

Place, publisher, year, edition, pages
2008. Vol. 35, no 3
Keyword [en]
Algorithms, Performance, Multi-adaptivity, individual time steps, local, time steps, multirate, ODE, continuous Galerkin, discontinuous, Galerkin, mcgq, mdgq, C plus, implementation, algorithms, DOLFIN, ordinary differential-equations, finite-element methods, locally, varying time, parabolic problems, galerkin methods, conservation-laws, approximations, integration, schemes, model
Identifiers
URN: urn:nbn:se:kth:diva-18245ISI: 000264243800001Scopus ID: 2-s2.0-56349106061OAI: oai:DiVA.org:kth-18245DiVA: diva2:336291
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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