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A new variational d...
A new variational discretization technique for initial value problems bypassing governing equations
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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)
- Elsevier, 2023
- 2023
- Engelska.
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Ingår i: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 477
- Relaterad länk:
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- Motivated by the fact that both the classical and quantum description of nature rest on causality and a variational principle, we develop a novel and highly versatile discretization prescription for classical initial value problems (IVPs). It is based on an optimization (action) functional with doubled degrees of freedom, which is discretized using a single regularized summation-by-parts (SBP) operator. Formulated as optimization task it allows us to obtain classical trajectories without the need to derive an equation of motion. The novel regularization we develop in this context is inspired by the weak imposition of initial data, often deployed in the modern treatment of IVPs and is implemented using affine coordinates. We demonstrate numerically the stability, accuracy and convergence properties of our approach in systems with classical equations of motion featuring both first and second order derivatives in time.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- Initial value problem
- Summation by parts
- Variational principle
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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