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A symmetry and Noet...
A symmetry and Noether charge preserving discretization of initial value problems
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- Rothkopf, Alexander (författare)
- University of Stavanger, Norway
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- Nordström, Jan, 1953- (författare)
- Linköpings universitet,Tekniska fakulteten,Tillämpad matematik,University of Johannesburg, South Africa
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(creator_code:org_t)
- ACADEMIC PRESS INC ELSEVIER SCIENCE, 2024
- 2024
- Engelska.
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Ingår i: Journal of Computational Physics. - : ACADEMIC PRESS INC ELSEVIER SCIENCE. - 0021-9991 .- 1090-2716. ; 498
- Relaterad länk:
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Abstract
Ämnesord
Stäng
- Taking insight from the theory of general relativity, where space and time are treated on the same footing, we develop a novel geometric variational discretization for second order initial value problems (IVPs). By discretizing the dynamics along a world-line parameter, instead of physical time directly, we retain manifest translation symmetry and conservation of the associated continuum Noether charge. A non-equidistant time discretization emerges dynamically, realizing a form of automatic adaptive mesh refinement (AMR), guided by the system symmetries. Using appropriately regularized summation by parts finite difference operators, the continuum Noether charge, defined via the Killing vector associated with translation symmetry, is shown to be exactly preserved in the interior of the simulated time interval. The convergence properties of the approach are demonstrated with two explicit examples.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- Initial value problem; Summation by parts; Time-translation invariance; Conserved Noether charge; Adaptive mesh refinement
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