An algorithm for prescribed mean curvature using isogeometric methods

ANIBAL CHICCO RUIZ; PEDRO MORIN; MIGUEL SEBASTIÁN PAULETTI

JOURNAL OF COMPUTATIONAL PHYSICS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2016

0021-9991

We present a Newton type algorithm to find parametric surfaces of prescribed meancurvature with a fixed given boundary. In particular, it applies to the problem of minimalsurfaces. The algorithm relies on some global regularity of the spaces where it is posed,which is naturally fitted for discretization with isogeometric type of spaces. We introducea discretization of the continuous algorithm and present a simple implementation usingthe recently released isogeometric software library igatools . Finally, we show severalnumerical experiments which highlight the convergence properties of the scheme.