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SUMMARY:Approximating gradient flow evolutions of self-avoiding inextensib
 le curves and elastic knots
DTSTART:20190521T161500
DTEND:20190521T171500
DTSTAMP:20260509T142140Z
UID:5f567600028820cc8b22e20af4c965369751518bb5efd1725bfc08e0
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Soeren Bartels\, University of Freiburg\nComputational M
 athematics Seminar \n\nAbstract :..\n\nWe discuss a semi-implicit numerica
 l scheme that allows for minimizing the bending energy of curves within ce
 rtain isotopy classes. To this end we consider a weighted sum of a bending
  energy and a so-called tangent-point functional. We define evolutions via
  the gradient flow for the total energy within a class of arclength parame
 trized curves\, i.e.\, given an initial curve we look for a family of inex
 tensible curves that solves the nonlinear evolution equation.\n\nOur numer
 ical approximation scheme for the evolution problem is specified via a sem
 i-implicit discretization of the equation with an explicit treatment of th
 e tangent-point functional and a linearization of the arclength condition.
  The scheme leads to sparse systems of linear equations in the time steps 
 for cubic splines and a nodal treatment of the constraints. The explicit t
 reatment of the nonlocal and nonlinear tangent-point functional avoids wor
 king with fully populated matrices and furthermore allows for a straightfo
 rward parallelization of its computation.\n\nBased on estimates for the se
 cond derivative of the tangent-point functional and a uniform bi-Lipschitz
  radius\, we prove a stability result implying energy decay during the evo
 lution as well as maintenance of arclength parametrization.\n\nWe present 
 some numerical experiments exploring the energy landscape\, targeted to th
 e question how to obtain global minimizers of the bending energy in certai
 n knot classes\, so-called elastic knots. Moreover\, we discuss the incorp
 oration of torsion quantities.\n\nThis is joint work with Philipp Reiter (
 University of Georgia).
LOCATION:MA A1 10 https://plan.epfl.ch/?room=MAA110
STATUS:CONFIRMED
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