Isogeometric de Rham complex discretization in solid toroidal domains

Abstract

In this work we define a spline complex preserving the cohomological structure of the continuous de Rham complex when the underlying physical domain is a toroidal solid. In the spirit of the isogeometric analysis, the spaces involved will be defined as pushforward of suitable spline spaces on a parametric domain. The singularity of the parametrization of the solid will demand the imposition of smoothness constraints on the full tensor product spline spaces in the parametric domain to properly set up the discrete complex on the physical domain.