An algorithm for prescribed mean curvature using isogeometric methods

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• 作者：An&iacute ; bal Chicco-Ruiz ^{achicco@santafe-conicet.gov.ar" class="auth_mail" title="E-mail the corresponding author} ; Pedro Morin ; ^{pmorin@santafe-conicet.gov.ar" class="auth_mail" title="E-mail the corresponding author} ; M. Sebastian Pauletti ^{pauletti@santafe-conicet.gov.ar" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Minimal surfaces ; Prescribed curvature ; Isogeometric analysis ; Quasi-Newton
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：15 July 2016
• 年：2016
• 卷：317
• 期：Complete
• 页码：185-203
• 全文大小：2104 K

文摘

We present a Newton type algorithm to find parametric surfaces of prescribed mean curvature with a fixed given boundary. In particular, it applies to the problem of minimal surfaces. 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 introduce a discretization of the continuous algorithm and present a simple implementation using the recently released isogeometric software library igatools. Finally, we show several numerical experiments which highlight the convergence properties of the scheme.