Autor(en): | Andreia, Merlin Meyer, Christian |
Titel: | An adaptive time stepping scheme for rate-independent systems with non-convex energy |
Sprache (ISO): | en |
Zusammenfassung: | We investigate a local incremental stationary scheme for the numerical solution of rate-independent systems. Such systems are characterized by a (possibly) non-convex energy and a dissipation potential, which is positively homogeneous of degree one. Due to the non-convexity of the energy, the system does in general not admit a time-continuous solution. In order to resolve these potential discontinuities, the algorithm produces a sequence of state variables and physical time points as functions of a curve parameter. The main novelty of our approach in comparison to existing methods is an adaptive choice of the step size for the update of the curve parameter depending on a prescribed tolerance for the residua in the energy-dissipation balance and in a complementarity relation concerning the so-called local stability condition. It is proven that, for tolerance tending to zero, the piecewise affine approximations generated by the algorithm converge (weakly) to a so-called V-parametrized balanced viscosity solution. Numerical experiments illustrate the theoretical findings and show that an adaptive choice of the step size indeed pays off as they lead to a significant increase of the step size during sticking and in viscous jumps. |
Schlagwörter: | rate-independent systems parametrized balanced viscosity solutions local incremental minimization schemes |
URI: | http://hdl.handle.net/2003/40855 http://dx.doi.org/10.17877/DE290R-22712 |
Erscheinungsdatum: | 2022-04 |
Enthalten in den Sammlungen: | Ergebnisberichte des Instituts für Angewandte Mathematik |
Dateien zu dieser Ressource:
Datei | Beschreibung | Größe | Format | |
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Ergebnisbericht Nr. 652.pdf | DNB | 630.96 kB | Adobe PDF | Öffnen/Anzeigen |
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