Adaptive Filtered Schemes for First Order Hamilton-Jacobi Equations
| Autor: | Silvia Tozza, Maurizio Falcone, Giulio Paolucci |
|---|---|
| Přispěvatelé: | Falcone, Maurizio, Giulio, Paolucci, Tozza, Silvia, Maurizio Falcone, PAOLUCCI, GIULIO, Silvia Tozza |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
high-order schemes
Smoothness (probability theory) filtered scheme high-order schemes Hamilton-Jacobi equations filtered schemes finite difference schemes Hamilton-Jacobi equation First order Hamilton–Jacobi equation Hamilton-Jacobi equations filtered schemes finite difference schemes Monotone polygon Feature (computer vision) high-order scheme Scheme (mathematics) Applied mathematics Order (group theory) Node (circuits) Mathematics |
| Zdroj: | Lecture Notes in Computational Science and Engineering ISBN: 9783319964140 |
| Popis: | In this paper we consider a class of “filtered” schemes for some first order time dependent Hamilton-Jacobi equations. A typical feature of a filtered scheme is that at the node xj the scheme is obtained as a mixture of a high-order scheme and a monotone scheme according to a filter function F. The mixture is usually governed by F and by a fixed parameter ε = ε(Δt,Δx) > 0 which goes to 0 as (Δt, Δx) is going to 0 and does not depend on n. Here we improve the standard filtered scheme introducing an adaptive and automatic choice of the parameter ε = ε^n(Δt, Δx) at every iteration. To this end, we use a smoothness indicator in order to select the regions where we can compute the regularity threshold ε^n. The numerical tests presented confirms the effectiveness of the adaptive scheme. |
| Databáze: | OpenAIRE |
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