Algorithms and data structures for multi-adaptive time-stepping
Journal article, 2008
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. © 2008 ACM.
Individual time steps
C++
Local time steps
Continuous Galerkin
Mcgq
Multirate
Discontinuous Galerkin
Algorithms
Mdgq
Multi-adaptivity
ODE
Implementation
DOLFIN
Author
Johan Jansson
Anders Logg
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
ACM Transactions on Mathematical Software
0098-3500 (ISSN)
Vol. 35 3Subject Categories
Mathematics
Computational Mathematics
DOI
10.1145/1391989.1391990