An adaptive time stepping scheme for rate-independent systems with non-convex energy

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dc.contributor.authorAndreia, Merlin
dc.contributor.authorMeyer, Christian
dc.date.accessioned2022-04-14T09:13:14Z
dc.date.available2022-04-14T09:13:14Z
dc.date.issued2022-04
dc.description.abstractWe 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.en
dc.identifier.issn2190-1767
dc.identifier.urihttp://hdl.handle.net/2003/40855
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-22712
dc.language.isoen
dc.relation.ispartofseriesErgebnisberichte des Instituts für Angewandte Mathematik;652
dc.subjectrate-independent systemsen
dc.subjectparametrized balanced viscosity solutionsen
dc.subjectlocal incremental minimization schemesen
dc.subject.ddc610
dc.titleAn adaptive time stepping scheme for rate-independent systems with non-convex energyen
dc.typeText
dc.type.publicationtypepreprint
dcterms.accessRightsopen access
eldorado.secondarypublicationfalse

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