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- Title
Discrete Lie Advection of Differential Forms.
- Authors
Mullen, P.; McKenzie, A.; Pavlov, D.; Durant, L.; Tong, Y.; Kanso, E.; Marsden, J. E.; Desbrun, M.
- Abstract
In this paper, we present a numerical technique for performing Lie advection of arbitrary differential forms. Leveraging advances in high-resolution finite-volume methods for scalar hyperbolic conservation laws, we first discretize the interior product (also called contraction) through integrals over Eulerian approximations of extrusions. This, along with Cartan's homotopy formula and a discrete exterior derivative, can then be used to derive a discrete Lie derivative. The usefulness of this operator is demonstrated through the numerical advection of scalar fields and 1-forms on regular grids.
- Subjects
LIE algebras; DIFFERENTIAL forms; HOMOTOPY theory; EULER characteristic; ABSTRACT algebra
- Publication
Foundations of Computational Mathematics, 2011, Vol 11, Issue 2, p131
- ISSN
1615-3375
- Publication type
Article
- DOI
10.1007/s10208-010-9076-y