We introduce a new paradigm for immersed finite element and isogeometric methods based on interpolating function spaces from an unfitted background mesh into Lagrange defined foreground that captures the domain geometry but is otherwise subject to minimal constraints quality or connectivity. This generalization of concept extraction analysis literature also related certain variants cell materia...

Isogeometric methods were introduced by Hughes et al. in 2005. Since its introduction these methods have been used in many practical problems in science and engineering. However, so far, only few papers appeared in the field of iterative solvers for these methods. This thesis contributes to the development of fast iterative solvers for the matrices arising in isogeometric discretization of elli...

We study the spectral properties of stiffness matrices that arise in the context of isogeometric analysis for the numerical solution of classical second order elliptic problems. Motivated by the applicative interest in the fast solution of the related linear systems, we are looking for a spectral characterization of the involved matrices. In particular, we investigate non-singularity, condition...